Tidal sedimentology
Transcript of Tidal sedimentology
-
7/23/2019 Tidal sedimentology
1/637
-
7/23/2019 Tidal sedimentology
2/637
Principles of Tidal Sedimentology
-
7/23/2019 Tidal sedimentology
3/637
-
7/23/2019 Tidal sedimentology
4/637
Richard A. Davis, Jr. Robert W. DalrympleEditors
Principles of TidalSedimentology
-
7/23/2019 Tidal sedimentology
5/637
EditorsRichard A. Davis, Jr.Harte Research InstituteTexas A&M UniversityOcean Drive 6300Corpus Christi, TX 78412USA
Coastal Research LaboratoryDepartment of GeologyUniversity of South FloridaTampa, FL [email protected]
Robert W. DalrympleDepartment of Geological Sciences andGeological EngineeringQueens UniversityMiller HallKingston, ON K7L 3N6
ISBN 978-94-007-0122-9 e-ISBN 978-94-007-0123-6DOI 10.1007/978-94-007-0123-6Springer Dordrecht Heidelberg London New York
Library of Congress Control Number: 2011939475
Springer Science+Business Media B.V. 2012No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by anymeans, electronic, mechanical, photocopying, microfilming, recording or otherwise, without writtenpermission from the Publisher, with the exception of any material supplied specifically for the purpose ofbeing entered and executed on a computer system, for exclusive use by the purchaser of the work.
Cover illustration: Fig. 5.13 (upper part) from this book.
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
-
7/23/2019 Tidal sedimentology
6/637
v
Tides have fascinated humans for millennia. Their regularity and their apparent
correlation with lunar behavior intrigued natural philosophers, even the Greeks, who
live on an essentially tideless sea although there are strong tidal currents in localized
constrictions. Apparently, they learned about tides from areas outside the Straits of
Gibralter and from the Arabs who experienced significant tides in the Persian Gulf.
From a practical perspective, tidal changes in water elevation and the currents
associated with these changes were of great importance for shipping and militarypurposes. In areas such as the countries surrounding the southern North Sea, such
considerations required accurate tidal predictions, which in turn drew the attention of
some of the greatest astronomers and mathematicians.
Among the notable individuals who devoted at least part of their careers to the
study of tides, and have contributed to our understanding of them are Galileo,
Descartes, Bacon, Kepler, Euler, Laplace, and Lord Kelvin (Cartwight 1999). Indeed,
many of the widely used mathematical techniques that we now take for granted were
developed to help understand the behavior of the tides. More recently, interest in tides
and storm surges has been fostered by the need to protect ever-increasing coastal
population centers from catastrophic inundation, and by the desire to reclaim tidal
flats for agricultural and industrial purposes. Foremost in this activity have been TheNetherlands, Germany, and adjacent parts of Denmark.
Research on the nature of tidal deposits has been underway for about 50 years.
Early studies on the Wadden Sea along the North Sea coast of The Netherlands and
Germany were among the original landmark efforts in this area (e.g. van Straaten
1954; Postma 1961; Reineck 1963), and were followed closely by work in England
(Evans 1965) and France (Bajard 1966). Such efforts were driven by the dual need to
understand the coastal zone for the protection of population centers and to provide an
actualistic analog for ancient sedimentary successions. In North America, Kleins
work on the Bay of Fundy (Klein 1963) initiated detailed efforts in that part of the
world. The early German work in the North Sea had a major biological and ichno-
logical component, a topic that was pursued systematically at the Skidaway Institute
of Oceanography in the southeastern United States (e.g. Frey and Howard 1969).
Despite having some of the most widespread tidal flats in the world, work along the
Chinese coast was relatively slow to develop, although there were notable early studies
(e.g. Wang 1963). In the carbonate realm, pioneering studies were conducted on the
tidal flats of Andros Island, the Bahamas (e.g. Shinn et al. 1969), and the Persian Gulf
(Evans et al. 1969).
In spite of important work on the shallow-marine tidal deposits in the seas of
northwestern Europe (e.g. Stride 1963), most of the early work on modern tidal
Preface
-
7/23/2019 Tidal sedimentology
7/637
vi Preface
deposits was devoted to study of intertidal environments, mainly because they were
readily accessible. This fixation on the intertidal zone is perhaps nowhere more
evident in the influential compilation of examples contained in the book Tidal
Deposits: A Casebook of Recent Examples and Fossil Counterparts(Ginsburg 1975).
Indeed, the upward-fining succession developed by the progradation of a tidal flat
was among the very first facies models created. Application of these studies to the
rock record was widespread in the carbonate literature, with numerous documentedexamples being published through the 1960s, 1970s and 1980s. By comparison, the
extension of the work on the modern tidal deposits to ancient siliciclastic successions
was slow. At least one impediment to the widespread application to the ancient was
the notion put forward by Irwin (1965), and since largely disproven, at least for
siliciclastic sediments, that the expansive epicontinental seas of the past were largely
tideless, as a result of frictional damping of the tidal wave. An even greater impedi-
ment was the lack of definitive criteria for the recognition of tidal deposits, given that
exposure indicators are much less easily preserved in siliciclastic tidal deposits than
they are in carbonates. Thus, a milestone in the study of tidal deposits occurred in
1980 with the publication by Visser (1980) of tidal bundles in cross beds formed by
subaqueous dunes, which provided the first documentation of a definitive indicator oftidal sedimentation, spawned the widespread recognition of ancient tidal deposits in
an ever-growing number of localities.
Gradually, the focus of research on modern tidal environments has shifted away
from tidal flats, toward a more comprehensive examination of tidal sedimentation in
a wide range of settings, including even the deep ocean. Studies have tended to become
more holistic in their treatment of entire depositional systems, rather than concentrating
on only one part (e.g. tidal flats) of the whole. This more comprehensive approach is
evident in many of the papers in this volume.
Because of the increasing attention given to tidal deposits it became important to
organize a uniform nomenclature and approach to their study. As a consequence, Robert
N. Ginsburg organized and hosted a conference of interested researchers in February of1973. It included field experiences in both siliciclastic (Sapelo Island, Georgia, USA)
and carbonate areas (Florida Keys, USA and the Bahamas), followed by presentations
of research on tidalites (a term coined by George deVries Klein (1971)) by all in
attendance. The next similar conference was held in The Netherlands in 1986, followed
in regular succession by a series International Conferences on Tidal Sedimentology that
has met in Calgary, Canada (1989), Wilhelmshaven, Germany (1992), Savannah,
Georgia USA (1996), Seoul, Korea (2000), Copenhagen, Denmark (2004) and, most
recently, in Qingdao, China (2008). The next meeting will be in Caen, France in 2012.
The meeting in 2008 in China was particularly stimulating with an attendance that
surpassed any previous meeting. The expansion of interest in tidal deposits appears to
be spurred by two factors: the need to understand coastal tidal environments in order
to predict how these sensitive environments might respond to sea-level rise and
climate change; and providing data and interpretations to help in understanding
ancient depositional environments that were influenced by tides. Davis thought it was
a good time to assemble a principles-type volume on the topic of tidal sedimentology
given that no such synthesis exists, and because there has been so much new research
on tidal environments and deposits over the last few years. Dalrymple agreed to be
co-editor and the result of their efforts is this volume.
The purpose of this volume is to provide the first-ever, high-level overview of tidal
sedimentology. Many of the chapters contain the first-ever synthesis of information
-
7/23/2019 Tidal sedimentology
8/637
viiPreface
on the particular topic! The approach is comprehensive with state-of-the-art reviews
of the full spectrum of tidal depositional environments, from supratidal salt marshes,
through the full range of coastal environments and continental shelves, to the deep
sea. Examples from modern environments and ancient deposits are provided, and
both siliciclastic and carbonate environments are discussed. The book is organized in
the following four parts. (1) Chapters 14 provide overviews of the fundamentals of:
the generation of tides, the nature of sediment transport by tidal currents, the criteriaby which tidal deposits can be recognized, and the ichnology of tidal deposits. The
later chapter represents the first time that the ichnological characteristics of tidal depo-
sits have been reviewed systematically. (2) Chapters 514 review the characteristics
of the full range of siliciclastic tidal environments, including both tide-dominated
estuaries and deltas, as well as the various tidal components of barrier-lagoon systems.
These chapters cover all aspects of the sedimentology of these environments, from
the details of the physical processes operating in them, through the morphodynamics
and facies, and the stratigraphic organization of the deposits. (3) Chapters 1518
provide syntheses of particular times and places in earth history where tidal deposits
are particularly notable. The chapter on the Precambrian reviews tidal sedimentation
at a time when the Moon was significantly closer to the Earth and the tide-generatingforce should have been stronger. The reviews of the tidal deposits in the Illinois Basin
(Carboniferous age), Western Interior Seaway (Cretaceous) and Spanish Pyrenean Basin
(Eocene) provide unique insights into the large-scale (tectonic and relative sea level)
controls on the spatial and temporal distribution of tidal sedimentation. (4) Chapters
1921 discuss tidal sedimentation in modern and ancient carbonate environments.
Experts from throughout the world have been chosen to be the lead authors on
each of the chapters. They and their co-authors build on their considerable personal
experience to present insightful syntheses of the latest research in the particular topic.
Each chapter has abundant illustrations, many of which are in color to enhance their
effectiveness. References are extensive and include historically important ones as
well as those on the leading edge of each topic.Because of the uniquely broad coverage within each of the chapters, and in the
volume as a whole, this book should be of value to a wide range of researchers. Workers
who study modern sedimentary environments, and especially coastal settings, including
environmental managers and coastal engineers, will find much about the dynamics of
these environments that will assist them to develop protection strategies that are
compatible with the natural behavior of these complex systems, including their
response to potentially rising sea level. Geologists who study ancient sedimentary
successions, whether for more academic or more applied reasons, will find a wealth
of information about the behavior of tidal environments, ranging from the nature of
the facies, through small-scale sedimentary successions, to the largest-scale sequence-
stratigraphic control on tidal sedimentation.
The editors and authors gratefully acknowledge the financial support of numerous
funding agencies that have provided support for their respective research activities.
They also thank the people who have provided excellent and constructive reviews
(see below). The editors appreciate the cooperation of Dr. Robert Doe and his staff at
Springer Publishers.
-
7/23/2019 Tidal sedimentology
9/637
viii Preface
Chapter Reviewers
Clark Alexander
Serge Bern
Sean Bingham
Ron BoydMargie Chan
Kyungsik Choi
Poppe de Boer
Robert Dott
Paul Enos
Jon French
Shu Gao
Murray Gingras
Liviu Giosan
Steven Greb
Gary Hampson
Steve Hasiotis
Christopher Kendall
George Klein
Erik Kvale
Tim Lawton
Don McNeil
Bruce Nocita
Nora Noffke
David PiperPiret Plink-Bjorklund
Brian Pratt
Denise Reed
Joshiki Saito
Gene Shanmugam
Gene Shinn
Ronald Steel
John Suter
S. Temmerman
Bernadette Tessier
Ad van der Spek
Grant Wach
Ping Wang
Colin Woodruff
Paul Wright
References
Bajard J (1966) Figure et structures sdimentaires dans la partie orientale de la baie de MontSaint-Michel. Rev Geog Phys Geol Dyn 8:39112
Cartwright DE (1999) Tides: a scientific history. Cambridge University Press, Cambridge, 292 pEvans G (1965) Intertidal flat sediments and their environments of deposition in The Wash. J Geol
Soc Lond 121:209245Evans G, Schmidt V, Bush P, Nelson H (1969) Stratigraphy and geologic history of the Sabkha,
Persian Gulf. Sedimentology 12:145159Frey RW, Howard JD (1969) A profile of biogenic sedimentary structures in a Holocene barrier
island-salt marsh complex, Georgia. Gulf Coast Assoc Geol Soc Trans 19:427444Ginsburg RN (1956) Environmental relationships of grain size and constituent particles in some
south Florida carbonate sediments. Bull Am Assoc Petrol Geol 40:23842427
Ginsburg RN (1975) Tidal deposits: a casebook of recent examples and fossil counterparts. Springer,New York, 426 p
Irwin ML (1965) General theory of epeiric clear water sedimentation. Bull Am Assoc Petrol Geol49: 445459
Klein deV G (1971) A sedimentary model for determining paleotidal range. Geol Soc Am Bull82:25852592
Postma H (1961) Transport and accumulation of suspended matter in the Dutch Wadden Sea. NethJ Sea Res 1:148190
Reineck H-R (1963) Sedimentgefge im Bereich der sdlichen Nordsee. Abhandl SenckenberNaturforsch Ges 505:1138
Shinn EA, Lloyd RM, Ginsburg RN (1969) Anatomy of a modern carbonate tidal flat, Andros Island,Bahamas. J Sediment Petrol 39:112123
-
7/23/2019 Tidal sedimentology
10/637
ixPreface
Stride AH (1963) Current-swept sea floors near the southern half of Great Britain. Q J Geol SocLond 119:175199
van Straaten LMJU (1954) Composition and structure of recent marine sediments in the Netherlands.Leidse Geol Mededel 19:1110
Visser MJ (1980) Neap-spring cycles reflected in Holocene subtidal large-scale bedform deposits: apreliminary note. Geology 8:543546
Wang Y (1963) The coastal dynamic geomorphology of the northern Bohai Bay. In: Wang Y (ed)
Collected oceanic works of Nanjing University. Nanjing University Press, Nanjing (in Chinesewith English abstract)
Corpus Christi, Texas USA
Kingston, Ontario, Canada
-
7/23/2019 Tidal sedimentology
11/637
-
7/23/2019 Tidal sedimentology
12/637
xi
Contents
1 Tidal Constituents of Modern and Ancient
Tidal Rhythmites: Criteria for Recognition and Analyses. . . . . . . . . . 1
Erik P. Kvale
2 Principles of Sediment Transport Applicable
in Tidal Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Ping Wang 3 Tidal Signatures and Their Preservation
Potential in Stratigraphic Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Richard A. Davis, Jr.
4 Tidal Ichnology of Shallow-Water Clastic Settings . . . . . . . . . . . . . . 57
Murray K. Gingras and James A. MacEachern
5 Processes, Morphodynamics,
and Facies of Tide-Dominated Estuaries . . . . . . . . . . . . . . . . . . . . . . . . 79
Robert W. Dalrymple, Duncan A. Mackay,
Aitor A. Ichaso, and Kyungsik S. Choi
6 Stratigraphy of Tide-Dominated Estuaries . . . . . . . . . . . . . . . . . . . . . . 109
Bernadette Tessier
7 Tide-Dominated Deltas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Steven L. Goodbred, Jr. and Yoshiki Saito
8 Salt Marsh Sedimentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Jesper Bartholdy
9 Open-Coast Tidal Flats. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Daidu Fan
10 Siliciclastic Back-Barrier Tidal Flats . . . . . . . . . . . . . . . . . . . . . . . . . . . 231Burghard W. Flemming
11 Tidal Channels on Tidal Flats
and Marshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Zoe J. Hughes
12 Morphodynamics and Facies Architecture
of Tidal Inlets and Tidal Deltas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Duncan FitzGerald, Ilya Buynevich, and Christopher Hein
13 Shallow-Marine Tidal Deposits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
Jean-Yves Reynaud and Robert W. Dalrymple
-
7/23/2019 Tidal sedimentology
13/637
xii Contents
14 Deep-Water Tidal Sedimentology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
Mason Dykstra
15 Precambrian Tidal Facies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
Kenneth A. Eriksson and Edward Simpson
16 Hypertidal Facies from the Pennsylvanian Period:
Eastern and Western Interior Coal Basins, USA. . . . . . . . . . . . . . . . . . 421Allen W. Archer and Stephen F. Greb
17 Tidal Deposits of the Campanian Western
Interior Seaway, Wyoming, Utah and Colorado, USA . . . . . . . . . . . . . 437
Ronald J. Steel, Piret Plink-Bjorklund, and Jennifer Aschoff
18 Contrasting Styles of Siliciclastic Tidal Deposits
in a Developing Thrust-Sheet-Top Basins The Lower
Eocene of the Central Pyrenees (Spain). . . . . . . . . . . . . . . . . . . . . . . . . 473
A.W. Martinius
19 Holocene Carbonate Tidal Flats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507Eugene C. Rankey and Andrew Berkeley
20 Tidal Sands of the Bahamian Archipelago. . . . . . . . . . . . . . . . . . . . . . . 537
Eugene C. Rankey and Stacy Lynn Reeder
21 Ancient Carbonate Tidalites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567
Yaghoob Lasemi, Davood Jahani, Hadi Amin-Rasouli,
and Zakaria Lasemi
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609
-
7/23/2019 Tidal sedimentology
14/637
xiii
Contributors
Hadi Amin-Rasouli Department of Geosciences, University of Kurdistan, Sanandaj,
Iran, [email protected]
Allen W. Archer Department of Geology, Kansas State University, Manhattan, KS
66506, USA, [email protected]
Jennifer Aschoff Department of Geology and Geologic Engineering, Colorado
School of Mines, Golden, CO, USA, [email protected]
Jesper Bartholdy Department of Geography and Geology, University of Copenhagen,
10 ster Voldgade, Copenhagen DK-3050, Denmark, [email protected]
Andrew Berkeley Department of Evironmental & Geographical Sciences,
Manchester Metropolitan University, John Dalton Extension Building, Chester
Street, Manchester M1 5GD, UK
Ilya Buynevich Department of Earth and Environmental Sciences, Temple
University, 313 Philadelphia, PA 19122, USA, [email protected]
Kyungsik S. Choi Faculty of Earth Systems and Environmental Sciences, Chonnam
National University, Gwangju 500-757, South Korea, [email protected]
Robert W. Dalrymple Department of Geological Sciences and Geological
Engineering, Queens University, Kingston, ON K7L 3N6, Canada, dalrymple@geol.
queensu.ca
Richard A. Davis, Jr. Department of Geology, Coastal Research Laboratory,
University of South Florida, Tampa, FL 33620, USA, [email protected]
Harte Research Institute for Gulf of Mexico Studies, Texas A&M University
Corpus Christi, TX 78412, USA
Mason Dykstra Department of Geology and Geological Engineering, Colorado
School of Mines, Golden, CO 80401, USA, [email protected]
Kenneth A. Eriksson Department of Geosciences, Virginia Tech, Blacksburg,
VA 24061, USA, [email protected]
Daidu Fan State Key Laboratory of Marine Geology, Tongji University, Shanghai
200092, China, [email protected]
Duncan FitzGerald Department of Earth Sciences, Boston University, Boston, MA
02215, USA, [email protected]
Burghard W. Flemming Senckenberg Institute, Suedstrand 40, 26382 Wilhelmshaven,
Germany, [email protected]
-
7/23/2019 Tidal sedimentology
15/637
xiv Contributors
Murray K. Gingras Department of Earth and Atmospheric Sciences, University of
Alberta, Edmonton, AB T6G 2E3, Canada, [email protected]
Steven L. Goodbred, Jr. Department of Earth and Environmental Sciences,
Vanderbilt University, Nashville, TN 37240, USA, [email protected]
Stephen F. Greb Kentucky Geological Survey, University of Kentucky, Lexington,
KY 40506, USA, [email protected]
Christopher Hein Department of Earth Sciences, Boston University, Boston, MA
02215, USA, [email protected]
Zoe J. Hughes Department of Earth Sciences, Boston University, Boston, MA 01778,
USA, [email protected]
Aitor A. Ichaso Department of Geological Sciences and Geological Engineering,
Queens University, Kingston, ON K7L 3N6, Canada, [email protected]
Davood Jahani Department of Geology, Faculty of Basic Sciences, North Tehran
Branch, Islamic Azad University, Tehran, Iran, [email protected]
Erik P. Kvale Devon Energy Corporation, 20 North Broadway, Oklahoma City, OK
73102, USA, [email protected]
Yaghoob Lasemi Illinois State Geological Survey, Prairie Research Institute,
University of Illinois at Urbana-Champaign, Champaign, IL 61820, USA, ylasemi@
illinois.edu
Zakaria Lasemi Illinois State Geological Survey, Prairie Reserarch Institute,
University of Illinois at Urbana-Champaign, Champaign, IL 61820, USA,
James A. MacEachern Department of Earth Sciences, Simor Fraser Univeraity,
8888 University Drive, Burnaby, BC V5A 1S6, Canada, [email protected]
Duncan A. MacKay Department of Geological Sciences and Geological Engineering,
Queens University, Kingston, ON K7L 3N6, Canada, [email protected]
A.W. Martinius Statoil Research and Development, Arkitekt Ebbels vei 10, N-7005
Trondheim, Norway, [email protected]
Piret Plink-Bjorklund Department of Geology and Geologic Engineering, Colorado
School of Mines, Golden, CO, USA, [email protected]
Eugene C. Rankey Department of Geology, University of Kansas, 1475 Jayhawk
Blvd., 120 Lindley Hall, Lawrence, KS 66045, USA, [email protected]
Stacy Lynn Reeder Schlumberger-Doll Research, One Hampshire Street, Cambridge,
MA 02139, USA, [email protected]
Jean-Yves Reynaud Dpartement Histoire de la Terre UMR 7193 ISTeP, Musum
National dHistoire Naturelle, Gologie, CP 48, 43, rue Buffon, F-75005 Paris,
France, [email protected]
Yoshiki Saito Geological Survey of Japan, AIST, Central 7, Higashi 1-1-1, Tsukuba
305-8567, Japan, [email protected]
-
7/23/2019 Tidal sedimentology
16/637
xvContributors
Edward Simpson Department of Physical Sciences, Kutztown University, Kutztown,
PA 19530, USA,[email protected]
Ronald J. Steel Department of Geological Sciences, University of Texas Austin,
Austin, TX 78712, USA, [email protected]
Bernadette Tessier Morphodynamique Continentale et Ctire, University of Caen,
UMR CNRS 6143, 24 Rue des Tilleuls, 14000 Caen, France, [email protected]
Ping Wang Coastal Research Laboratory, Department of Geology, University of
South Florida, Tampa, FL 33620, USA, [email protected]
-
7/23/2019 Tidal sedimentology
17/637
-
7/23/2019 Tidal sedimentology
18/637
-
7/23/2019 Tidal sedimentology
19/637
2 E.P. Kvale
lamina is directly and positively related to tidal current
strength, which in turn is directly and positively related
to the magnitude of the daily rise and fall of the tide
(tidal range). Over periods of days, months, or years,
changes in tidal current strengths associated with
various lunar/solar cycles are mirrored by the change
in thicknesses of the vertically stacked laminae.Modern and ancient tidal rhythmites have been found
on every continent in the world except Antarctica. In
modern environments, tidal rhythmites occur in depos-
its associated with tide-dominated deltas, tidal embay-
ments, and estuaries. Tidal rhythmites can be used for
reconstructing ancient paleogeographies and paleocli-
mates (e.g. this chapter, Hovikoski et al. 2005; Kvale
et al. 1994), estimating paleotidal ranges (e.g. Archer
1995; Archer and Johnson 1997), understanding chan-
nel migration in the fluvio-estuaring transition (Choi
2010) determining lunar-retreat rates through time (e.g.
Williams 1989; Kvale et al. 1999), and most recently,
have been used to infer the major tidal constituents
associated with the tides that deposited them (e.g.
Kvale 2006). In order to understand tidal rhythmites,
however, one has to understand how tides are generated
and what controls their genesis.
The impact of diurnal, semidiurnal, and semimonthly
(neap-spring) tidal cycles on sediment deposition has
been well documented since the early 1980s (e.g. Visser
1980; Boersma and Terwindt 1981; Allen 1981). For
many geologists these became benchmark papers when
they were published because they showed how deposi-
tional packages within sedimentary successions can be
linked to a tidal origin. However, it was the discovery
of modern and ancient tidal rhythmites in the late 1980s
and 1990s that showed that a hierarchy of tidal cycles,
beyond simple semidaily, daily or fortnightly events,
could be preserved in the rock record (e.g. Kvale et al.
1989; Williams 1989; Dalrymple and Makino 1989;
Archer et al. 1991; Kvale et al. 1994; Miller and
Eriksson 1997). Tidal cycles associated with monthly,
semiannual, annual (usually includes a significant sea-
sonal climatic component), and even an approximately
18-year cycle have been identified from ancient tidal
rhythmites.
Studies, however, showed that the understanding of
one of the most basic of the tidal cycles, the neap-spring
or fortnightly tidal cycle, by most geologists, and
apparently many oceanographers, and astronomers as
well, was over-simplified. Many college-level textbooks
today continue to propagate a basic misunderstanding
of the neap-spring cycles and the origin of oceanic
tides in general (e.g. Duxbury et al. 2002).
The intent of this chapter is neither to outline a
history of the study of tides and tidal deposits nor to
document the current state of knowledge regarding
the history of the Earth-Moon system. These issues
are treated in some detail in Klein (1998), Rosenberg(1997), Williams (2000), and Coughenour et al.
(2009). Rather, it is to explain some basic tidal theory
and show how a more complete knowledge of ancient
tides can be extracted from the rock record. Most of
the information contained within this chapter is dis-
tilled from two summary papers: Kvale et al. (1999)
and Kvale (2006).
To truly understand tidal systems and, in particular,
the genesis of tidal rhythmites it is useful to understand
both an equilibrium tidal model and a dynamic tidal
model. The former explains the driving forces behind
the formation of tides and is commonly taught to
geology, oceanography, and astronomy undergraduates,
whereas the later, more accurately explains real-world
tides and is more useful in interpreting the rock record.
An understanding of both models is essential to anyone
who studies tides and tidal deposits, and both will be
discussed.
1.2 Equilibrium Tidal Theory
Most geologists understand tidal periodicities in the
context of equilibrium tidal theory. Tides are generated
by the gravitational forces of the Moon and, to a lesser
degree, the Sun on the Earth. The Moon accounts for
approximately 70% of the tide-raising force because of
its proximity to the Earth. In an equilibrium world, the
Earth is covered by an ocean of uniform depth that
responds instantaneously to changes in tractive forces
(MacMillan 1966). The equilibrium model can be used
to explain five of the six tidal periodicities that have
been commonly detected in rhythmite successions.
These six cycles are illustrated in Figs. 1.11.6(previ-
ously illustrated in Kvale et al. 1998). A seventh cycle
known as the nodal cycle, an approximately 18 year-
tidal cycle, and very well documented by Miller and
Eriksson (1997) within the Pride Shale, a lower
Carboniferous succession found in West Virginia, is
not illustrated here.
The figures each illustrate (from upper left to lower
right): A diagram and explanation of the equilibrium
-
7/23/2019 Tidal sedimentology
20/637
31 Tidal Constituents of Modern and Ancient Tidal Rhythmites: Criteria for Recognition and Analyses
tidal theory of five of the six tidal periods; a bar chart
of tidal height data (high tide elevations) from a modern,
real-world setting that shows how the astronomical
effects are reflected in cyclic changes in daily high
tides; a core from an ancient tidal rhythmite succession
showing how these cyclic tidal effects might be mani-
fested in a laminated tidal rhythmite; and a bar chart of
laminae thicknesses interpreted in the context of the
modern tidal cycle.
1.2.1 Semidiurnal (12.42 h)
Within the equilibrium tidal model, the interaction of
tidal forces from the Moon and Sun produce two oce-
anic bulges on opposite sides of the Earth (Fig. 1.1).
The rotation of a point on the Earth through these
bulges once a day produces two tides (the semidiur-
nal tide). Typically, these tides are not equal (termed
diurnal inequality), as one tide is higher (dominant)
than the other (subordinate) because the Moons
orbital plane and the Earths equatorial plane are not
parallel. The angular difference between the two
planes is termed lunar declination.
1.2.2 Synodic (29.53 Days)
Daily high tides are higher when the Earth, Moon, and
Sun are nearly aligned (full or new moon); this is
referred to as syzygy (Fig. 1.2). Conversely, lower
tides occur when the Sun and Moon are at right angles
to the Earth (first or third quarter phase), also known as
quadrature. Tides during full or new moon are
referred to as spring tides: spring in this context
refers to lively or energetic rather than implying a
seasonal connotation. Tides at quarter phases are
referred to as neap tides. The neap-spring tidal period
Fig. 1.1 Semidiurnal equilibrium model. (a) Two oceanic tidalbulges are produced on opposite sides of the Earth by the gravita-
tional forces of the Sun and the Moon. (b) Two tides are produced
each day by the spin of the Earth through these bulges. The diur-
nal inequality is produced when the tidal bulges are not centered
above the Earths equator. Semidiurnal tides can be recognized in
the rock record by the coupling of thick and thin lamina (c) and
graphically in the thickness measurements of laminated sequences
(d) as preserved in the tidal rhythmite succession from the
Pennsylvanian Mansfield Formation (Hindostan whetstone beds)
from Orange County, Indiana, USA (From Kvale and others
(1998) and used by permission from SEPM)
-
7/23/2019 Tidal sedimentology
21/637
4 E.P. Kvale
in the equilibrium model is related to the changing
phases of the Moon associated with the half-synodic
month. The synodic month (new moon to new moon,
or full moon to full moon) has a modern period of
29.53 days and encompasses two neap-spring cycles.
1.2.3 Tropical (Semidiurnal, 27.33 Days)
The tidal force also depends on the declination of the
Moon (Fig. 1.3). In this usage, declination refers to
the tilt or angle of the Moons orbit relative to the
Earths equatorial plane. The period of the variation in
declination is called the tropical month the interval of
time it takes the Moon to complete one full orbit from
its maximum northern declination to its maximum
southern declination and then return. The effect of the
tropical month in an equilibrium semidiurnal tidal
system is to cause the diurnal inequality of the tides.
Ideally, diurnal inequality is greatest when the Moon is
at its maximum declination. This inequality is reduced
to zero when the Moon is over the equator, producing a
crossover in the tidal data (Fig. 1.3). The current length
of the tropical month is 27.32 days (2 days shorter than
the synodic month see synodic discussion above).
Because of this difference, equatorial passages of the
Moon, called crossovers, have a shorter periodicity than
the periodicity related to synodic neap-spring tides.
1.2.4 Tropical (Diurnal, 27.32 Days)
In modern, dominantly diurnal systems (primarily
one tide per day), the tropical period described above
Fig. 1.2 Synodic equilibrium model. (a) In an equilibriumtidal model, spring tides occur when the Earth, Moon, and Sun
align during full or new moon (also known as syzygy).
Equlibrium neap tides occur when the Moon-Earth alignment is
90 from an Earth-Sun alignment (also known as quadrature).
The synodic month (currently 29.53 days) is the time it takes forthe Moon to orbit the Earth when measured from a new Moon
to the next new Moon. When neap-spring tides can be timed to
phases of the Moon they are referred to as synodic neap-spring
tides (Kvale 2006). (b) Graph of tidal heights of a portion of
the 1991 predicted high tides for Kwajalein Atoll, Pacific
(NOAA 1990) showing the effects of changing lunar phases.
(c) Portion of a core from the Mansfield Formation (Hindostan
whetstone beds), Indiana, USA with neap and spring tidal
deposits labeled. (d) Measurements of laminae thicknessesfrom Hindostan whetstone beds with neap and spring tidal
deposits labeled (From Kvale et al. (1998) and used by permis-
sion from SEPM)
-
7/23/2019 Tidal sedimentology
22/637
51 Tidal Constituents of Modern and Ancient Tidal Rhythmites: Criteria for Recognition and Analyses
is responsible for generating neap-spring cycles. In
contrast to the synodic system, tides in a tropical sys-
tem behave as though the Suns gravitational effects
are dampened, which is impossible to explain in an
equilibrium tidal model (Fig. 1.4). In such cases, the
dominant tidal force depends on the declination of
the Moon relative to the Earths equator with the
force being greatest when the Moon is most directly
over the site in question. In these systems, the pre-
dicted and ancient tide data reveal that equatorial
passages of the Moon (crossovers) occur in phase
with the generation of neap-spring tides, in contrast
to the variable relationship exhibited by tropical
(semidiurnal) tides.
1.2.5 Anomalistic (27.55 Days)
Another tidal effect arises from the changing distance of
the Moon relative to the Earth during the lunar orbit
(Fig. 1.5). Because the lunar orbit forms an ellipse, with
the Earth slightly offset from the center, the Moon alter-
nates between perigee (closest approach to the Earth) and
apogee (the farthest distance from the Earth). During the
lunar synodic month there will be two spring tides (see
synodic periods described above). These spring tides,
however, will be of unequal magnitude producing alter-
nating high-spring and low-spring tides, which corre-
spond to spring tides during or near perigee (high spring)
and spring tides during or near apogee (low spring).
Fig. 1.3 Tropical, semidiurnal equilibrium model. (a) Model of theMoon in orbit around the Earth. The lunar declination is exaggerated
from its modern range of 1828. The tropical month (currently
27.32 days) is the time it takes for the Moon to move from its
maximum northern declination to its southernmost declination and
back to its northernmost declination in a single orbit. (b) Graph
of tidal heights of a portion of the same modern tidal record shown
in Fig. 1.2b illustrating diurnal inequality of semidiurnal tides.
Note diurnal inequality goes to zero when the Moon passes
directly over the Earths equator. (c) Image of core shown in
Fig. 1.2cshowing approximate position (labeled C) when Moon
was above the Earths equator during deposition. Note the approx-
imate equal thicknesses of the lamina on either side of the arrow.
(d)Bar chartshown in Fig. 1.2dwith arrows denoting passages
of the Moon above the Earths equator during deposition (From
Kvale et al. (1998) and used by permission from SEPM)
-
7/23/2019 Tidal sedimentology
23/637
6 E.P. Kvale
The semimonthly inequality of the spring tides disappears
when the Moon lies along the minor axis of the lunar
orbit and the difference in lunar distance is minimized
during subsequent spring tides. The time it takes for the
Moon to move from perigee to perigee is called the
anomalistic month, which is at present 27.55 days.
1.2.6 Semiannual (182.6 Days)
The synodic, tropical, and anomalistic periods have
slightly different values. Because of this, these periods
will interact constructively twice each year causing tidal
forces at these times to reach a maximum (as shown by
the dashed line in Fig. 1.6). In the equilibrium tidal
model, the date of this tidal maximum is a function of
latitude that is related to the declinational effects of the
Moon and Sun. An annual inequality has been docu-
mented in several ancient tidal rhythmite successions
(Kvale et al. 1994). This inequality is interpreted to be
climatic (non-tidal) in origin.
1.3 Dynamic Tidal Theory
As noted in the introduction, the equilibrium tidal
model explains the driving forces that cause tides but
does not explain real-world tides. For instance, the
Fig. 1.4 Tropical diurnal model. (a) Model of the Moon in itsorbit around the Earth (see Fig. 1.3a). (b) Graph showing the
1994 predicted relative high tides (mixed, predominantly diur-nal) for the Barito River estuary in Borneo (NOAA 1993). Note
the passages of the Moon above the Earths equator perfectly
track the neap tides and spring tides to the maximum declinations
of the Moon in its orbit around the Earth, a pattern not predicted
by equilibrium tidal theory. Such neap-spring tidal cycles are
termed tropical neap-spring tides (Kvale 2006). (c) Photograph
of a portion of a core from the Pennsylvanian Brazil Formation,
Daviess County, Indiana, USA. Arrowsindicate lamina depos-
ited with the Moon was above the Earths equator. (d)Bar chartof lamina thicknesses measured from core obtained from the
Brazil Formation. This unit also is mixed, predominantly diurnal.
Note the diurnal inequality of the semidiurnal component goes to
zero only in the neap tide deposits. This corresponds to the Moon
above the Earths equator during deposition (From Kvale and
others (1998) and used by permission from SEPM)
-
7/23/2019 Tidal sedimentology
24/637
71 Tidal Constituents of Modern and Ancient Tidal Rhythmites: Criteria for Recognition and Analyses
world does not spin through two tidal bulges. Instead,
oceanic tides rotate as waves around fixed (amphidro-
mic) points within individual ocean basins (Fig. 1.7).
Equilibrium tidal theory indicates that diurnal tides
should exist only at very high latitudinal positions,
which is not the case. For example, the Gulf of Mexico
and large tracts in the Indian and western Pacific oceans
are dominated by diurnal tides. Tides like those found
in Immingham, England, where the semidiurnal tides
have minimal diurnal inequality, cannot be explained
by equilibrium tidal theory, which requires such tides
to exist only in equatorial positions. Finally, equilib-
rium tidal theory does not explain neap-spring tidal
cycles which are synchronous with the 27.32 tropical
monthly period such as illustrated in Fig. 1.4.
The difficulties in understanding and explaining
real-world tides can be addressed by a dynamic tidal
model. This model is built around the concept of a
harmonic analysis of the components that compose
real-world tides. For instance, the Moon and Sun each
generate their own tide within the Earths oceans. Since
the orbits of the Earth around the Sun and the Moon
around the Earth are not perfectly circular, the ampli-
tude of the tides generated by each of these bodies, in
part, fluctuates depending on the Earths proximity
to the Sun and, much more importantly, the Moons
distance from the Earth. Periodically each of these
tides will constructively or destructively interact with
each other. The tides associated with changes in Moon-
Earth distance or Earth-Sun distance can be considered
to be a constituent of the overall tide, which can affect
any coastline.
To model these tidal constituents (also known as
tidal species) oceanographers conceptualize each
Fig. 1.5 Anomalistic equilibrium model. (a) Polar view of theMoon in orbit around the Earth. Note that lunar orbit is not
perfectly circular but somewhat elliptical (greatly exaggerated
in the diagram) and that the Earth is not position in the direct
center of the orbit path. The time it takes for the Moon to go
from perigee (closest approach) to apogee (furthest from the
Earth) and return is called the anomalistic month, which is27.55 days long at present. (b) Graph showing the 1992 pre-
dicted high tides for Saint John, New Brunswick, Canada
(NOAA 1991) showing the effects of the anomalistic month on
the Saint John tides. Note the semimonthly inequality goes to
zero when the Moon and Sun are aligned with the Moons
minor orbital axis (termed phase flip). (c) Photograph of a
core from the Mississippian Tar Springs Formation, Indiana,
USA showing the effects of the anomalistic month on neap-
spring tidal deposition. (d) Graph illustrating thicknesses as
measured between neap-to-neap tide deposits from the TarSprings Formation core, a portion of which is shown in
Fig. 1.5c. Note the position of the phase flip (From Kvale
et al. (1998) and used by permission from SEPM)
-
7/23/2019 Tidal sedimentology
25/637
8 E.P. Kvale
constituent as a phantom satellite that has its own
mass (that of the Moon, Sun, or a combination of the
two). Each phantom satellite has a motion within a
plane or is fixed relative to the stars and each generates
its own tide with a unique period, response time, and
amplitude (Pugh 1987) (Table 1.1). For instance S2
represents the twice-daily tide generated at a fixed
point on the Earth by a satellite that has the mass of
the Sun in a perfectly circular orbit around the Earths
equator. O1 represents the daily tide generated at a
fixed point on the Earth by a satellite with a mass of
the Moon and a motion above the Earths equator. For
each of the tidal constituents, the subscript indicates
if the tide is diurnal (1) or semidiurnal (
2).
The relative intensity for each of these tidal constitu-
ents along any oceanic coastline in the world can be
determined by a harmonic decoupling of an extended
hourly tidal record. These measurements typically are
recorded in most major harbors and other tidal stations
around the world. More than 100 tidal constituents have
been identified from a harmonic extraction of Earths
tides, however, seven of these (Table 1.1) account for
more than 80% of any real-world tide (Defant 1961).
The resonate amplification or destruction of these tidal
constituents determines the resulting tide for a specific
area within the Earths oceans (Fig. 1.8).
As noted above, each of these tidal constituents
corresponds to a unique tidal wave. These waves do
not travel around the world as predicted by equilibrium
tidal theory, but rather rotate around a point (referred
to as an amphidromic point) within a region of the
ocean at a speed determined by their constituents
orbital periodicity or the periodicity of the Earths spin
(Fig. 1.7). The location of these points is determined
by basin geometries and the Coriolis force.
Ideally, amphidromic circulation should be counter-
clockwise in the Northern Hemisphere and clockwise
in the Southern Hemisphere and never on the equator
Fig. 1.6 Semiannual equilibrium model. (a) View of the con-figuration of the Earth, Moon, and Sun representing the maxi-
mum spring tides formed when the Moon is at perigee, maximum
northern declination and new. Such spring tides occur every
182.6 days. (b) 1992 predicted high tides from Saint John, New
Brunswick, Canada (NOAA 1991) showing the effects of the
semiannual convergence of maximum spring tides. (c) Photograph
of a core from the Pennsylvanian Lead Creek Limestone, Indiana,
USA. In this core the neap-spring cycles thicken and thin in a
semiannual pattern. (d) Graph showing the thicknesses of
individual lamina from the Brazil Formation, Indiana. These
thicknesses are also organized into semiannual tidal cycles. Each
number records an individual neap-spring cycle (From Kvale
et al. (1998) and used by permission from SEPM)
-
7/23/2019 Tidal sedimentology
26/637
91 Tidal Constituents of Modern and Ancient Tidal Rhythmites: Criteria for Recognition and Analyses
but, as shown above, real-world tides dont always
follow convention and exceptions are known (Open
University Course Team 1999).
The major tidal cycles discussed under the equilib-
rium model can be understood in the context of the
dynamic model and tidal constituents. Specifically, the
synodic neap-spring cycle is generated through the
interaction of the S2and M
2constituents. In the modern
world, these two tides come into phase and amplify the
resulting tide every 14.77 days. The result is a syn-
odic spring tide. Conversely, every 13.66 days K1and
O1 converge and generate a tropical spring tide.Whether a spring tide along a specific coastline is
dominated by the synodic spring tide or the tropical
spring tide is determined by the basin geometry. For
instance, the Gulf of Mexico is dominated by the K1
and O1tides, therefore neap-spring tides cycle with the
tropical month (Fig. 1.9). The east coast of the USA,
however, is dominated by S2and M
2tides resulting in
neap-spring tides that cycle with the synodic month
(Fig. 1.9). The semimonthly inequality of spring tides
occurs because of the convergence of M2and N
2every
27.55 days. A diurnal inequality is driven by the inter-
action of O1and M
2(in phase once a day) and is noted
in coastal tides when these constituents are of suffi-
cient amplitude.
One can look at the progressive change in relative
intensity of particular tidal constituent along a coast
and see how that affects the resulting tides. For exam-
ple, Figs. 1.10and 1.11shows the amplitudes for the
seven dominant tidal constituents for the Gulf of
Carpentaria, Australia and the tidal patterns that result
from changes in the relative amplitudes of the various
constituents (from Kvale 2006). At the mouth of the
gulf at Booby Island, the tides are dominated by M2,
K1 and O
1. Given the dominance of O
1 and K
1, the
neap-spring cycle occurs every 27.32 days and corre-
sponds to the tropical monthly period. However, unlike
many regions whose neap-spring cycles are tropically
driven, there is a relatively strong M2tide (but relatively
weak S2 tide) at the mouth of the gulf. The resultant
Fig. 1.7 Diagram showing the amphidromic circulation for theM
2tide in the North Sea. Co-tidal lines indicate times of high
water. And co-range lines indicate lines of equal tidal range.
Figure is modified from Dalrymple (1992) which was based on
a map first drawn by J. Proudman and A. T. Doodson (From
information found in Cartwright 1999) (From Kvale (2006) and
used by permission from Marine Geology)
Table 1.1 List of the seven most common tidal constituents, their rotational speed (number of degrees a tidal wave generated bythe constituent can travel around its amphidromic point in 1 h), description, and period in solar hours (Defant 1961)
Tidal constituent Speed (degrees/hour) Origin Period in solar hours
M2
28.9841 Principal lunar 12.42
S2
30 Principal solar 12
N2
28.4397 Larger elliptical lunar 12.66
K2
30.0821 Combined declinational lunar
and declinational solar
11.97
K1
15.0411 Combined declinational lunar
and declinational solar
23.93
O1
13.943 Principal lunar 25.82
P1 14.9589 Principal solar 24.07
-
7/23/2019 Tidal sedimentology
27/637
10 E.P. Kvale
tide at Booby Island exhibits a tropically driven
neap-spring cyclicity comparable to the tide depicted
in Fig. 1.4except that it also exhibits a strong semidi-
urnal component that is driven by M2. Progressing fur-
ther south into the Gulf of Carpentaria, the strengths of
K1and O
1increase relative to M
2creating a tide that is
dominantly diurnal.
1.4 Ancient Tides
Some tidal rhythmites in the rock record preserve long
(several months worth), relatively complete succes-
sions of daily or semidaily tidal deposition. Particularly
complete records can be interpreted in the context of
the dynamic tidal model and several examples are
noted below.
1.4.1 Hindostan Whetstone Beds
(Pennsylvanian, Indiana)
Figures 1.2and 1.3show both a segment of core and a
bar chart of the laminae thicknesses from the Hindostan
Whetstone beds found in Orange County, Indiana
(Kvale et al. 1989). Neap-spring cycles in this chart
occur more frequently than crossovers indicating that
these tides were synodically driven and hence related
to the dominance of the M2and S
2over the O
1and K
1
constituents. Some caution is needed, however, in
interpreting crossover patterns because the absence of
a single half-day event could cause an apparent cross-
over. Ways to infer completeness of a tidal pattern are
discussed by Kvale et al. (1999). Suffice it to state that
with suitably long tidal rhythmite records, such as
presented here, it is possible to interpret crossover
patterns with some confidence.
This example clearly shows a diurnal inequality,
and, as such, O1must be significant. There appears to
be a lack of a pronounced semimonthly inequality
(anomalistic cycle) suggesting that N2 was relatively
weak. Therefore, tides that deposited the Hindostan
Whetstone beds were dominated by the constituents
M2, S
2, and O
1followed by K
1and N
2.
1.4.2 Brazil Formation (Pennsylvanian,Indiana)
Figure 1.4show a segment of core and a bar chart of
laminae thicknesses from the Brazil Formation of
Daviess County, Indiana (Kvale and Archer 1990;
Kvale and Mastalerz 1998). The neap-spring cycles in
this example occur at the same frequency as the cross-
overs indicating that these tides were driven by the
tropical period and hence reflect a dominance of O1
and K1 over S
2 and M
2. A weak semidiurnal signal
occurs during the neap tides and indicates that M2had
some amplitude and importance in the resulting tide.
The Brazil Formation rhythmites, like the whetstone
beds discussed above, lack a prominent semimonthly
inequality suggesting a weak N2 tidal constituent. It
can be inferred from this data base that the Brazil
Fig. 1.8 Resulting tide predicted from the stacking of 9 differenttidal constituents. Horizontal units are in hours (Modified from
MacMillan, 1966 in Kvale, (2006) and used by permission from
Marine Geology)
-
7/23/2019 Tidal sedimentology
28/637
111 Tidal Constituents of Modern and Ancient Tidal Rhythmites: Criteria for Recognition and Analyses
Fig. 1.9 Graphs showing predicted high-data for two tidalreferences stations from the east coast and Gulf coast USA. The
Port Manatee example is typical of the tides in the Gulf coast
and the Hunniwell graph typifies east coast tides. Both tidal
records cover the same interval of time from January through
early May, 2005 (National Oceanographic and Atmospheric
Administration Web site 2004). Note that the equatorial pas-
sages of the Moon are fixed with the neap tides in the Gulf
coast station but move through the graph in the east coast exam-
ple. As such, Gulf coast neap-spring tides are driven by the
tropical month but the east coast neap-spring tides are controlled
by the phase changes of the Moon associated with the synodic
month (From Kvale (2006) and used by permission from Marine
Geology)
-
7/23/2019 Tidal sedimentology
29/637
12 E.P. Kvale
Fig. 1.10 Graphs andlocation map for predicted
high-tide data from three tidal
reference station in the Gulf
of Carpentaria, Australia.
The time interval for each
graph spans January through
early June, 2004 (AustralianNational Tidal Centre, Bureau
of Meteorology Web site,
2004) (From Kvale (2006)
and used by permission from
Marine Geology)
-
7/23/2019 Tidal sedimentology
30/637
131 Tidal Constituents of Modern and Ancient Tidal Rhythmites: Criteria for Recognition and Analyses
Formation tides were dominated by O1, K
1, followed
by M2with very weak contributions from S
2and N
2.
1.4.3 Abbott Sandstone (TradewaterFormation, Pennsylvanian, Illinois)
Figure 1.12shows an outcrop and bundle thicknesses from
some flaggy, large-scale tidal bundles along Interstate 57
in Johnson County, Illinois (Kvale and Archer 1991). A
histogram of bundle thicknesses indicates a strong semidi-
urnal signal throughout the record. While not as clean a
tidal record as the two previous examples, the Abbott
sandstone example appears to exhibit minimal diurnal
inequality during the neap tides. When the diurnal inequal-
ity tracks neap tides, it indicates that neap-spring cyclicity
is driven by the tropical period (e.g. Fig. 1.4). As such, the
Abbott Sandstone tidal record resembles that of Booby
Island, Australia (Fig. 1.10), in which M2, O
1and K
1dom-
inate the resultant tide over S2. There is a suggestion of a
semimonthly inequality to the Abbott sandstone record
indicating that N2was stronger than S
2 and sufficiently
strong to influence the tidal record.
These examples illustrate that tidal constituents
can be extracted from the rock record in well-preserved
tidal rhythmites. While it is not always possible to
draw conclusions regarding so many tidal constitu-
ents, deposits can generally be determined to be either
diurnal or semidiurnal in nature based on the absence
or occurrence of alternating thick-thin laminae. Most,
but not all, semidiurnal tidal deposits can be related
to the synodic period and the convergence of M2and
S2constituents. Exceptions of semidiurnal, tropically
driven neap-spring tides or tidal deposits, such as
Booby Island and the Abbott Sandstone, are known
and can be discerned if the tidal record is long and
clean enough. All diurnal deposits should have been
deposited in tropically driven neap-spring cycles.
Semidiurnal depositional systems that lack strong K1
or O1constituents (like Effingham, England), and in
which tidal sediments were deposited only on high
intertidal zones might mimic a diurnal tidal deposit
(Archer and Johnson 1997). In such a case, additional
outcrop work might result in the discovery of lower
intertidal or subtidal facies that would resolve the
issue.
Fig. 1.11 Line graph showing the changes in tidal amplitudefor the seven most dominant tidal constituents for several tidal
reference stations located along the eastern side of the Gulf of
Carpentaria (locations noted in Fig. 1.10. Constituent data was
extracted using the Seafarer Tides software package by the
Australian National Tidal Centre, Bureau of Meteorology and
provided to Kvale (2006) (From Kvale (2006) and used by per-
mission from Marine Geology)
-
7/23/2019 Tidal sedimentology
31/637
14 E.P. Kvale
1.5 Summary and Implications
The equilibrium tidal model is very useful for explain-
ing the gravitational forces that generate tides on the
Earth. However, it is an over-simplification and does not
explain the tides in most of the oceans of the world. To
explain real-world tides requires a basic understanding
of the dynamic tidal model. The dynamic tidal model
has been used to estimate changes in the Earth-Moon
distance through time (Williams 1989; Kvale et al.
1999) and has even been suggested as a way to better
understand the impact that tides have on biological
systems (Kvale 2006). It has also been used to model
tidal basin dynamics for determining the importance of
tidal facies within a basin or region (e.g. Ericksen and
Slingerland 1990; Wells et al. 2007). In the Abbott
example, an interpretation of neap-spring cyclicity could
be done with both the equilibrium and dynamic model,
but interpretation of the relative importance of the M2,
Fig. 1.12 Tradewater Formation, (a) Photo of the Abbottsandstone outcrop. This is part of a much more extensive
dune mesoform. Examples of dominant (D) and subordinate
(S) semidiurnal foresets are labeled. Rock hammer for
scale (lower part of photo) (b) Bar chart showing foreset
(depositional event) thickness variability with spring tides (S),
neap tides (N) and lunar crossover (arrows) events labeled.
Notice the semimonthly inequality of the spring tides related
to perigee and apogee effects. Also note that the lunar
passages of the equator (arrows) track the neap tide deposits
fairly closely suggesting that the neap-spring cycles are in
phase with the tropical month
-
7/23/2019 Tidal sedimentology
32/637
151 Tidal Constituents of Modern and Ancient Tidal Rhythmites: Criteria for Recognition and Analyses
S2, O
1, K
1, and N
2constituents using the dynamic model
allows much more specific comparisons to be made to
real-world analogues (in this case Booby Island tides)
than would otherwise be possible. In fact, utilizing this
approach within the Illinois Basin one can interpret the
dominance of diurnal (O1and K
1) tides versus semidiurnal
(M2and S
2) tides for various tidal rhythmite packages
that span the Mississippian-Pennsylvanian systems
(Fig. 1.13). As Fig. 1.13shows, tidal rhythmites older
than the upper Morrowan Blue Creek Coal appear to
have been deposited within synodically driven systems
dominated by M2 and S
2. Younger tidal rhythmites
appear to have been deposited within tropically driven
systems. This change from synodically driven to tropically
driven tidal systems may reflect the closure of the
Iapetus Ocean during the early Pennsylvanian and a
Fig. 1.13 Stratigraphic chart for the Indiana portion of the IllinoisBasin showing stratigraphic intervals where good tidal rhythmite
records have been identified by the author. The solid grey line
marks the boundary below which tidal rhythmites seem to be con-
trolled primarily by the synodic monthly cycle and above which
the tidal rhythmites appear to reflect the tropical monthly cycle
-
7/23/2019 Tidal sedimentology
33/637
16 E.P. Kvale
major change in tidal dynamics within the midcontinent
Carboniferous sea of North America.
While teaching and understanding the dynamic
tidal system represents a bit of a paradigm shift to most
geologists, it creates possible research venues not
accessible through an understanding of equilibrium
tidal theory alone.
References
Allen JRL (1981) Lower Cretaceous tides revealed by cross-
bedding with mud drapes. Nature 289:579581
Archer AW (1995) Modeling of tidal rhythmites based on a
range of diurnal to semidiurnal tidal-station data. Mar Geol
123:110
Archer AW, Johnson TW (1997) Modeling of cyclic tidal
rhythmites (Carboniferous of Indiana and Kansas,
Precambrian of Utah, USA) as a basis for reconstruction ofintertidal positioning and paleotidal regimes. Sedimentology
44:9911010
Archer AW, Kvale EP, Johnson HR (1991) Analysis of modern
equatorial tidal periodicities as a test of information encoded
in ancient tidal rhythmites. In: Smith DG, Reinson GE,
Zaitlin BA, Rahmani RA (eds) Clastic tidal sedimentology.
Canadian Soc Petrol Geol Mem 16:189196
Boersma JR, Terwindt JHJ (1981) Neap-spring tide sequences
of intertidal shoal deposits in a mesotidal estuary.
Sedimentology 28:151170
Cartwright DE (1999) Tides: a scientific history. Cambridge
University Press, Cambridge, UK, 292 pp
Choi K (2010) Rhythmic climbing cross-lamination in inclined het-
erolithic stratification (IHS) of a macrotidal estuarine channel,Gomso Bay, west coast of Korea. J Sediment Res 80:550561
Coughenour CL, Archer AW, Lacovera KJ (2009) Tides,
tidalites, and secular changes in the Earth-Moon system.
Earth Sci Rev 97:5979
Dalrymple RW (1992) Tidal depositional systems. In: Walker
RG, James NP (eds) Facies models response to sea level
changes. Geological Association of Canada, St. Johns,
pp 195218
Dalrymple RW, Makino Y (1989) Description and genesis of
tidal bedding in the Cobequid Bay-Salmon River estuary,
Bay of Fundy, Canada. In: Taira A, Masuda F (eds)
Sedimentary facies in the active plate margin. Terra Science
Publication Co., Tokyo
Defant A (1961) Physical oceanography, vol 11. Pergamon, NewYork, 598 pp
Duxbury AB, Duxbury AC, Sverdrup KA (2002) Fundamentals
of oceanography, 4th edn. McGraw Hill, Boston, 344 pp
Ericksen MC, Slingerland R (1990) Numerical simulations
of tidal and wind-driven circulation in the Cretaceous
Interior Seaway of North America. Geol Soc Am Bull
102:14991516
Hovikoski J, Rsnen M, Gingras M, Roddaz M, Brusset S,
Hermosa W, Romero-Pittman L, Lertola K (2005) Miocene
semidiurnal tidal rhythmites in Madra de Dios, Peru. Geology
33:177180
Klein GD (1998) Clastic tidalites-a partial retrospective view.
In: Alexander C, Davis RA, Henry VJ (eds) Tidalites: pro-
cesses and products, vol 61, Special publication (SEPM
(Society for Sedimentary Geology)). Society of Sedimentary
Geology, Tulsa, pp 514
Kvale EP (2006) The origin of neap-spring tidal cycles. Mar
Geol 235:518
Kvale EP, Archer AW (1990) Tidal deposits associated withlow-sulfur coals, Brazil formation (lower Pennsylvanian),
Indiana. J Sediment Petrol 60:563574
Kvale EP, Archer AW (1991) Characteristics of two
Pennsylvanian-age semidiurnal tidal deposits in the Illinois
Basin, U.S.A. In: Smith DG Reinson GE Zaitlin BA Rahmani
RA (eds), Clastic tidal sedimentology. Canada Soc Petrol
Geol Mem 16:179188
Kvale EP, Mastalerz M (1998) Evidence of ancient freshwater
tidal deposits. In: Alexander C, Davis RA, Henry VJ (eds)
Tidalites: processes and products, vol 61, Special publication
(SEPM (Society for Sedimentary Geology)). Society of
Sedimentary Geology, Tulsa, pp 95107
Kvale EP, Archer AW, Johnson HR (1989) Daily, monthly, and
yearly tidal cycles within laminated siltstones of the Mansfieldformation (Pennsylvanian) of Indiana. Geology 17:365368
Kvale EP, Fraser GS, Archer AW, Zawistoski A, Kemp N, McGough
P (1994) Evidence of seasonal precipitation in Pennsylvanian
sediments in the Illinois Basin. Geology 22:331334
Kvale EP, Sowder KH, Hill BT (1998) Modern and ancient tides.
Poster and explanatory notes, SEPM, Tulsa, OK, and Indiana
Geological Survey, Bloomington, IN
Kvale EP, Johnson HW, Sonett CP, Archer AW, Zawistoski A
(1999) Calculating lunar retreat rates using tidal rhythmites.
J Sediment Res 69:11541168
MacMillan DH (1966) Tides. American Elsevier Publishing
Company, New York, 240 pp
Miller DJ, Eriksson KA (1997) Late Mississippian prodeltaic
rhythmites in the Appalachian Basin: a hierarchical record oftidal and climatic periodicities. J Sediment Res 67:653660
National Oceanographic and Atmospheric Administration
(2004) http://www.co-ops.nos.noaa.gov/tides04/ 2004 date
accessed, Sept
NOAA (1990) Tide tables 1991, high and low water predictions,
Central and Western Pacific Ocean and Indian Ocean, U.S.
Department of Commerce, National Oceanic and
Atmospheric Administration, Riverdale, Maryland
NOAA (1991) Tide tables, 1992 high and low water predictions,
Central and Western Pacific Ocean and Indian Ocean, U.S.
Department of Commerce, National Oceanic and
Atmospheric Administration, Riverdale, Maryland
NOAA (1993) Tide tables, 1994 high and low water predictions,Central and Western Pacific Ocean and Indian Ocean, U.S.
Department of Commerce, National Oceanic and
Atmospheric Administration, Riverdale, Maryland
Open University Course Team (1999) Waves, tides and shallow-
water processes, 2nd edn. Open University, Butterworth
Heinemann, Oxford, 227 p
Pugh DT (1987) Tides, surges and mean sea level. Wiley, New
York, 472 p
Rosenberg GD (1997) How long was the day of the dinosaur?
And why does it matter? In: Wolberg DL, Stump E,
Rosenberg GD (eds) Dinofest international: proceeding
-
7/23/2019 Tidal sedimentology
34/637
171 Tidal Constituents of Modern and Ancient Tidal Rhythmites: Criteria for Recognition and Analyses
symposium sponsored by Arizona State University, The
Academy of Sciences, Philadelphia, pp 493512
Visser MJ (1980) Neap-spring cycles reflected in Holocene sub-
tidal large-scale bedform deposits; a preliminary note.
Geology 8:543546
Wells MR, Allison PA, Piggott MD, Gorman GJ, Hampson GJ,
Pain CC, Fang F (2007) Numerical modeling of tides in the
late Pennsylvanian midcontinent seaway of North America
with implications for hydrography and sedimentation.
J Sediment Res 77:843865
Williams GE (1989) Late Precambrian tidal rhythmites in South
Australia and the history of the Earths rotation. J Geol Soc
Lond 146:97111
Williams GE (2000) Geological constraints on the Precambrian
history of Earths rotation and the Moons orbit. Rev Geophys
38:3759
-
7/23/2019 Tidal sedimentology
35/637
-
7/23/2019 Tidal sedimentology
36/637
19R.A. Davis, Jr. and R.W. Dalrymple (eds.), Principles of Tidal Sedimentology,
DOI 10.1007/978-94-007-0123-6_2, Springer Science+Business Media B.V. 2012
2Principles of Sediment TransportApplicable in Tidal EnvironmentsPing Wang
Notations and Conventional Units
a: a reference level (typically defined at the top level
of the bedload layer) for suspended sediment con-
centration. (m)
c: suspended sediment concentration (dimension-
less for volume concentration, kg/m3for mass
concentration)
ca: reference concentration (dimensionless for vol-
ume concentration, kg/m3for mass concentration)
c(z): suspended sediment concentration profile
(dimensionless for volume concentration, kg/
m3for mass concentration)P. Wang (*)
Coastal Research Laboratory, Department of Geology,
University of South Florida, Tampa, FL 33620, USA
e-mail: [email protected]
Abstract
Physical processes of sediment transport in tidal environments are extremely
complicated and are influenced by numerous hydrodynamic and sedimentological
factors over a wide range of temporal and spatial scales. Both tide and wave forcingplay significant roles in the entrainment and transport of both cohesive and
non-cohesive particles. Present understanding of sediment transport is largely
empirical and based heavily on field and laboratory measurements. Sediment
transport is composed of three phases: (1) initiation of motion (erosion), (2) trans-
port, and (3) deposition. In tidal environments, the coarser non-cohesive sediments
are typically transported as bedload, forming various types of bedforms. The finer
cohesive sediments tend to be transported as suspended load, with their deposition
occurring mostly during slack tides under calm conditions. Rate of sediment
transport is generally proportional to flow velocity to the 3rd to 5th power. This
non-linear relationship leads to a net transport in the direction of the faster velocity
in tidal environments with a time-velocity asymmetry. Due to the slow settling
velocity of fine cohesive sediment and a difference between the critical shear stress
for erosion and deposition, scour and settling lags exist in many tidal environ-
ments resulting in a landward-fining trend of sediment grain size. The periodic
reversing of tidal flow directions results in characteristic bi-directional sedimen-
tary structures. The relatively tranquil slack tides allow the deposition of muddy
layers in between the sandy layers deposited during flood and ebb tides, forming
the commonly observed lenticular, wavy, and flaser bedding.
-
7/23/2019 Tidal sedimentology
37/637
20 P. Wang
c : depth averaged concentration (dimensionless
for volume concentration, kg/m3 for mass
concentration)
D: sediment grain size (m)
D*: dimensionless sediment grain size (dimension-
less)
Dw: wave-energy dissipation due to breaking(kg/s3)
dm: mean sediment grain size (m)
d50
: 50th percentile sediment grain size (m)
E: wave energy per unit water volume (kg/s2)
fc: bottom friction coefficient (dimensionless)
H: wave height (m)
h: water depth (m)
kd: empirical coefficients used in suspended sediment
concentration profile modeling (dimensionless)
kx: dispersion coefficient in x direction (dimen-
sionless)ky: dispersion coefficient in y direction (dimen-
sionless)
L: wave length (m)
Ls: turbulent mixing length (m)
Qb: volumetric bed-load transport rate (m3/m/s)
qs: volume rate of suspended sediment transport
(m3/m/s)
S = source and sink terms
s: sediment specific density =s/
w (dimension-
less)
T: wave period (s)
U: near bottom wave orbital velocity (m/s)
u(z): current velocity with respect to depthz(m/s)
u : depth-averaged current velocity (m/s)
u*: current related bed-shear velocity (m/s)
u*_c
: critical bed shear velocity (m/s)
u*_crs
: critical shear velocity for sediment suspension
(m/s)
cru : depth-averaged critical velocity (m/s)
v : depth average velocity inydirection (m/s)
ws: settling velocity (m/s)
ws_s
: settling velocity of single suspended particle
in clear water used in the calculation of the
settling velocity of flocs (m/s)
z: vertical coordinate representing water depth (m)
zo: vertical level with zero velocity, also often
referred to as bed roughness (m)
1: empirical coefficients used in suspended sedi-
ment concentration profile modeling (dimen-
sionless)
a2: empirical coefficients used in suspended sedi-
ment concentration profile modeling (dimen-
sionless)
b: empirical coefficients used in suspended sedi-
ment concentration profile modeling (dimen-
sionless)
s: sediment mixing coefficientq: Shields parameter (dimensionless)
qc: critical Shields parameter (dimensionless)
qcrs
: critical Shields parameter for sediment
suspension (dimensionless)
: Von Karmans constant, typically taken as 0.4
(dimensionless)
: an efficiency factor to incorporate the influ-
ence of bedforms on bedload transport used in
the Meyer-Peter and Mueller (1948) bedload
transport formula (dimensionless)
n: kinematic viscosity (m2/s)
s: sediment density (kg/m3)
rw: density of water (seawater in the case of tidal
environment) (kg/m3)
tb: bed shear stress (N/m2)
tc: critical bed shear stress (N/m2)
flocf : flocculation factor (dimensionless)
hs
f : hindered settling factor (dimensionless)
2.1 Introduction
Coastal sedimentology and morphodynamics are con-
trolled by a variety of interactive factors, including forces
from ocean tides and waves, trends and rates of sea-
level changes, sediment supply, climatic and oceano-
graphic settings, and antecedent geology. Depending
on the relative dominance of wave and tide forcing,
coastal environments can be classified as tide-dominated
and wave-dominated (Davis and Hayes 1984). This
chapter focuses on general physical processes of sedi-
ment transport that are applicable to the tide-dominated
environments. In this chapter, tidal environments are
defined generally as shallow marine environments that
are significantly influenced by tides.
The rise and fall of tides provide the main mecha-
nism for sediment transport and morphology changes
in tidal environments. In addition to generating tidal
current which constitutes the dominant forcing in tidal
environments, this regulated water-level fluctuation
can also modulate wave action. For example, higher
-
7/23/2019 Tidal sedimentology
38/637
212 Principles of Sediment Transport Applicable in Tidal Environments
waves were often measured at a fixed location on a
tidal flat during higher tides due to less friction related
wave dissipation (Lee et al. 2004; Talke and Stacey
2008). Sediment transport by wave forcing can be
significant locally, as well as during storm conditions.
Bottom shear stress, and therefore initiation of sedi-
ment motion and transport, is also strongly influencedby water depth, which varies substantially in tidal
environments. When the tidal water-level fluctuations
are confined by channels, e.g., tidal inlets and creeks,
strong tidal-driven flows can be generated. As com-
pared to other types of channelized flow, tidal flow
reverses direction periodically with a slack water period
in between, which may create unique bi-directional
sedimentary structures. In the case of tidal inlets
between barrier islands, large flood and ebb tidal deltas
can be deposited through the interaction of tide and
wave forcing. The cyclical rising, slacking, and fallingtide and the associated flow variation leave signature
sedimentary records through geological history, pro-
viding valuable information for understanding earth
history (e.g. Kvale et al. 1989).
Sediment grain size in tidal environment typically
ranges from non-cohesive medium sand to cohesive
clay. Compositionally, tidal sediments can be silici-
clastic, carbonate, and organic materials. A variety of
sedimentary structures, ranging from millimeter-scale
sand-mud laminations on tidal flats to subaqueous
dunes of tens of meters in tidal channels, exists in
tidal environments, indicating a wide range of sedi-
ment transport and deposition processes. Transport
and deposition of mixed cohesive and non-cohesive
sediments are poorly understood and provide cutting
edge research topics (Van Rijn 2007a, b, c)
Given the wide range of both cohesive and non-
cohesive sediments, and the energetic and highly vari-
able hydrodynamic processes driven by both tides and
waves, sediment transport processes in tidal environ-
ments are extremely complicated. This chapter aims
at providing a basic review of the principals of sedi-
ment transport applicable in tidal environments.
Various transport formulas and their general applica-
tions in tidal environments are discussed. It is worth
emphasizing that methods of computing the rates of
sediment transport are largely empirical, based
heavily on field and laboratory experiments.
Calibration and verification based on site-specific
data are essential to accurate applications of the formulas.
The transport principles and formulae can also be
applied qualitatively to interpret the sedimentary
processes observed in the field, and to design field
experiments. More detailed and further in-depth
mechanics of sediment transport can be found in
several dedicated texts, e.g., Mehta (1986b), Fredsoe
and Deigaard (1992), Nielsen (1992),Van Rijn (1993),
Pye (1994), Allen (1997), and Soulsby (1997).
2.2 Principles of Sediment Transport
Transport of sediment in coastal environments results
from the interaction between moving fluid (seawater in
this case) and sediment. Present knowledge on sedi-
ment transport processes is largely empirical, based on
numerous field and laboratory experiments. Insightful
parameterization is crucial in describing the compli-cated fluid-sediment interaction. In the following
section, key parameters describing fluid motion, sedi-
ment, and fluid-sediment interaction are discussed,
followed by the presentation of the commonly-used
methods for the calculation of non-cohesive and
cohesive sediment transport, respectively.
2.2.1 Fundamental Parameters
Fluid motion over a sediment bed exerts a horizontal
drag force and a vertical lift force. Generally, when
these forces overcome the gravity of a sediment grain,
transport is initiated. A theoretical analysis of the ini-
tiation of motion of an individual grain typically starts
with a force balancing between the drag-lift forces and
the gravitational force on the grain. The sediment grain
is put in motion if the moments of the fluid drag (FD
) and
lift (FL) forces exceed the moments of the submerged
gravitational force (FG) on the grain (Fig. 2.1). However,
due to our limited understanding of the very compli-
cated fluid-sediment interaction, sediment transport in
the natural environments cannot be quantified from the
force analysis of each grain. Instead, it is quantified
empirically through insightful parameterization of sediment-
fluid interaction, as discussed in the following.
When viscous fluid, e.g., seawater, flows over a sur-
face, a shear stress is generated by the fluid flow. This
shear stress is responsible for entraining and transport-
ing sediment. On the other hand, the friction at the
fluid-sediment interface exerts a drag on the fluid flow,
-
7/23/2019 Tidal sedimentology
39/637
22 P. Wang
yielding the commonly observed logarithmic velocityprofile over depth, i.e., the law of the wall:
*( ) ln
o
u zu z
zk
(2.1)
Where u(z) = current velocity with respect to depth,
z= vertical coordinate representing water depth,
u*= current related bed-shear velocity, = Von Karmans
constant, typically taken as 0.4, and zo= vertical level
with zero velocity, also often referred to as bed rough-
ness. A list of notation and conventional units are pro-
vided at the beginning of this chapter. Figure 2.2
illustrates an example of a logarithmic profile. The
dynamics of the bottom boundary layer where the cur-
rent velocity decreases rapidly with respect of depth is
crucial to sediment entrainment and transport. For plane
bed, the bed roughness (Fig. 2.2) is a function of sedi-
ment grain size. When bedforms exist, the bed roughness
is related to the geometry of the bedform. The bed shear
velocity is directly related to bed shear stress (tb) as:
2
*b wut r (2.2)
where rw= density of water (seawater in the case of tidal
environments). The bed shear velocity and bed shear
stress are two of the key parameters describing the fluid-
sediment interaction and are commonly used in comput-
ing sediment transport. Determining bed shear velocity
and bed shear stress can be difficult and often comprises
an essential part of a sediment transport study. By mea-
suring a velocity profile through the water column,
Eq. 2.1can be used to determine bed shear velocity and
bed shear stress, as well as the bottom roughness.
Another commonly used approach to determine the bot-
tom shear stress, especially for depth-averaged models,
is to relate bottom stress to velocity squared as:
21
2b w c
f ut r (2.3)
Fig. 2.1 Schematic forcebalancing of individual
grains on a horizontal bed
Fig. 2.2 An example of a logarithmic current profile, showing thebed roughness (z
o) and the schematic bottom boundary layer
-
7/23/2019 Tidal sedimentology
40/637
232 Principles of Sediment Transport Applicable in Tidal Environments
where fc is a bottom friction coefficient, determined
experimentally, and u = depth-averaged current velocity.
Equation 2.3describes the so-called quadratic friction
law, i.e., the friction exerted by a fluid flow is pro-
portional to its velocity squared. Equations 2.12.3
suggest that the faster the flow velocity and the rougher
the bed, the greater the shear stress, and therefore thegreater potential of sediment transport.
Although wave forcing is not the dominant factor in
determining the overall morphology and sedimentation
pattern in tidal environments, it is important in local
sediment entrainment and transport. For example,
numerous studies have shown that wave forcing can
have significant influence on the sedimentology and
morphodynamics of tidal flats (Christie et al. 1999;
Dyer 1998; Dyer et al. 2000; Li et al. 2000; Talke and
Stacey 2003, 2008; Lee et al. 2004). Wave motion can
be visualized as a circular motion of an imaginarywater particle. This wave orbital velocity, especially
near the bottom, can induce considerable shear stress
to entrain and transport sediment. Based on linear
wave theory, the maximum value of near bottom orbital
velocity (U) is:
2sinh
HU
hT
L
d
p
p
(2.4)
where h= water depth, L= wave length, T= wave
period, andH= wave height.
In a more simplified larger scale approach, wave-
induced sediment transport is often evaluated based on
the amount of energy that is carried by the wave.
Higher wave energy typically results in more active
sediment transport. Wave energy per unit water
volume (E) is determined as:
21
8 w
E gHr (2.5)
Equation 2.5shows that wave energy is proportional to
wave height squared, e.g., a 2 m wave will carry four
times the energy than a 1 m wave.
Waves break as they propagate from deep water
into shallow water. The energy that is carried by the
wave motion is dissipated rapidly through wave break-
ing. A large portion of this energy is expended to
transport sediment. Due to the intense turbulence gen-
erated by wave breaking, sediment transport associated
with wave breaking tends to be much greater than that
under non-breaking waves and a typical current.
Various empirical formulas were developed to evaluate
when waves break (Kaminsky and Kraus 1994),
one of the simplest and also reasonably accurate
formulas is:
0.78
b bH h (2.6)
where Hb= breaking wave height, h
b= water depth at
which waves break. In other words, waves break when
their height is about 80% of the water depth. Wells and
Kemp (1986) found that muddy bottoms, typical of
some tidal environments, can dissipate wave energy
to such an extent that the above breaking criterion is
never reached. Although wave forcing is secondary in
tidal environments, it can contribute significantly to
local sediment transport, especially in the ne