Controlling of internal processes on estuarine sediment dispersal: internal hydraulic jump

and enhanced turbulence mixing

Jesse Wu（吳加學） , Huan Liu & Chaoyu Wu

Center of Coastal Ocean Science and Technology, Sun Yat-sen University,

Guangzhou 510275, China.E-mail: jesse-wu@tongji.edu.cn

2009 International Sediment Transport Symposium, Kaohsiung, Taiwan, 23th-27th March, 2009

Background

Estuarine sediment dispersal are closely associated with • Estuary and delta evolution • Shelf deposition • Environmental and ecological issues (e.g. HAB)

But the processes and mechanism of river-borne sediment transport are not yet completely unclear (see Ocean Science at the New Millennium, NSF).

Two case studies in tropical estuaries:1. The Herbert Estuary, AU: a small mountainous river, an internal jump;2. The Pearl Estuary, CHN: a larger river, the BBL dynamics.

Part 2: The BBL flows in the Pearl Estuary

Motivation and Questions

BBL flows and sediment transport are important processes in estuarine dynamics;

BBL structures and parameters (e.g. bottom stress, frictional velocity) are usually inferred from mean flow profiles under some hypotheses;

But these hypotheses can not be well achieved in the estuarine BBL.Accordingly, we need (a) to rigorously verify/validate these hypotheses by turbulence

investigation, (b) to quantitatively determine the difference between the theoretical

and actual state, and (c) to identify the possible mechanism for this difference.

Three aspects of the BBL flows will be examined to understand the mechanism of turbulence responses to the large-scale estuarine forcings:

a. the flow structures (profile, anisotropy, and spectra), b. shearing strains and stresses, and c. the balance of turbulent kinetic energy (TKE)

(Liu et al., submitted to ECSS)

Four tripod mooring sites: YM01:estuarine, tide + current + wave; YM02: rock-bound gorge, the tripod overturned; YM03: straight tide-affected river; YM04: sinuous tide-affected river.

Survey time: 17-22 July 2007 25 hr each site

The Huangmaohai Estuary,the Pearl Estuary Complex

Schematic figure of a bottom-mounted tripod used.

• ADV: 64 Hz;• PC-ADP: 1Hz, a bin size 1.6 cm;• XR-420 CTD: 1 Hz; • XR-620 OBS: 6 Hz

Two regimes in the BBL flow:

• Log regime (self-similar, inertial);

• Non-log regime (non-similar, accel/deceleration)

0

*

z

zIn

uU z

Log-law velocity profiles

Breakdown of the Log Law at slack tides at Site YM01

•non-log velocity profiles (Fig. 4e, f),

•two-layer exchange flow (Fig. 4g)

•Mid-depth halocline (Fig. 4b, c),

•Benthic halocline (Fig. 4d)

Log profile: constant stress layer

rmsrmsrms wvu '''

rmsrmsrms wvu '''

0R

2

002*00

z

Uzu

''0R wu

Isotropic turbulence:

222 '','','' wwvvuu rmsrmsrms

Equivalent conditions for the isotropic log BBL flow

zuzU *Mean shear Turbulence shear

zwvu rmsrmsrms ''' ,,*u

Turbulenceanisotropy

0 0 .1 0 .2 0 .3 0 .4 0 .5

0 .0

0 .4

0 .8

1 .2

0 0 .2 0 .4 0 .6 0 .8 1

0 .0

0 .4

0 .8

1 .2

1 .6

0 0 .1 0 .2 0 .3 0 .4 0 .5

M ean S h ear (d U /d z)

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

Tur

bule

nt S

hear

(u' /z

)

( a ) Y M 0 1 , u '

(d ) Y M 0 3 , u '

(g ) Y M 0 4 , u '

0 0 .1 0 .2 0 .3 0 .4 0 .5

0 .0

0 .4

0 .8

1 .2

0 0 .2 0 .4 0 .6 0 .8 1

0 .0

0 .4

0 .8

1 .2

1 .6

0 0 .1 0 .2 0 .3 0 .4 0 .5

M ean S h ear (d U /d z)

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0T

urbu

lent

She

ar (

v' /z)

(b ) Y M 0 1 , v '

(e ) Y M 0 3 , v '

(h ) Y M 0 4 , v '

0 0 .1 0 .2 0 .3 0 .4 0 .5

0 .0

0 .4

0 .8

1 .2

0 0 .2 0 .4 0 .6 0 .8 1

0 .0

0 .4

0 .8

1 .2

1 .6

0 0 .1 0 .2 0 .3 0 .4 0 .5

M ean S h ear (d U /d z)

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

Tur

bule

nt S

hear

(w

' /z)

( c ) Y M 0 1 , w '

(f) Y M 0 3 , w '

( i) Y M 0 4 , w '

2 .63 .5

1 .0

1 .9

3 .5

1 .0

3 .5

1 .0

1 .5

1 .0

1 .5

1 .0

1 .5

1 .0

1 .8

2 .5

1 .0

1 .7

2 .5

1 .0

2 .5

1 .0

*' uw rms

rmsrms wu '6.2'

rmsrms wv '9.1'

rmsrmsrms wvu '5.1''

rmsrmsrms wvu '8.1''

at three sites;

(a-c) Site YM01:

(d-f) Site YM03:

(g-i) Site YM04:

Straining cascade from mean shear to vertical turbulence shear!

Breakdown of the hypothesis of constant stress

0 .0 0 1 0 .0 1 0 .1 1 1 0

0 .0 0 1

0 .0 1

0 .1

1

1 0

0 .0 0 1 0 .0 1 0 .1 1 1 0

0 .0 0 1

0 .0 1

0 .1

1

1 0

0 .0 0 1 0 .0 1 0 .1 1 1 0

L o g -law b o tto m stre ss (N /m 2)

0 .0 0 1

0 .0 1

0 .1

1

1 0A

DV

-bas

ed R

eyno

lds

stre

ss (

N/m

2)

( a ) Y M 0 1

(b ) Y M 0 3

(c) Y M 0 4

1 .0

0 .1

1 .0

1 .0

1 .0

0 .3 4

0 .1

0 .1

0 .3 1

0 .2 4

Y = 0 .3 1 X(R 2 = 0 .9 1 , N = 8 6 )

Y = 0 .2 4 X(R 2 = 0 .8 0 , N = 6 9 )

Y = 0 .3 4 X(R 2 = 0 .5 2 , N = 8 1 )

''0R wu

2

000

z

Uz

34.00 R

31.00 R

24.00 R

3/53/2)( kkE iii

The Kolmogorov’s first universality assumption (for isotropic turbulence)

TKE Spectra of the vertical fluctuationin the log regime

Bandwidth of the inertial subrange

0 .1 1 .0 1 0 .0 1 0 0 .0

1 E -0 0 7

1 E -0 0 5

1 E -0 0 3

1 E -0 0 1

0 .1 1 .0 1 0 .0 1 0 0 .0

1 E -0 0 8

1 E -0 0 6

1 E -0 0 4

1 E -0 0 2

0 .1 1 .0 1 0 .0 1 0 0 .0

F req u en cy (H z)

1 E -0 0 6

1 E -0 0 4

1 E -0 0 2

Ene

rgy

spec

trum

(m

2 /s)

( a ) Y M 0 1

(b ) Y M 0 3

(c) Y M 0 4

2 1 :4 5 , 1 7 Ju l 2 0 0 7 , R e= 1 3 0 0

0 2 :0 0 , 1 8 Ju l 2 0 0 7 , R e= 1 4 0 0

1 0 :4 5 , 2 0 Ju l 2 0 0 7 , R e= 6 9 0

0 4 :3 0 , 2 1 Ju l 2 0 0 7 , R e= 2 2 0

0 1 :0 0 , 2 2 Ju l 2 0 0 7 , R e= 4 7 0

0 6 :0 0 , 2 2 Ju l 2 0 0 7 , R e= 1

-3 /5

-3 /5

-3 /5

Breakdown of the -3/5 Power Lawat slack tides (non-log regime)

A first-order balance between TKE production and dissipation for log profiles (isotropic turbulence)

DP 1 E -0 0 7 1 E -0 0 5 1 E -0 0 3

1 E -0 0 7

1 E -0 0 5

1 E -0 0 3

1 E -0 0 7 1 E -0 0 5 1 E -0 0 3

1 E -0 0 7

1 E -0 0 5

1 E -0 0 3

1 E -0 0 7 1 E -0 0 5 1 E -0 0 3

P ro d u ctio n (W /k g )

1 E -0 0 7

1 E -0 0 5

1 E -0 0 3D

issi

patio

n (

W/k

g)

( a ) Y M 0 1

(b ) Y M 0 3

(c) Y M 0 4

1 0

1 .0

0 .1

1 0

1 .0

1 0

1 .0

0 .1

1 .0 2

1 .4 7

0 .3 4

D = 0 .3 4 P(R 2 = 0 .7 9 , N = 6 9 )

D = 1 .0 2 P(R 2 = 0 .7 5 , N = 8 6 )

D = 1 .4 7 P(R 2 = 0 .7 4 , N = 8 1 )

zUwu ''P 0

0D

47.1D P

02.1D P

34.0D P

)(2 2/32/52/3 fSfU iii

where

''B wg

BDP

BUT the effect of sediment stratification may be very important in BBL!

where

ConclusionsThe unsteadiness of the tidal current determines the BBL flo

w structures, and the degree of turbulence anisotropy results in the invalidation of the similarity or phenomenological relations, e.g. the constant stress hypothesis and the first-order TKE balance.

The logarithmic law, constant stress hypothesis, isotropy and an inertial subrange all seem to be the states or conditions of being equivalent in the BBL flow.

The non-log regime near the slack tide exhibits a stronger acceleration effect and more complicated flow regimes. How the external forcing influences the BBL flow at the transient slack needs to be further explored. Meanwhile, the turbulence anisotropy induced by large-scale estuarine forcing is for certain a key problem to further investigate into.

Part 1: The internal hydraulic jump in a small mountainous estuary

General patterns of riverine outflows

cagg

'

cb

csS

c

UFr

0' g

Positively

Buoyant

10 S

River plume

1Fr

Subcritical

0S

Bottom

intrusion 0' g

Negatively

Buoyant

1S

Neutral

intrusion

1Fr

Supercritical

Internal Jump

1 4 6 .3 1 4 6 .4 1 4 6 .5

L O N G (d eg )

-1 8 .6

-1 8 .5

-1 8 .4

LA

T (

deg)

1 2 3 4 5

67891 0

C 3

J2 J7

C T D , N ep h e lo m ete r

A D C P , C T D ,N ep h e lo m ete r

P ie r

(b)

Wu et al. (2006), JGR

Part 1: Internal hydraulic jump in the Herbert Estuary

1 4 6 .1 1 4 6 .2 1 4 6 .3 1 4 6 .4 1 4 6 .5 1 4 6 .6 1 4 6 .7

L O N G (d eg )

-1 8 .8

-1 8 .7

-1 8 .6

-1 8 .5

-1 8 .4

-1 8 .3

-1 8 .2

LA

T (

deg)

H in ch inb rook Is land

H erb e rt R iv e rH alifax

In g h am

A u stra lia

S tu d y A rea

W in d S ta tio n

T id e G au g in g S ta tio n

H inch inb rook C hanne l

(a)

A highly-stratified river plume

A sandwiched pattern of sediment dispersal offshore

0

1

2

3

4

0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

-1 0 0

0

1 0 0

2 0 0

3 0 0

-2 0

-1 0

0

1 0

2 0

3 0

0

1

2

3

4

5

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 40

z = 1 2 .4 6 m ab

z = 1 2 .5 7 m ab

z = 1 2 .5 7 m ab

z = 1 2 .5 7 m abF ro n t

0

1

2

3

4

Tid

al le

vel (

m)

0

2 0 0

4 0 0

6 0 0

8 0 0

Spee

d (m

m/s

)

-4 0 0

0

4 0 0

8 0 0

U (

mm

/s)

-8 0

-4 0

0

4 0W

(m

m/s

)

0

2 0

4 0

6 0

8 0

1 0 0

Tur

bidi

ty (

NT

U) z = 7 .6 9 m ab

z = 7 .8 2 m ab

F ro n t

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 40

8:21

9:01

9:41

10:2

1

11:0

1

11:4

1

12:2

1

13:0

1

13:4

1

14:2

1

15:0

1

(a ) S ite J2 (b ) S ite J7

z = 7 .8 2 m ab

z = 7 .8 2 m ab

H o u rs o n 1 8 F eb ru ary 2 0 0 4

0

0 .4

0 .8

1 .2

1 .6

2

8:21

9:01

9:41

10:2

1

11:0

1

11:4

1

12:2

1

13:0

1

13:4

1

14:2

1

15:0

1

15:4

1

7:41

H o u rs o n 1 9 F eb ru ary 2 0 0 4

0

2

4

6

8

Fr

Site J2supercritical in the near field

Site J7subcritical in the far field

Internal Hydraulic Jump

2 22

2 20

d W Nk W

dz c

expz i t kx

W ik

2 22

2 20

d Nk

dz c

sin expn

w A z i t kxh

1,2,3n

2

sin

2 cos sin

u u z t kx

A l lz t kx

22

2

2cos

Au zFr

c Nh h

1n 1kh

expw W z i t kx

The specific mechanical energy of each layer in

terms of the Bernoulli equations

21 1 1 1 2E gH u

22 1 2 2 2 2E gH g h b u

Normal interface geometry in the two-layer

stratified flow

11222 2

1 11 0 0' '

0

sec2 2

q qh t k x

g g A

2 1G

A critical interface in the two-layer stratified flow

If , i.e. at the lift-off point, then ,

2 1G

122

1 22 1c

b

q sh

r

2 0ch b

0b is always required

b bbl form 1 H

form x bgs dzdx

x

H o u rs o n 1 8 F eb ru ary 2 0 0 4

0

2

4

6

8

1 0

h 2c (

m)

0

2

4

6

8

1 0

h int (

m)

1 6 .3 h 2 c

h in t

8 :2 1 9 :4 1 1 1 :0 1 1 2 :2 1 1 3 :4 1 1 5 :0 1

Mechanical energy loss within the internal

hydraulic jump

21

11 1

2E B Fr

11 1 1

2E B r

1

1

c

n

h

h

'1 1 1n cE B g h h

31 10r O 1 2r where

Sediment Mass Balance Equation

1

bCC CU

t x h

1

bCCU

x h

0 01

exp bC C x DUh

1

b

Uh

( may be defined as a dispersal coeff)

C( indicates SSC, the outflow velocity, the river plume thickness, bulk settling velocity )

U1h

b

Bulk Effective Settling Velocity

4

1

3.59 10b

Uh

0.07 0.14b mm/s

0.1 mm/s in the Eel River flood plume estimated by Hill et al. [2000]

2 18 1.4 /s g d mm s Stokes terminal settling velocity

0 .0 0 1

0 .0 1

0 .1

TSS

(kg

/m3 )

1

23

4 5

1 0

9

87 6

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0

O ffsh o re D is tan ce (m )

-2

-1

0

1

2

Rel

ativ

e E

rror

1

2 3 4

51 0

98 7

6

R 2 = 0 .7 8

(a )

(b )

b

Conclusions

An internal hydraulic jump in a supercritical outflow was investigated both experimentally and theoretically in a mountainous estuary.

A sandwiched dispersal system occurred at the jump section. The two nepheloid flows (upper and lower) have different dispersal behaviors and mechanisms. The upper flow primarily controlled by advection and settling, satisfies an exponential decay law of the SSC versus the offshore distance.

Thanks for your attention!

Mean flow measurements have demonstrated non-log velocity profiles induced primarily by acceleration (or deceleration) at slack tides and salinity stratification. The hypothesis of constant stress can not be strictly satisfied under larger bottom stresses.

In a word, the combined effects of internal hydraulic jump, salinity intrusion, and tidal straining have significant influences on sediment dispersal through the change of the flow structures and turbulent mixing near the head of salt intrusion.

the BBL flow is controlled primarily by the acceleration of unsteady currents, and turbulence anisotropy is an essential response of various turbulence properties or relations to large-scale ambient processes.

A bottom-mounted instrumental tripod was deployed in the tidally energetic Zhujiang (Pearl River) Estuary to examine the contrasting properties of the bottom boundary layer (BBL) flows between estuarine and tide-affected river systems. Three aspects of the BBL flows were discussed to understand the mechanism of the turbulence responses to the large-scale ambient forcing: the flow structures (profile, anisotropy, and spectra), shearing strains and stresses, and the balance of turbulent kinetic energy (TKE). Single log-law profiles and turbulence anisotropy predominated in the two systems, but the non-log regime and stronger anisotropy occurred more frequently at the slack tide in the estuary. The ADV-based turbulence intensities and shearing strains both exceeded their low-frequency counterparts (frictional velocity and mean shear) derived from the logarithmic law. On the contrary, the ADV-based Reynolds stress was smaller than the bottom stress, so the hypothesis of a constant stress layer can not be well satisfied, especially in the river. The balance between shear production and viscous dissipation was better achieved in the straight river. This first-order balances were significantly broken in the estuary and in the meandering river, by non-shear production/dissipation due to wave-induced fluctuations or sediment-induced stratification. All these disparities between two systems in turbulence properties are essentially controlled by the anisotropy induced by the large-scale processes such as secondary currents, stratification. In conclusion, the intensity of acceleration of unsteady flows determines the profile structure of the BBL flow, and the degree of turbulence anisotropy results in the invalidation of the phenomenological relations such as the constant stress hypothesis and the balance of TKE production and dissipation.