Modeling the Effect of

Stratification on Sediment

DepositionKeisuke NakayamaKeisuke Nakayama

National Institute for Land National Institute for Land and Infrastructure and Infrastructure

ManagementManagementVisiting Associate Professor, Tokyo Institute of Technology

Currently visiting Centre for Water Research on Gledden Senior Fellowship

Background of the studyBackground of the studyTokyo Bay

Background of the studyBackground of the study

1973 1989 1994

COD>5 5>COD>4

20km

60km

Red tide in Tokyo BayRed tide in Tokyo Bayda

ys

Num

ber

of o

ccur

renc

e

1979 1990 1999

Red tide and POM in Red tide and POM in summersummer Nutrient Flux from rivers

Nutrient Flux

Red tide

(Nakayama and Imberger, JPO, submitted, 2005)(Wallace and Wilkinson, JFM, 1988)(Gloor et al., Hydrobiologia, 1994)(Steinman et al., WASP, 1997)(Sutherland, JPO, 1996)

Internal wave effectsInternal wave effectsHorizontal circulation due to wind

(Nakayama, HP, submitted, 2005)

139.7 139.8 139.9 140

35.2

35.25

35.3

35.35

35.4

35.45

35.5

35.55

35.6

35.65

20m/s

図－5　 2001年8月10日の風の分布●（ は風の観測地点）

1

139.7 139.8 139.9 140

35.2

35.25

35.3

35.35

35.4

35.45

35.5

35.55

35.6

35.65

-50

-40

-30

-20

-10

0

10

20

30

40

x10-4[1/s]

0 5 10 15 20 25 30-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

x10-4[1/s]

August 2001 [day]

WindVorticity of wind

Time series of vorticity of wind in August 2001

Internal wave effectsInternal wave effects

Vertical circulation due to stratificationTurner J.S., Buoyancy effects in fluids, 1973Imberger, J. and Ivey G.N., Boundary mixing in stratified reservoirs, JFM, 248, 477-491, 1993

Benthic boundary layer (BBL)

POM in Tokyo BayPOM in Tokyo Bay

MEL3DMEL3D Finite difference methodFinite difference method Immersed boundaryImmersed boundary CIP methodCIP method Non-hydrostatic modelNon-hydrostatic model First order LES for horizontal planeFirst order LES for horizontal plane Second order closure for vertical coordinateSecond order closure for vertical coordinate ALE methodALE method Residual cutting method for solving the Residual cutting method for solving the

Poisson’s equationPoisson’s equation

(Nakayama, Okada and Nomura, ECSS, 2005)(Nakayama, IJNMF, 2005)(Arthur, Imberger and Nakayama, JGR, in preparation, 2005)

Target and Initial Target and Initial conditioncondition

Target: Clarification of the mechanisms of vertical circulation due to stratification

case 1: stratified fieldcase 2: no stratification

Modified Tokyo Bay: 60km x 6km x 100m (60 x 6 x 40)Modified Tokyo Bay: 60km x 6km x 100m (60 x 6 x 40)

Residual current and Residual current and densitydensityWith stratification Without stratification

POM transportPOM transport180 days computationFalling speed is taken as 0.3 m day-1

Theoretical analysisTheoretical analysis

The first layer:

111

1

111

1

2F

xhg

xH

gxu

utu

1111 Ehu

xth

The second layer:

xH

gxH

gxu

utu

2

2

121

2

122

2

2221

12 2

Fx

hx

hg

2222 Ehu

xth

The third layer:

xH

gxH

gxH

gxu

utu

3

3

232

3

121

3

133

3

3332

21

13 2

Fx

hx

hx

hg

3333 Ehu

xth

Assumption used in the Assumption used in the theoretical analysistheoretical analysis

Water depths for each layer are taken as a Water depths for each layer are taken as a function of space not a function of time function of space not a function of time (Steady state assumption).(Steady state assumption).

Well mixed in the third layer.Well mixed in the third layer. No residual current in the first layer.No residual current in the first layer.

Comparisons with the Comparisons with the numerical computationnumerical computation

Bay headBay mouth

ConclusionConclusion

On-slope residual current due to On-slope residual current due to stratification effect is confirmed to be stratification effect is confirmed to be reproduced by using non-hydrostatic reproduced by using non-hydrostatic model, MEL3D.model, MEL3D.

The spatially distributed POM The spatially distributed POM concentration was found to be influenced concentration was found to be influenced by BBL.by BBL.

The applicability of theoretical solution The applicability of theoretical solution was verified through good agreements was verified through good agreements with the numerical computations.with the numerical computations.

Thank you very much.