1 University of Utrecht

Modelling lateral entrapment of sediments in well-mixed estuaries

Photo: mudbanks in the Ems

Huib de Swart

Karin Huijts, Henk Schuttelaars, Arnoldo Valle-Levinson

Institute for Marine and Atmospheric Research Utrecht

2 University of Utrecht

Lateral entrapment of suspended sediment: James River estuary Introduction

Washington

Chesapeake Bay

100 km

Sediment trappedat the left bank

From ADCP data A. Valle-Levinson(view into estuary)

3 University of Utrecht

Introduction

Here: simple model to study physical processesthat cause lateral trapping of sediment

Specific focus:1. Coriolis deflection of tidal currents and

of along-estuary density-driven flow

2. Lateral density gradients

Main question:

why is sediment in James River estuarytrapped at the left bank?

4 University of Utrecht

• Geometry• Local (L~10 km)

• Along-estuary uniform

• Here: lateral bathymetry of James estuary

• 3D Shallow water equations • Tidal estuary

• Density gradients (prescribed)

• Coriolis

• M2 + M0

• Sediment mass balance equations• Advection diffusion equation for suspended sediment

• No mean lateral sediment transport

• Non-cohesive sediment, uniform size

• M2 + M0

Domain and equations of motion Model

sea

river

5 University of Utrecht

Analysis Model

where primes~tides and bars~time mean

• Scaling and perturbation analyses → reduce eq's to essential physics

• Analytical solutions:

• and 'ccc

Tidal flow equations Residual flow equations2

2

2

2

0

z

z

u ufv g A

t x z

v vfu g A

t y z

v w

y z

.0

,

,

2

2

0

2

2

0

z

w

y

v

z

vA

ygz

y

guf

z

uA

xgz

x

gvf

z

z

yx uuuu '

6 University of Utrecht

Effects of tides and density gradients on the transport is investigated

separately by substituting and :

1. Tides:

2. Along-estuary density gradient:

3. Lateral density gradient:

Mean lateral sediment transport

Mean lateral transport due to

0

dzcv-D

0

dzcv x-D

0

dzcv y-D

Model

+

'ccc

By definition: T = 0

dzvc-D

yxvvvv '

7 University of Utrecht

Results

Mean sediment concentration (mg l-1)

Case 1: Tides and along-estuary density gradient

0

dzcv-D

0

dzcv x-D

xv'v 3 cm/s

0.5 cm/s

Highest concentrations near the bed → Lateral near-bed flow crucial for lateral transport

trapping at right bank

Tra

nspo

rt

Mean lateral sediment transport induced by…

xv v

8 University of Utrecht

Mean density-driven flow

ResultsCase 1: Tides and along-estuary density gradient

In deep channel: inflow

Coriolis deflection =>

Sediment is transported to the right bank

9 University of UtrechtTrapping at left bank

Case 2: Tides and both horizontal density gradients Results

Mean flow component due to lateral density gradient (cm/s)

← max. 6 cm/s

Mean sediment concentration Mean sediment transport due to…

…along-estuary density gradient

…tides…lateral density gradient

0

dzcv y-D

xv'v 3 cm/s

0.5 cm/s

6 cm/syv

Tra

nspo

rt

salter

fresher

10 University of Utrecht

Tidal amplitude Comparison to observations

Courtesy observations:

A. Valle-Levinson

11 University of Utrecht

Mean flow Comparison to observations

Asymmetric bed profile!Symmetric

}

12 University of Utrecht

Mean concentration Comparison to observations

Lateral density gradient mechanism dominates in James River!

13 University of Utrecht

Conclusions

Sediments are trapped at the left bank of the James-transect, as

• Lateral near-bed flow induced by lateral density gradient

induces mean sediment transport towards that side

• Tides erode bed sediments

The effects of tides and density gradients on lateral sediment trapping can be studied separately, providing insight in underlying mechanisms.