S.A. Talke , H.E. de Swart, H.M. Schuttelaars

Feedback between residual circulations and sediment distribution in highly turbid

estuaries: an analytical model

Netherlands

•Observation: Some estuaries have extremely high suspended sediment concentrations and fluid mud layers at their Estuarine Turbidity Maximum

•We present a simple model to explain how turbidity currents affect the longitudinal distribution of suspended sediment

Overview

Observationsof Ems Estuary

Ems Estuary

Amsterdam

Utrecht

~350 km

Germany

Netherlands

0 km 45 km

100 km(Tidal Weir)

Longitudinal Survey

Variations in sediment concentration huge(!) along longitudinal axisvariation from < 100 mg/L (marine) to > 10 g/L (brackish)

Thus, longitudinal distribution of sediment concentration affects density gradients

Sediment Concentrations

Low Flow Conditions

Q ~ 20 m3/s

Distance from N. Sea (km)

Large salinity and turbidity gradients in longitudinal direction

Gradients oppose each other downstream of ETM

Gradients in same direction upstream of ETM

UpstreamDownstream

Q=35 m3/s

What controls shape,extent and position of ETM?

Longitudinal Distribution of Turbidity and Salinity

Development of a simple model(1) Assumptions

Non-cohesive, fine grained sediments

Constant settling velocity

Constant Eddy viscosity and diffusivity

Salinity well mixed

Constant Width

Constant Depth

<Tidally Averaged>

Development of a simple model(2) Gravitational Circulation

Z

X

Sea River

Essentially, gravitational circulation reproduced with a convergence zone

z

uA

zx

pz0 g

z

p

H

QubdzCso (1) (2) (4)(3)

Longitudinal Salinity Profile

Development of a simple model(3) Add sediment dynamics

z

uA

zx

pz0 g

z

p

H

Qubdz

Z

X

Sea River

(1) (2) (4)(3)

•Vertically integrated flux of sediment vanishes during equilibrium conditions

H

dzx

CKuC 0(6)

MorphodynamicEquilibrium

(5) 0)(

z

CKCw

z zs

Solution now closed to arbitrary constant, c*

c* is total integrated

bottom sediment

Cso

Data Points

CTD Profile

Exponential Profile

Model Sensitivity StudyParameters

Z

X

Model shows that distribution of sediment sensitive to these parameters

Ws = 1 mm/s

Av = 0.001 m2/s

Q= 15 m3/sq= 0.03 m2/sH = 7 m

C* = 2 g/L

K = 100 m2/s

As reference concentration is increased, Longitudinal spread of ETM increasesLocation of ETM stays the same!

At ETM, dc/dx is zero. Thus, location set bythe balance between freshwater flow and salinity

Morphodynamic Equilibrium

Morphodynamic Equilibrium

Example forHigh sedimentConcentration

c*= 200 g/ls* = 12 psu

Gravitational Circulation

Turbidity Circulation

Combined Circulation

Velocity structure:Reduced residual circulation downstream: Maximum turbidity currents and salinity currents occur at the same (downstream) location Turbidity currents zero at maximumpersistent near-bottom upstream flow of > 2 mm/s

> 200 m per day!

Three Basic Conditions predicted by model:Low Flow Sediment concentration largest at upstream boundaryIntermediate FlowETM forms with asymmetric profileHigh Flow Sediment is flushed out of estuary

Affect of varying freshwater flow, q

Morphodynamic Equilibrium

Morphodynamic Equilibrium

As the eddy viscosity is increased, the ETM moves downstream

Affect of varyingeddy viscosity and diffusivity

Morphodynamic Equilibrium

As depth is increased, the ETM moves upstream asymmetry of ETM shape enhanced

Affect of varying depth

High Sediment concentration Less vertical mixing (50%)

ETM moves upstream Higher Concentration causes larger upstream spread

Increased depth ETM moves upstream

Conceptual Model for theeffect of deepening a river(low flow conditions) H= 5m

(1980, Ems)

H=7 m(2005, Ems)

Dredging Scenario

Discussion

• Recall longitudinal transect of sediment concentration

Consistent with model for low flow conditions!– Sediment piles up at

Tidal weir

Discussion

• No feedback between salinity field and turbidity currents

• Tidally varying processes not included– Literature and measurements show this to be

important

Sediment Concentration at a cross section

Strong variation in sediment concentration w.r.t. tidal phase

Cross Sectional Measurements

Salinity over a tide

Salinity 3ppt less atbottom thanmiddle of water column!

During flood, salty clean water is moved over fresh, muddy waterIn upper layer, ‘normal’ salinity stratification (interaction in lateral direction?)

Complex, tidally varying mixing and residual circulation

Conventionalstratification

Conclusions

• Longitudinal gradients of both sediment concentration and salinity drive tidally-averaged circulation

• Large Sediment concentrations result in an increased upstream extent of turbid zone

• The upstream migration of ETM in Ems is likely both due to increased water depth and reduced mixing due to high sediment concentrations