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

Observations of Ems Estuary Ems Estuary Amsterdam Utrecht ~350 km Germany Netherlands 0 km45 km 100 km (Tidal Weir) Longitudinal Survey

Variations in sediment concentration huge(!) along longitudinal axis  variation from 10 g/L (brackish) Thus, longitudinal distribution of sediment concentration affects density gradients Sediment Concentrations Low Flow Conditions Q ~ 20 m 3 /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 Upstream Downstream Q=35 m 3 /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

Development of a simple model (2) Gravitational Circulation Z X SeaRiver Essentially, gravitational circulation reproduced with a convergence zone (1)(2)(4)(3) Longitudinal Salinity Profile

Development of a simple model (3) Add sediment dynamics Z X SeaRiver (1)(2)(4)(3) Vertically integrated flux of sediment vanishes during equilibrium conditions (6) Morphodynamic Equilibrium (5) Solution now closed to arbitrary constant, c*  c* is total integrated bottom sediment Data Points CTD Profile Exponential Profile

Model Sensitivity Study  Parameters Z X Model shows that distribution of sediment sensitive to these parameters Ws = 1 mm/s Av = m 2 /s Q= 15 m 3 /s q= 0.03 m 2 /s H = 7 m C* = 2 g/L K = 100 m 2 /s

As reference concentration is increased,  Longitudinal spread of ETM increases  Location of ETM stays the same!  At ETM, dc/dx is zero. Thus, location set by the balance between freshwater flow and salinity Morphodynamic Equilibrium

Example for High sediment Concentration c*= 200 g/l s* = 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 maximum  persistent 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 boundary Intermediate Flow  ETM forms with asymmetric profile High Flow  Sediment is flushed out of estuary Affect of varying freshwater flow, q Morphodynamic Equilibrium

As the eddy viscosity is increased, the ETM moves downstream Affect of varying eddy 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 the effect 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 at bottom than middle of water column! During flood, salty clean water is moved over fresh, muddy water In upper layer, ‘normal’ salinity stratification (interaction in lateral direction?)  Complex, tidally varying mixing and residual circulation Conventional stratification

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