Initial Formation of Estuarine Sections

Henk Schuttelaarsa,b, George Schramkowskia

and Huib de Swarta

aInstitute for Marine and Atmospheric Research, Utrecht UniversitybDelft University of Technology

Contents

• Introduction

• Model Formulation

• Instability Mechanisms

• Numerical Experiments

• Conclusions + Future Research

Tidal Embayments:

Introduction

•Semi-enclosed bodies of water•Connected to the open sea•Driven by tides

Examples:

•Frisian Inlet System•Western Scheldt•Inlets East Coast of the US

Marine Part of the Western Scheldt

(From Jeuken, 2000)

Research Questions

• Can Estuarine Sections be modelled as Free Instabilities

• Can the Physical Mechanisms be understood• How do these results depend on Physical Parameters

Model Equations and Assumptions

• Depth Averaged Shallow Water Equations

• Only Bed Erodible

• Noncohesive Material

• Suspended Load Transport

• Sediment Balance:

hole bar

Fine Sand

Geometry

Side View:

Top View:

Linear Stability Analysis

•Find a (one dimensional) equilibrium solution heq(x).•This equilibrium heq(x) is usually not stable w.r.t. small perturbations with a 2D structure: h = heq(x) + h’(x,y,t)•The perturbation h’ can be found by solving an eigen value problem. The resulting eigenfunction reads h’mn = ewt fm(x) cos(ln y)•If Re(w) > 0 : unstable bedform Re(w) < 0 : stable bedform •If Im(w) = 0 : migrating bedforms

Instability Mechanisms

Net (tidally averaged) Sediment Transport:

• Advective Transport:

• Diffusive Transport:

• Fadv = <u C>x + <v C>y

• ~ (A/H)2

• Fdiff = - < C>xx - <C>yy

• ~ L2

Diffusive Mechanism

Advective Mechanism

Numerical Experiments

• Short Embayment:

• Long Embayment:

• L=20 km, H=10 m, A=1.75m, B=5km.

• = 25 m2 s-1

• Focus on influence of frictional strength

• L=60 km, H=10 m, A=1.75m, B=5km.

• = 25 m2 s-1, weak friction

• Focus on local/blobal modes

Short Embayment

Realistic Friction Advectively Dom. Unstable Mode Local Mode

Weak Friction Diffusively Dom. Stable Mode Global Mode

Bed Profile Fluxes

Long Embayment

Global Mode Diffusively Dom. Stable Mode Global Mode

Local Mode Advectively Dom. Unstable Mode Local Mode

Bed Profile Flux

Conclusions

Two Types of Modes:

Very Sensitive for Frictional Strength

• diffusively dominated:

• advectively dominated:

Scale with L

Non-migrating

Scale with B, U/s

Migrating and Non-Migrating

Future Research

• Are Estuarine Sections Free Instabilities?

• What Determines the Position of the Advective Instabilities in the Estuary?

• Why are Advective and Diffusive Divergences of Fluxes (Always) Out of Phase?

Diffusive Instabilities?

Strongly Nonlinear Advective Instabilities?