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Initial Formation of Estuarine Sections

Initial Formation of Estuarine Sections. Henk Schuttelaars a,b , George Schramkowski a and Huib de Swart a. a Institute for Marine and Atmospheric Research, Utrecht University. b Delft University of Technology. Contents. Introduction Model Formulation Instability Mechanisms

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Initial Formation of Estuarine Sections

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  1. Initial Formation of Estuarine Sections Henk Schuttelaarsa,b, George Schramkowskia and Huib de Swarta aInstitute for Marine and Atmospheric Research, Utrecht University bDelft University of Technology

  2. Contents • Introduction • Model Formulation • Instability Mechanisms • Numerical Experiments • Conclusions + Future Research

  3. 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

  4. Marine Part of the Western Scheldt

  5. (From Jeuken, 2000)

  6. Research Questions • Can Estuarine Sections be modelled as Free Instabilities • Can the Physical Mechanisms be understood • How do these results depend on Physical Parameters

  7. Model Equations and Assumptions • Depth Averaged Shallow Water Equations • Only Bed Erodible • Noncohesive Material • Suspended Load Transport • Sediment Balance: Fine Sand hole bar

  8. Geometry Side View: Top View:

  9. 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

  10. Instability Mechanisms Net (tidally averaged) Sediment Transport: • AdvectiveTransport: • Diffusive Transport: • Fadv = <u C>x + <v C>y • ~ (A/H)2 • Fdiff = -m < C>xx - m <C>yy • ~ m / s L2

  11. Diffusive Mechanism

  12. Advective Mechanism

  13. Numerical Experiments • Short Embayment: • Long Embayment: • L=20 km, H=10 m, A=1.75m, B=5km. • m= 25 m2 s-1 • Focus on influence of frictional strength • L=60 km, H=10 m, A=1.75m, B=5km. • m= 25 m2 s-1, weak friction • Focus on local/blobal modes

  14. Short Embayment Bed Profile Fluxes • Weak Friction • Diffusively Dom. • Stable Mode • Global Mode • Realistic Friction • Advectively Dom. • Unstable Mode • Local Mode

  15. Long Embayment Flux Bed Profile • Local Mode • Advectively Dom. • Unstable Mode • Local Mode • Global Mode • Diffusively Dom. • Stable Mode • Global Mode

  16. 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

  17. 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?

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