1. Dpt. of Civil and Environmental Engineering University of Trento (Italy) Long term evolution of self-formed estuarine channels Ilaria Todeschini, Marco Toffolon and Marco Tubino

2. 1/15 TIDE-DOMINATED ESTUARIES (Thames, Bristol Channel, Columbia River, etc.) Delaware Bay Bristol Channel Long-term evolution of self-formed estuarine channels

3. 2/15 Scheldt Potomac L e = 77 km L b = 54 km L e = 184 km L b = 54 km Thames L e = 95 km L b = 25 km (data from Lanzoni and Seminara, 1998) Long-term evolution of self-formed estuarine channels

4. 3/15 Which reasons could explain this FUNNEL- SHAPE ? SEA ACTION SEA LEVEL COASTAL UPLIFT INTERNAL DYNAMICS SEA ACTION SEA LEVEL COASTAL UPLIFT BIDIMENSIONAL PROCESSES ONEDIMENSIONAL PROCESSES etc … LONG-TERM EQUILIBRIUM CONFIGURATION Schuttelaars & de Swart 2000 Lanzoni & Seminara 2002 … Equilibrium bed profile HERE A simplified model to try to explain the shape of the estuary Long-term evolution of self-formed estuarine channels

5. 4/15 FORMULATION OF THE PROBLEM D * = water depth B * = channel width h * = bottom elevation a* = tidal amplitude T 0 * = tidal period Long-term evolution of self-formed estuarine channels RECTANGULAR CROSS SECTION AREA INTERTIDAL AREAS ARE NEGLECTED

6. ONE-DIMENSIONAL MODEL 5/15 SEDIMENT FLUX q s * ENGELUND & HANSEN FORMULA (1967) FRICTIONAL TERM Long-term evolution of self-formed estuarine channels Continuity equation Momentum equation Exner equation

7. SEAWARD BOUNDARY H(t) =  sin(2t) (M 2 ) q s = q s equilibrium BOUNDARY CONDITIONS 6/15 HYDRODYNAMICS: finite differences  MacCormack + TVD filter to avoid oscillations (second order accurate both in space and in time) EXNER EQUATION: finite differences  First-order upwind since T bed >>T 0 Hydrodynamic problem decoupled from the morphodynamic one NUMERICAL SCHEME LANDWARD BOUNDARY Q = 0 Q = Q river q s =q s equilibrium 2 CASES: Long-term evolution of self-formed estuarine channels

8. 7/15 FIXED BANKS (Lanzoni & Seminara, 2002; Todeschini et al, 2003) Convergent channel Long-term evolution of self-formed estuarine channels LENGTH OF THE DOMAIN EQUILIBRIUM LENGTH LONG-TERM BED EVOLUTION DEGREE OF CONVERGENCE

9. 8/15 from : http://sposerver.nos.noaa.gov/bathy/finddata.htm (National Ocean Service, USA) TIDE-DOMINATED ESTUARIES Delaware BayColumbia River D * water depth B * width  * bottom elevation Long-term evolution of self-formed estuarine channels

10. 9/15 A MODEL FOR WIDTH CHANGE Physically-based erosional law In literature few contributions can be found, most of them refer to rivers e.g. Darby & Thorne, 1996 provided the velocity exceeds a threshold value u crit PROBLEMS: estimate of the two parameters u crit k Darby & Thorne (1996)Gabet (1998) intermediate value: Long-term evolution of self-formed estuarine channels

11. 10/15 RESULTS BOTTOMBANKS BOTTOM PROFILE BANKS PROFILE time Long-term evolution of self-formed estuarine channels time SHORTER TIME SCALELONGER TIME SCALE THE BOTTOM EVOLUTION IS ALMOST THE SAME ! THE BANKS PROFILE IS CONCAVE !

12. 11/15 Long-term evolution of self-formed estuarine channels Given the same tidal forcing Despite the different initial depths at the mouth, the bottom and the banks equilibrium profile are quite similar IS THE CHOICE OF THE INITIAL DEPTH AT THE MOUTH D 0 IMPORTANT?

13. 12/15 Long-term evolution of self-formed estuarine channels on the other hand its value deeply influences the solution it’s very difficult to obtain a reliable estimate of this parameter IS THE CHOICE OF THE CONSTANT K IMPORTANT?

14. 13/15 FIXED HORIZONTAL BED Long-term evolution of self-formed estuarine channels Irrealistic situationCould other factors induce a funnel- shape geometry? The banks profile displays a convex shape (e.g. with an increasing rate of widening seaward) BANKS PROFILE EVOLUTIONEQUILIBRIUM BANKS PROFILE Moveable bed Fixed bed

15. 14/15 NON NEGLIGIBLE RIVER DISCHARGE at the landward boundary Long-term evolution of self-formed estuarine channels CONVEX SHAPE MILD BOTTOM SLOPE THE RIVER DISCHARGE STRONGLY INFLUENCES THE SOLUTION with a river discharge vanishing river discharge with a river discharge

16. 15/15 Long-term evolution of self-formed estuarine channels comparison between: NON NEGLIGIBLE DISCHARGE REFLECTIVE BARRIER CONDITION PHYSICAL INTERPRETATION RESIDUAL SEDIMENT FLUX at the beginning of the simulation at equilibrium NO RIVER DISCHARGE WITH RIVER DISCHARGE at equilibrium