Potential mechanism for the initial formation of rhythmic coastline features

M.van der Vegt, H.M. Schuttelaars and H.E. de SwartInstitute for Marine and Atmospheric research Utrecht, Utrecht University, The

Netherlands

“ Tidal motion can cause coastline variations with wave lengths of a couple of kilometers “

Mesoscale rhythmic coastlines

Shoreline sand waves: planimetric variations of coastline

1-10 km

C 100m/yr

A10-100 m

Red colors: protrudingBlue colors: retreating

(adapted from Ruessink&Jeuken,2002)

Protruding or retreating coast

Motivation

• Waves and tides are potentially important

• Tides not considered so far

• Can tidal motion cause initial formation of rhythmic coastline features?

• What are the underlying physical mechanisms?

Research questions

Physical model

• Geometry:

• Assumptions: - Near shore zone has constant width- Sediment transport q only in near shore zone- Sediment transport determined by velocities at transition line

20 m

5 m

10 km

500 m

q

Side view

Top view

CoastlineTransition line

Inner shelfTideNear shore

zone

Physical model

• 2-DH Shallow water equations, no diffusion, rigid lid approximation. Only on inner shelf.

• Boundary conditions: at x=xt and at x

• Width-integrated sediment transport for the near shore zone:

• Tm>>T Coastline evolution is slow and tidally averaging is allowed

• Alongshore variations of sediment transport causes changes of shoreline position. No change of bathymetry.

0nu

0u

txxuq

//

Basic state and perturbations

• The model allows for a basic state with uniform alongshore conditions

• Note that basic state velocity has vorticity: • Basic state is perturbed by perturbation of coastline• Solutions cyclic in y and t. Model calculates initial

complex growth rate

xV

imre iC

oastV(x,t)

Sea 1 m/s

NearShorezone

Results: Growth rate curve

)1(155)( / foldingexexH

Residual flow on inner shelf

• Tidal residual circulations cells Vorticity dynamics?• Growth determined by depth dependent friction• Coriolis force migration

Without Coriolis effects With Coriolis effects

Mechanism behind model results: vorticity dynamics

vdx

dH

H

rω

H

r

y

Ωv

y

ωV

x

Ωu2

Basic state velocity:V

Basic state vorticity:

xV

Perturbed velocity: u,v

Perturbed vorticity:

yx uv

UnstableStable

Battle between the fluxes

• Stabilizing fluxes in cross-shore, destabilizing in alongshore direction

• Convergence cross-shore flux ~ width of inner shelf

• Convergence alongshore flux ~ wave length

Positive growth rate for < width inner shelf

Conclusions

• Tidal motion can initially form rhythmic coastlines• Length scale in the range of shoreline sand waves • Steeper profile Critical wave length shorter • Mechanism can be understood in terms of vorticity

fluxes. Cross-shore Alongshore fluxes• No damping mechanism• With diffusion a preferred mode will occur

• Inclusion of wave action diffusion• Model parameterization

Future work