Nonlinear channel shoal dynamics in long tidal embayments
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Nonlinear channel-shoal dynamics in long tidal embayments. H.M. Schuttelaars 1,2 , G.P. Schramkowski 1,3 and H.E. de Swart 1. “Finite amplitude behaviour of large scale alternating bars can be understood and modelled”. Observations on large scale alternating bars:.

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Nonlinear channel-shoal dynamics in long tidal embayments

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Nonlinear channel shoal dynamics in long tidal embayments

Nonlinear channel-shoal dynamics in long tidal embayments

H.M. Schuttelaars1,2, G.P. Schramkowski1,3 and H.E. de Swart1

“Finite amplitude behaviour of large scale alternating bars

can be understood and modelled”


Nonlinear channel shoal dynamics in long tidal embayments

Observations on large scale alternating bars:

  • length scales ~ 20 km.

  • environments with strong tides

  • fine sand

Previous studies: Seminara & Tubino (1998), Hibma et al. (2002)

Aim of this talk: to model and understand the

observed dynamical behaviour of large scale

alternating bars


Nonlinear channel shoal dynamics in long tidal embayments

Model setup

• idealised model

• straight channel

• only bed erodible

• depth-averaged SW eqns

• suspended load transport

• uniform M2 tidal forcing,

velocity scale ~ 1 m/s

Length scales << channel length, tidal wavelength

Typically: • channel width B

• horizontal tidal excursion length ~ 7 km


Nonlinear channel shoal dynamics in long tidal embayments

Model approach

Use a finite number of spatial patterns obtained from a linear stability

analysis to describe the finite amplitude bed behaviour:

M

N

h’ = S SAmn(t) cos (m kcx) cos (npy/B)

m=0

n=0

  • kc: wavenr. of critical mode

  • channel length Lc

  • Lc= ~ 60 km

  • B ~ 5 km.

  • N,M: truncation numbers

2p

kc

kc

Growth curves


Nonlinear channel shoal dynamics in long tidal embayments

Model approach

0

0

0

0

Use a finite number of spatial patterns obtained from a linear stability

analysis to describe the finite amplitude bed behaviour:

M

N

h’ = S SAmn(t) cos (m kcx) cos (npy/B)

m=0

n=0

B

m=1,n=1

Lc

B

m=1,n=2

Lc

B

m=2,n=1

Growth curves

0

Lc


Nonlinear channel shoal dynamics in long tidal embayments

Model approach

Use a finite number of spatial patterns obtained from a linear stability

analysis to describe the finite amplitude bed behaviour:

M

N

h’ = S SAmn(t) cos (m kcx) cos (npy/B)

m=0

n=0

Insert expansion in complete nonlinear equations.

equations describing the behaviour of Amn(t):

  • steady state solutions

  • cyclic behaviour


Nonlinear channel shoal dynamics in long tidal embayments

Example: channel width ~ 3.5 km.

• multiple steady state

solns:

• trivial soln.

• nontrivial soln.

• no steady equilibrium

soln for r/sH > 0.0213

periodic soln.


Nonlinear channel shoal dynamics in long tidal embayments

Steady state solution (r~0.0213)

Periodic solution (r~0.0214)


Nonlinear channel shoal dynamics in long tidal embayments

Sensitivity study: variation of bed friction and channel width

  • R<rcr(B): horizontal bed

  • B<3.6 km: stable static solns. exist

  • B>3.6 km: no static solns. time-dependency

  • Small region of multiple stable steady states


Conclusions

Conclusions

  • existence of finite amplitude alternating bars explicitly

  • demonstrated

  • qualitative behaviour depends on channel width and

  • strength of bed friction

  • saturation mechanism: importance of destabilizing

  • sediment fluxes decreases relative to bedslope effects

Present work

  • explore towards realistic values of bed friction

  • further identification of physical processes

  • comparison with more complex models


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