Modelling the finite amplitude dynamics of tidal sand waves with
SWASH
T. Van Oyen
1, T. Suzuki
1,2, M. Zijlema
3, P. Rauwoens
1and P. Troch
11
Department of Civil Engineering, Ghent University, Belgium.
2
Flanders Hydraulics Research, Antwerp, Belgium.
3
Environmental Fluid Mechanics Section, Delft University of Technology, The Netherlands.
tomas.vanoyen@ugent.be E NG I NE E R ING A R C H IT E C T UR E
Sand waves ?
- These bed forms occur inshallow seas(30 m)
-WavelengthofO(100) m
-Amplitudeof a few metres
- Able tomigrate
- Perpendicular to the main tidal
cur-rent direction
Approach
Hydrodynamics
SWASH [Zijlema et. al, 2011] : - OPEN-source, finite difference - Staggered, orthogonal curvilinear grid - Non-hydrostatic, with pressure cor-rection technique
- k− ϵ model
- Tidal wave imposed with additional force in momentum balance
Morphodynamics
- Bottom roughness due to ripples - Shear stress evaluated with constitu-tive law
- Bed load transport [Van Rijn, 1991] - Bed slope transpost following van den Berg et. al [2012]
Results: Flow field
x* z* −0.2 0 0.2 0.4 0.6 0.8 1 1.2 −1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 −0.01 −0.005 0 0.005
0.01 Contourplot of the residual horizontal
flow for a sand wave with amplitude of 4 m in a depth H of 20 m and a max-imum depth averaged flow velocity of 0.5 ms−1. The dimensionless distance in the horizontal direction x∗ and the vertical direction z∗ is plotted on the x and z-axes, respectively.
Results: Evolution profile of the bed forms
-20 -18 -16 -14 -12 -10 -8 -6 -4 0 50 100 150 200 250 300 350 400
Depth (m)
Evolution bed profile
Initial
110 years
150 years
173 years
176 years
A flattening of the troughs and a sharpening of the wave crests is found similar to the results of van den Berg and van Damme [2007].
Motivation and aim
Motivation
Employing a stability analysis, [Blondeaux and Vittori, 2011] illustrated the influence of the non-hydrostatic pressure com-ponent on the generation of sand waves.
Aim
Analyse of the impact of non-hydrostatic part of the flow field on the fi-nite amplitude dynamics of sand waves.
Results: Impact non-hydrostatic pressure
0 50 100 150 200 250 300 350 400 0.2 0.4 0.6 0.8 1 1.2 Coefficient of determination wavelength (m) R x* z*
Difference residual hydrostatic − non−hydrostatic
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 −1.2 −1 −0.8 −0.6 −0.4 −0.2 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 x 10−5
Results: Evolution amplitude
-14 -12 -10 -8 -6 -4 0 50 100 150 200 250 300 Depth (m) Time (years) Evolution amplitude Numerical model Linear stab. anal.
-15
-100 0 100 200 300 400 500
Depth (m)
Initial bed profile (m)
-7 -6 -5 -4
177 177.5 178 178.5
- Initial amplification resembles lin. stab. analyses - Finite amplitude is characterised by oscillations however.
Discussion and conclusions
• Development of morphodynamic model for the finite-amplitude evolution of
tidal sand waves based on SWASH is presented.
• Finite amplitude dynamics of the bed forms is not yet well resolved. • Non-hydrostatic component of the flow field impacts particularly bed forms
with small wavelengths, in accordance with results presented by Blondeaux and Vittori [2011].
• Impact of bottom boundary condition!
References
Blondeaux P. and Vittori G. 2011 The formation of tidal sand waves: Fully three-dimensional versus shallow water approaches. Cont. Shelf Res. 31, 990 - 996
Zijlema M., Stelling G. and Smit P. 2011 SWASH: An operational public code for simu-lating wave fields and rapidly varied flows in coastal waters. Coastal Engng. 58, 992-1012 Van Rijn L., 1991 Sediment transport in combined waves and currents. Proc. of Eu-romech 262
van den Berg J. and van Damme R. 2007 Sand wave simulation on large domains. Proc. of RCEM conference
van den Berg J., Sterlini F., Hulscher S.J.M.H. and van Damme R. 2012 Non-linear process based modelling of offshore sand waves. Cont. Shelf Res. 37
