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Book Chapter

Nonlinear and linear bottom interaction effects in shallow water


Hasselmann,  Klaus F.
MPI for Meteorology, Max Planck Society;

Herterich,  Klaus
MPI for Meteorology, Max Planck Society;

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Shemdin, O., Hasselmann, K. F., Hsiao, S. V., & Herterich, K. (1978). Nonlinear and linear bottom interaction effects in shallow water. In A. Favre, & K. Hasselmann (Eds.), Proceedings of the NATO Symposium on Turbulent Fluxes Through the Sea Surface, Wave Dynamics, and Prediction (pp. 347-372). Plenum Publ. Corp.

Cite as: http://hdl.handle.net/21.11116/0000-0008-8456-2
Spectral wave transformation in shallow water is investigated by examining nonlinear and linear bottom interaction effects. The effect of nonlinear wave-wave interaction in shallow water is investigated by including the depth dependent dispersion relationship in the nonlinear calculations. Dissipative mechanisms examined are bottom friction, percolation within the sand layer, and wave motion in the mud layer induced by hydrodynamic forces acting at the mud line. Comparisons with observations suggest that bottom motion can be one order of magnitude more pronounced than friction or percolation when soft mud occupies the top layer such as found in the Gulf of Mexico. In the North Sea (JONSWAP area) coarse sand with mean grain diameter ≥ 0.3 mm is found in the top sediment layer. Here swell energy dissipation can be explained by the linear percolation mechanism. When bottom sand is fine (mean grain diameter ≤ 0.4 mm), such as found offshore of Panama City and Marine-land, Florida, nonlinear bottom friction is found to explain swell dissipation adequately. A nonlinear bottom scattering mechanism was investigated by Long (1973) who found the effect to be possibly important in the JONSWAP area but required detailed directional wave measurements to derive conclusive results. This paper examines five different data sets on wave transformation in shallow water and offers explanations in terms of bottom interaction mechanisms