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Generalized evolution equations for nonlinear surface gravity waves over two-dimensional topography
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DOI：10.1017/S0022112006008743.png)
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摘要
En 中文
Evolution equations are derived for weakly nonlinear, multi-frequency and directional surface gravity waves propagating from deep to shallow water over weakly twodimensional bottom topography. A uniform transition from cubic resonances in deep intermediate water (Stokes regime) to quadratic near resonances in shallow water (Boussinesq regime) is obtained by extending the ordered solution to include additional higher-order terms for the bound wave components. The model assumes a leading-order, alongshore-uniform bottom with a two-dimensional depth perturbation that is incorporated through a Taylor series expansion of the bottom boundary condition. Numerical implementations of the model and comparisons to experimental data are presented that demonstrate the model's ability to describe: (i) cubic wavewave interactions in deep-intermediate water depth; (ii) harmonic generation over a one-dimensional submerged obstacle; (iii) harmonic generation over two-dimensional topography.
Keyword:
ANGLE WATER-WAVES
REFRACTION-DIFFRACTION
PERIODIC-WAVES
PROPAGATION
DERIVATION
MODULATION
TRANSPORT
AMPLITUDE
MODELS
FIELD
