Journal article
A Fourier-Boussinesq method for nonlinear water waves
A Boussinesq method is derived that is fully dispersive, in the sense that the error of the approximation is small for all 0⩽kh<∞ (k the magnitude of the wave number and h the water depth). This is made possible by introducing the generalized (2D) Hilbert transform, which is evaluated using the fast Fourier transform.
Variable depth terms are derived both in mild-slope form, and in augmented mild-slope form including all terms that are linear in derivatives of h. A spectral solution is used to solve for highly nonlinear steady waves using the new equations, showing that the fully dispersive behavior carries over to nonlinear waves.
A finite-difference–FFT implementation of the method is also described and applied to more general problems including Bragg resonant reflection from a rippled bottom, waves passing over a submerged bar, and nonlinear shoaling of a spectrum of waves from deep to shallow water.
Language: | English |
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Year: | 2005 |
Pages: | 255-274 |
ISSN: | 18737390 and 09977546 |
Types: | Journal article |
DOI: | 10.1016/j.euromechflu.2004.06.006 |
ORCIDs: | Bingham, Harry |