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A terrain-following Boussinesq system. (English) Zbl 1078.76015
The long paper examines a wave in an inviscid incompressible irrotational shallow water. The author establishes a model for a large class of bottom profiles, especially for profiles with rapidly varying topographies, in contrast with the mild slope topographies, where it is possible to simplify the flow equations. The study uses the results of J. Hamilton [J. Fluid Mech. 83, 289–310 (1977; Zbl 0382.76011)], where the two-dimensional conformal mapping technique was applied to long wave models for a fluid with rapidly varying depth. The computational tool for the conformal mapping can be found in T. Driscoll, The Schwarz-Christoffel Toolbox for MATLAB, http://www.math.udel.edu/ driscoll/software/SC. The paper describes the Boussinesq models and their linearization. The main result is the derivation of a weakly nonlinear dispersive Boussinesq system for multiple topographies. The theoretical results are confirmed numerically.

MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M40 Complex variables methods applied to problems in fluid mechanics
86A05 Hydrology, hydrography, oceanography
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