Rigorous derivation of weakly dispersive shallow-water models with large amplitude topography variations
Emerald L. Paulsen M.O.
July 2024John Wiley and Sons Inc
Studies in Applied Mathematics
2024#153Issue 1
We derive rigorously from the water waves equations new irrotational shallow-water models for the propagation of surface waves in the case of uneven topography in horizontal dimensions one and two. The systems are made to capture the possible change in the waves propagation, which can occur in the case of large amplitude topography. The main contribution of this work is the construction of new multiscale shallow-water approximations of the Dirichlet–Neumann operator. We prove that the precision of these approximations is given at the order (Formula presented.), (Formula presented.), and (Formula presented.). Here, (Formula presented.), (Formula presented.), and (Formula presented.) denote, respectively, the shallow-water parameter, the nonlinear parameter, and the bathymetry parameter. From these approximations, we derive models with the same precision as the ones above. The model with precision (Formula presented.) is coupled with an elliptic problem, while the other models do not present this inconvenience.
Dirichlet–Neumann operator , multiscale expansion , pseudo-differential operators , rigorous derivation , shallow-water models
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Department of Mathematics, Nazarbayev University, Astana, Kazakhstan
Department of Mathematics, University of Bergen, Bergen, Norway
Department of Mathematics
Department of Mathematics
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