Nonlinear waves over highly variable topography
Dept. of Math. Sci., New Jersey Institute of Technology, Newark, NJ, 07102-1982, USA
2 IMPA, Rio de Janeiro, 22460-320 RJ, Brazil
This paper reviews the authors' recent work on water waves in heterogeneous media, namely nonlinear reduced models for water waves propagating over a region of highly variable depth. Both surface and internal waves are considered. Through different strategies for the mathematical modeling, at the level of equations, we show how diferent types of water wave models (namely systems of partial differential equations) can arise: weakly or fully dispersive, weakly or strongly nonlinear. The applications for these types of long waves are usually from Geophysics: in particular oceanography and meteorology. Here the emphasis is on coastal waves related to Physical Oceanography. An overview of the mathematical formulation is presented together with different asymptotic simplifications at the level of the partial differential equations (PDEs). References for recent work on the asymptotic analysis of solutions is also provided. These describe the regime where long pulse shaped waves propagate over rapidly varying topographic heterogeneities, which are modeled through rapidly varying coefficients in the PDEs.
© EDP Sciences, Springer-Verlag, 2007