Forced capillary gravity surface waves over a bump – Critical surface tension case

Abstract

This paper concerns forced surface waves on an incompressible, inviscid fluid in a two-dimensional channel with nonzero surface tension on the free surface and a small bump on a horizontal rigid flat bottom. It is known that if non-dimensional wave speed, called Froude number, is near 1 and a non-dimensional surface tension, called Bond number, is near 1/3, the KdV theory fails and a time dependent fifth order KdV equation, called the Kawahara equation, can be derived to study the wave motion on the free surface. In this paper both time independent and time dependent forms of the Kawahara equation with a forcing are studied numerically and theoretically and various numerical results are presented. References

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