Abstract:
In the present paper, reflection and transmission phenomena of water
waves due to undulating permeable bottom in a two-layer fluid system are investigated
using two-dimensional linearized theory. The effect of surface tension on the free
surface is included in this work. In two-layer fluid system, there exist waves with
two different wave numbers (modes). When a wave of a particular wave number
encounters the undulating bottom, reflection and transmission phenomena occur in
both the layers. The reflection and transmission coefficients in both layers due to
incident waves of both modes are analyzed with the aid of perturbation analysis along
with Fourier transform technique. It is found that these coefficients are obtained in
terms of integrals which depend on the shape function of the undulating bottom. Two
different kinds of undulating bottoms are considered to determine these coefficients.
For a particular undulating bottom, namely sinusoidal bottom undulation the effect
of various physical parameters such as number of ripples, surface tension and porous
effect parameters are demonstrated graphically. The study further elaborates the
energy balance relations associated with the reflection and transmission coefficients
to ascertain the correctness of all the computed results.
