Abstract:
In the present paper, transformation of water-wave
energy in a two-layer fluid having irregular bottom is studied
including the effect of the surface tension. In such fluid system,
time harmonic waves of two distinct modes (wave numbers) exist.
When an incident wave with a particular wave number
encounters the irregular bottom, it is partially reflected as well as
partially transmitted into waves of both wave numbers. As a
result, some of the energy is transferred from one to another
wave number. Perturbation analysis followed by Fourier
transformation is used to study the reflection and transmission
phenomena. Reflection and transmission coefficients of both
modes are estimated up to the first-order. These coefficients are
obtained in integral forms and depend on the bottom profile. One
special type of shape function is considered to evaluate the
related coefficients. These coefficients are shown in graphical
forms to demonstrate the effects of some physical parameters like
number of ripples, surface tension on the transformation of wave
energy between the waves of two different modes. Moreover, a
comparison has been made between the present results and the
experimental results available in the literature.
