Finite amplitude tidal waves at the interface between two fluid saturated porous media (Eng)

Abstract

The propagation of finite amplitude tidal waves at the interface between two semi-infinite fluid saturated porous media of different densities with the external constraint of rotation is investigated using both analytical and numerical methods. The set of non-linear partial differential equations governing the wave motion have been reduced to the set of non-linear ordinary differential equations using a suitable integral. From this set, the phase portaits are obtained. The analytical results, obtained by neglecting the residue integral show that the periodic tidal waves exist in the case of a fluid saturated porous medium only for small values of porous parameter. When the governing non-linear wave equations are integrated directly, we found that the tidal waves are almost periodic for small values of porous parameter. The important conclusions are : (i) the Coriolis force has a significant effect on wavelength which is useful in the study of abnormality in the interior of the earth. (ii) the effect of porous parameter in the presence of rotation is to make the waves periodic only for small values of porous parameter and its effect is to reduce the amplitude of the waves, due to the dampening effect of Darcy's resistance.