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Evolution of a random field of surface gravity waves in a two fluid domain

Senapati S., Debsarma S., Das K. P.

International Journal of Applied Mechanics and Engineering

2012

Vol. 17, no. 2

481-493

A spectral transport equation is derived here that governs the evolution of a random field of surface gravity waves in a two layer fluid model. This equation is used to study the stability of an initially homogeneous Lorentz spectrum under long wave length perturbations. It is observed that the effect of randomness is to reduce the growth rate of instability. An increase in the thickness of the upper fluid results in an increase in the extent of instability. It is also found that the extent of instability becomes less for a smaller density difference of the two fluids.

Stability of small but finite amplitude interfacial capillary gravity waves for perturbations in two horizontal directions

Majumder D. P., Dhar A. K.

International Journal of Applied Mechanics and Engineering

2011

Vol. 16, no 2

425-434

By exact numerical computation Yuen (1984) obtained regions of type-I instability for waves propagating at the interface of two superposed fluids of infinite thickness in which the upper fluid has a constant streaming velocity. In the present paper it is shown that the long wavelength part of these instability regions can be obtained analytically from a fourth order nonlinear evolution equation for small but finite amplitude interfacial capillary gravity waves in the presence of air flowing over water.

Stability analysis from fourth order nonlinear evolution equation for two stokes wave trains in deep water in the presence of air flowing over water

Majumder D. P., Dhar A. K.

International Journal of Applied Mechanics and Engineering

2009

Vol. 14, no 4

989-1008

Fourth order nonlinear evolution equations are derived for two Stokes wave trains in deep water in the presence of air flowing over water. The importance of the fourth order term in the evolution equation was pointed out by Dysthe (1979). Stability analysis is then made for uniform two Stokes wave trains in the presence of air flowing over water. From these evolution equations the expressions for the maximum growth rate of instability, the wave number at marginal stability and the wave number separation of fastest growing side band are derived and graphs are plotted for the above three expressions against the wave steepness. Significant improvements can be achieved from the results obtained from the two coupled third order nonlinear Schrödinger equations.