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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...
Fourth order nonlinear evolution equations are derived for a three dimensional surface gravity wave packet in the presence of long wave length an interfacial wave in a two layer fluid domain in which the lower fluid depth is infinite. For derivation of evolution equations, the multiple-scale method is used. Using these evolution equations, stability of uniform stokes wavetrain is investigated for...
The fourth order nonlinear evolution equations are derived for a capillary-gravity wave packet for the case of resonant interaction with internal wave in the presence of a thin thermocline at a finite depth in deep water. These equations are used to make stability analysis of a uniform capillary-gravity wave train when resonance condition is satisfied. It is observed that for surface gravity waves...
A fourth order non-linear evolution equation is derived for a capillary-gravity wave packet in deep water in the presence of a thin thermocline including the effect of wind and viscous dissipation in water. In deriving this equation it has been assumed that the wind induced basic current in water is exponential and the effect of shear in air flow and viscous dissipation in water is accounted for by...
A fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves of wave-steepness up to 0.25, is used here to investigate the effect of randomness on stability of deep-water surface gravity waves in the presence of wind blowing over water. A spectral transport equation for narrow band Gaussian surface wave is derived. With the use of this transport...
A fourth order nonlinear evolution equation is derived for capillary gravity waves in deep water including the effect of a surface drift current in the water and shear in the air flow. From this evolution equation instability conditions are derived for a uniform capillary-gravity wave train. Graphs are plotted showing the maximum growth rate of instability and instability regions for weakly damped...
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