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4 International Journal of Applied Mechanics and Engineering

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Fourth order nonlinear evolution equation for capillary gravity waves in deep water in the presence of a thin thermocline including the effect of wind

100%

Debsarma S. , Das K. P.

2003

tom Vol. 8, no 2

177-193

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 including a term in the evolution equation. The nonlinear evolution equation is used to study the stability of a uniform capillary-gravity wave train. Expressions for the maximum growth rate of instability and wave number at marginal stability are obtained. From results shown graphically it is found that the inclusion of wind effect increases the growth rate of instability irrespective of the presence of a thin thermocline. For waves with a small wave number, a thin thermocline has a stabilizing influence both in the presence and in the absence of wind input and the maximum growth rate of instability decreases with the increase of thermocline depth. But for waves with a large wave number a thin thermocline has no influence.

On resonant interaction of capillary-gravity wave and internal wave

100%

Debsarma S. , Das K. P.

2008

tom Vol. 13, no 3

653-668

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 the instability region expands with the decrease of thermocline depth. For surface capillary-gravity waves the growth rate of instability is much higher if the thermocline is formed at lower depth and for a fixed thermocline depth it increases with the increase of wave amplitude.

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

80%

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

2012

tom 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.

Fourth-order evolution equations for a surface gravity wave packet in a two layer fluid

80%

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

tom Vol. 15, no 4

1215-1225

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 different values of density ratio of the two fluids and for different values of the depth of the lighter fluid.