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1
Content available remote 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
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2012
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Vol. 17, no. 2
481-493
EN
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.
2
Content available remote Fourth-order evolution equations for a surface gravity wave packet in a two layer fluid
Senapati S., Debsarma S., Das K. P.
International Journal of Applied Mechanics and Engineering
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2010
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Vol. 15, no 4
1215-1225
EN
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.
3
Content available remote On resonant interaction of capillary-gravity wave and internal wave
Debsarma S., Das K. P.
International Journal of Applied Mechanics and Engineering
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2008
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Vol. 13, no 3
653-668
EN
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.
4
Content available remote A higher order nonlinear evolution equation for much broader bandwidth gravity waves in deep water
Debsarma S., Das K. P.
International Journal of Applied Mechanics and Engineering
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2007
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Vol. 12, no 2
557-563
EN
A higher order nonlinear evolution equation for gravity waves in deep water is derived from Zakharov's integral equation which is valid for a much broader bandwidth gravity waves than considered previously. The instability regions in the perturbed wave-number space for a uniform Stokes wave obtained from this equation is shown to fit nicely those obtained by McLean et al. [Phys. Rev. Lett. 46, 817-820(1981)] by exact numerical method.
5
Content available remote Fourth order nonlinear evolution equation for capillary gravity waves in deep water in the presence of a thin thermocline including the effect of wind
Debsarma S., Das K. P.
International Journal of Applied Mechanics and Engineering
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2003
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Vol. 8, no 2
177-193
EN
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.
6
Content available remote The effect of randomness on stability of surface gravity waves from fourth order nonlinear evolution equation
Dhar A. K., Das K. P.
International Journal of Applied Mechanics and Engineering
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2001
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Vol. 6, no 1
11-34
EN
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 equation stability analysis is made for an initial homogeneous wave spectrum having a very simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained, in which higher order contribution comes from only one of the fourth order terms in the evolution equation, which is responsible for wave-induced mean flow. This higher order contribution in this expression for growth rate of instability produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and ultimately the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order terms in the evolution equation.
7
A fourth order evolution equation for capillary-gravity waves including the effects of wind input and shear in the water current
Dhar A. K., Das K. P.
Applied Mechanics and Engineering
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1999
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Vol. 4, no 1
5-24
EN
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 (linearly) and weakly growing (linearly) waves for some different values of friction velocity of the flow. From these graphs it is found that the effect of the wind input and shear in water current is to produce a decrease in the growth rate for weakly damped (linearly) waves and to produce an increase in growth rate for weakly growing (linearly) waves. The shear in the water current and the wind input are found to produce a shrinkage in the instability regions.
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