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Content available The effect of randomness on the stability of capillary gravity waves in the presence of air flowing over water
Majumder D. P., Dhar A. K.
International Journal of Applied Mechanics and Engineering
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2015
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Vol. 20, no. 4
835--855
EN
A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a 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 a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.
2
Content available Fourth order nonlinear evolution equation for interfacial gravity waves in the presence of air flowing over water and a basic current shear
Majumder D. P., Dhar A. K.
International Journal of Applied Mechanics and Engineering
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2015
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Vol. 20, no. 3
517--530
EN
A fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves as first pointed out by Dysthe (1979) is derived for gravity waves propagating at the interface of two superposed fluids of infinite depth in the presence of air flowing over water and a basic current shear. A stability analysis is then made for a uniform Stokes gravity wave train. Graphs are plotted for the maximum growth rate of instability and for wave number at marginal stability against wave steepness for different values of air flow velocity and basic current shears. Significant deviations are noticed from the results obtained from the third order evolution equation, which is the nonlinear Schrödinger equation.
3
Content available remote 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
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2011
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Vol. 16, no. 2
425-434
EN
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.
4
Content available remote 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
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2009
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Vol. 14, no. 4
989-1008
EN
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.
5
Content available remote Stability analysis from fourth order evolution equation for deep water capillary-gravity waves in the presence of air flowing over water
Majumder D. P., Dhar A. K.
International Journal of Applied Mechanics and Engineering
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2009
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Vol. 14, no. 2
433-442
EN
Fourth order nonlinear evolution equations, which are a good starting point for the study of nonlinear water waves as first pointed out by Dysthe (1979) and later elaborated by Janssen (1983), are derived for deep water capillary-gravity waves in the presence of air flowing over water. Stability analysis is then made for a uniform Stokes capillary gravity wave train. Graphs are plotted for the maximum growth rate of instability, the frequency at marginal stability and the frequency separation for fastest growing side-band component as a function of wave steepness. Significant deviations are noticed from the results obtained from the third-order evolution equation, which is the nonlinear Schrödinger equation.
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