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ORIGINAL PAPER
Fourth Order Nonlinear Evolution Equation For Interfacial Gravity Waves In The Presence Of Air Flowing Over Water And A Basic Current Shear
1
Department of Mathematics, Bengal Engineering and Science University, Shibpur, P.O. Botanic Garden, Shibpur, Howrah - 711103, West Bengal, INDIA
Online publication date: 2015-09-19
Publication date: 2015-08-01
International Journal of Applied Mechanics and Engineering 2015;20(3):517-530
KEYWORDS
ABSTRACT
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.
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