Abstract: Asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two counter propagating surface capillary gravity wave packets in deep water in the presence of wind flowing b over water. On the basis of these evolution equations stability analysis is made for a uniform standing surface capillary gravity wave trains for longitudinal perturbation. Instability condition is obtained and graphs are plotted for maximum growth rate of instability and for wave number at marginal stability against wave steepness for some different values of dimensionless wind velocity. Significant deviations are noticed from the results obtained from third order nonlinear evolution equations.
Keywords: Nonlinear evolution equation, capillary gravity, waves, stability analysis.
Title: Fourth Order Nonlinear Evolution Equations for Counter Propagating Capillary Gravity Wave Packets In The Presence Of Wind Flowing Over Water
Author: A.K. DHAR, J.MONDAL
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
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