STABILITY ANALYSIS FROM FOURTH ORDER NONLINEAR EVOLUTION EQUATIONS FOR TWO CAPILLARY GRAVITY WAVE PACKETS IN THE PRESENCE OF WIND OWING OVER WATER.

Mondal, J.; Dhar, K.

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	STABILITY ANALYSIS FROM FOURTH ORDER NONLINEAR EVOLUTION EQUATIONS FOR TWO CAPILLARY GRAVITY WAVE PACKETS IN THE PRESENCE OF WIND OWING OVER WATER.
Article 3, Volume 6, 2 (Spring), Winter 2016, Page 129-147 PDF (803 K)
Authors
J. Mondal¹; K. Dhar²
¹Department of Mathematics,Indian Institute of Engineering Science and Technology, P. O. Botanical Garden, Howrah - 711103, West Bengal, India;
²Department of Mathematics,IIEST, Howrah - 711103, West Bengal, India.
Abstract
Asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillary-gravity wave packets propagating in the same direction in the presence of wind flowing over water.We have used a general method, based on Zakharov integral equation.On the basis of these evolution equations,the stability analysis is made for a uniform capillary gravity wave train in the presence of another wave train having the same group velocity. 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.


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