EFFECT OF COUNTERPROPAGATING CAPILLARY GRAVITY WAVE PACKETS ON THIRD ORDER NONLINEAR ‎‎E‎VOLUTION EQUATIONS IN THE PRESENCE OF WIND FLOWING OVER WATER

Subject Areas : International Journal of Mathematical Modelling & Computations

A. K. Dhar ¹ , Joydev Mondal ²

1 -
2 - IIEST,WESTBENGAL,INDIA India IIEST,MATHEMATICS,SHIBPUR,WESTBENGAL, INDIA

Received: 2016-04-15 Accepted : 2016-04-15 Published : 2015-03-21

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Abstract :

Asymptotically exact and nonlocal third order nonlinear evolution equations are derivedfor two counterpropagating surface capillary gravity wave packets in deep water in thepresence of wind flowing over water.From these evolution equations stability analysis ismade for a uniform standing surface capillary gravity wave trains for longitudinal perturbation. Instability condition is obtained and graphs are plotted for maximum growth rateof instability and for wave number at marginal stability against wave steepness for some different values of dimensionless wind velocity.