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1 International Journal of Applied Mechanics and Engineering

1 2008

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On resonant interaction of capillary-gravity wave and internal wave

Debsarma S., Das K. P.

International Journal of Applied Mechanics and Engineering

2008

Vol. 13, no 3

653-668

The fourth order nonlinear evolution equations are derived for a capillary-gravity wave packet for the case of resonant interaction with internal wave in the presence of a thin thermocline at a finite depth in deep water. These equations are used to make stability analysis of a uniform capillary-gravity wave train when resonance condition is satisfied. It is observed that for surface gravity waves the instability region expands with the decrease of thermocline depth. For surface capillary-gravity waves the growth rate of instability is much higher if the thermocline is formed at lower depth and for a fixed thermocline depth it increases with the increase of wave amplitude.