Fifth order evolution equation of gravity-capillary waves

Dipankar Chowdhury, Suma Debsarma


We extend the evolution equation for weak nonlinear gravity–capillary waves by including fifth-order nonlinear terms. Stability properties of a uniform Stokes gravity–capillary wave train is studied using the evolution equation obtained here. The region of stability in the perturbed wave-number plane determined by the fifth-order evolution equation is compared with that determined by third- and fourth-order evolution equations. We find that if the wave number of longitudinal perturbations exceeds a certain critical value, a uniform gravity–capillary wave train becomes unstable. This critical value increases as the wave steepness increases.



evolution equation, gravity–capillary wave, modulational instability, wind effect.


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.