Evolution of a pair of random inhomogeneous wave systems over infinite-depth water

Suma Debsarma; Dipankar Chowdhury

doi:10.21914/anziamj.v61i0.12754

Authors

Suma Debsarma Department of Applied Mathematics, University of Calcutta.
Dipankar Chowdhury Department of Applied Mathematics, University of Calcutta.

DOI:

https://doi.org/10.21914/anziamj.v61i0.12754

Keywords:

crossing sea states, evolution equation, instability, randomness.

Abstract

A system of two coupled nonlinear spectral transport equations is derived for two obliquely interacting narrowband Gaussian random surface wavetrains, slowly varying in space and time. Using these two equations, stability analysis is performed for two initially homogeneous wave spectra, subject to unidirectional perturbations. We observe that the effect of randomness produces a decrease in the growth rate of instability, but it is higher than the growth for a single wavetrain. The growth rate of instability is observed to decrease with the increase in spectral width. doi:10.1017/S144618111900004X

Author Biography

Suma Debsarma, Department of Applied Mathematics, University of Calcutta.

Professor, Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India.