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EVOLUTION OF A PAIR OF RANDOM INHOMOGENEOUS WAVE SYSTEMS OVER INFINITE-DEPTH WATER

Part of: Incompressible inviscid fluids Hydrodynamic stability

Published online by Cambridge University Press:  15 May 2019

S. DEBSARMA Open the ORCID record for S. DEBSARMA [Opens in a new window]  and
D. CHOWDHURY Open the ORCID record for D. CHOWDHURY [Opens in a new window]
S. DEBSARMA*
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Kolkata 700009, India email [email protected], [email protected]
D. CHOWDHURY
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Kolkata 700009, India email [email protected], [email protected]
*
✉[email protected]
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Abstract

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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.

Keywords

crossing sea statesevolution equationinstabilityrandomness

MSC classification

Primary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Secondary: 76B07: Free-surface potential flows 76E99: None of the above, but in this section
Type
Research Article
Information
The ANZIAM Journal , Volume 61 , Issue 2 , April 2019 , pp. 233 - 247
Copyright
© 2019 Australian Mathematical Society 

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