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EFFECT OF UNIFORM WIND FLOW ON MODULATIONAL INSTABILITY OF TWO CROSSING WAVES OVER FINITE DEPTH WATER

Part of: Incompressible inviscid fluids Hydrodynamic stability

Published online by Cambridge University Press:  31 August 2018

SUMANA KUNDU Open the ORCID record for SUMANA KUNDU [Opens in a new window] ,
SUMA DEBSARMA Open the ORCID record for SUMA DEBSARMA [Opens in a new window]  and
K. P. DAS
SUMANA KUNDU*
Affiliation:
Salkia Mrigendra Dutta Smriti Balika Vidyapith (High), Salkia, Howrah-711106, India email [email protected]
SUMA DEBSARMA
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Kolkata 700009, India email [email protected], [email protected]
K. P. DAS
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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The effect of uniform wind flow on modulational instability of two crossing waves is studied here. This is an extension of an earlier work to the case of a finite-depth water body. Evolution equations are obtained as a set of three coupled nonlinear equations correct up to third order in wave steepness. Figures presented in this paper display the variation in the growth rate of instability of a pair of obliquely interacting uniform wave trains with respect to the changes in the air-flow velocity, depth of water medium and the angle between the directions of propagation of the two wave packets. We observe that the growth rate of instability increases with the increase in the wind velocity and the depth of water medium. It also increases with the decrease in the angle of interaction of the two wave systems.

Keywords

crossing seasevolution equationgravity wavesinstabilitywind effect

MSC classification

Primary: 76B07: Free-surface potential flows
Secondary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76E17: Interfacial stability and instability
Type
Research Article
Information
The ANZIAM Journal , Volume 60 , Issue 1 , July 2018 , pp. 118 - 136
Copyright
© 2018 Australian Mathematical Society 

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