Stability analysis from fourth order evolution equation for counter-propagating gravity wave packets in the presence of wind flowing over water

Authors

  • Asoke Kumar Dhar Department of Mathematics, Bengal Engineering and Science University, Shibpur, P.O. Botanic Garden, Howrah-711103, West Bengal, India
  • J. Mondal Department of Mathematics, Kandi Raj High School, P.O. Kandi, Murshidabad-742137, West Bengal, India

DOI:

https://doi.org/10.21914/anziamj.v56i0.8139

Abstract

Fourth order nonlinear evolution equations are derived for two counter-propagating surface gravity wave packets in deep water in the presence of wind flowing over water. The resulting equations are asymptotically exact and nonlocal. Stability analysis is made for a uniform standing surface gravity wave train for longitudinal perturbation on the basis of these equations. Graphs are plotted for maximum growth rate of instability and for wave number at marginal stability against wave steepness for some different values of dimensionless wind velocity. Significant deviations are noticed between the results obtained from third order and fourth order nonlinear evolution equations. This paper has an application in rough waves. References
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Author Biography

Asoke Kumar Dhar, Department of Mathematics, Bengal Engineering and Science University, Shibpur, P.O. Botanic Garden, Howrah-711103, West Bengal, India

MATHEMATICS, IIES&T

Published

2015-03-20

Issue

Section

Articles for Electronic Supplement