The effect of uniform wind flow in a situation of crossing sea states is studied here on the stability analysis for a pair of obliquely interacting uniform wave trains. It is observed that the growth rate of instability in crossing seas in the presence of wind flow is much higher than that in the absence of wind flow. It is also found that the growth rate of instability increases as the wind flow velocity increases up to some critical velocity beyond which the wave becomes linearly unstable and consequently the present analysis does not remain valid. The growth rate of instability obtained here is also greater than that for a single wave packet propagating in the presence of uniform wind flow. © 2016 Elsevier Masson SAS

SUMA DEBSARMA

Applied Mathematics

S SENAPATI

S KUNDU

K P DAS

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

European Journal of Mechanics, B/Fluids

In this study, we investigate modulational instability in the presence of wind flow in a situation where sea states crossed over water with a finite depth. It is assumed that the wind flows in a specific direction to produce angles with two directions of propagation by two wave systems with the same carrier wave number and same frequency. The evolution equations considered in this study represent a balance among the effects of wind forcing, dispersion, and nonlinearity at the lowest order. These evolution equations are used to study the stability of the uniform wave solution in crossing seas. We show that in the presence of wind flow, the uniform waves grow super-exponentially. We also demonstrate that the region of asymptotic instability in the perturbed wave number plane is larger than that in the absence of wind flow. © 2015 Elsevier Ltd.

Ocean Modelling

Modulational instability of two crossing waves in the presence of wind flow

The present work is motivated by the work of Leblanc ["Amplification of nonlinear surface waves by wind," Phys. Fluids 19, 101705 (2007)] which showed that Stokes waves grow super exponentially under fair wind as a result of modulational instability. Here, we have studied the effect of wind in a situation of crossing sea states characterized by two obliquely propagating wave systems in deep water. It is found that the wind-forced uniform wave solution in crossing seas grows explosively with a super-exponential growth rate even under a steady horizontal wind flow. This is an important piece of information in the context of the formation of freak waves. © 2014 AIP Publishing LLC.

Physics of Fluids

Wind-forced modulations in crossing sea states over infinite depth water

Starting from the Zakharov integral equation, two coupled fourth-order nonlinear equations have been derived for the evolution of the amplitudes of two capillary-gravity wave packets propagating in the same direction. The two evolution equations are used to investigate the stability of a uniform capillary-gravity wave train in the presence of another having the same group velocity. The relative changes in phase velocity of each uniform wave train due to the presence of the other one have been shown in figures for different wave numbers. The condition of instability of a wave of greater wavelength in the presence of a wave of shorter wavelength is obtained. It is observed that the instability region for a surface gravity wave train in the presence of a capillary-gravity wave train expands with the increase of wave steepness of the capillary-gravity wave train. It is found that the presence of a uniform capillary-gravity wave train causes an increase in the growth rate of instability of a uniform surface gravity wave train. © 2007 American Institute of Physics.

Fulltext

Fourth-order nonlinear evolution equations for a capillary-gravity wave packet in the presence of another wave packet in deep water

Asymptotically exact nonlocal fourth-order nonlinear evolution equations are derived for two counterpropagating capillary-gravity wave packets on the surface of water of infinite depth. On the basis of these equations a stability analysis is made for a uniform standing capillary-gravity wave for longitudinal perturbation. The instability conditions and an expression for the maximum growth rate of instability are obtained. Significant deviations are noticed between the results obtained from third-order and fourth-order nonlinear evolution equations. © 2002 American Institute of Physics.

Fourth-order nonlinear evolution equations for counterpropagating capillary-gravity wave packets on the surface of water of infinite depth

Fourth-order nonlinear evolution equations, which are a good starting point for the study of nonlinear water waves as first pointed out by Dysthe [Proc. R. Soc. London Ser. A 369, 105 (1979)] and later elaborated by Janssen [J. Fluid Mech. 126, 1 (1983)], are derived for a deep-water surface gravity wave packet in the presence of a second wave packet. Here it is assumed that the space variation of the amplitude takes place only in a direction along which the group velocity projection of the two waves overlap. Stability analysis is made for a uniform Stokes wave train in the presence of a second wave train. Graphs are plotted for maximum growth rate of instability and for wave number at marginal stability against wave steepness. Significant deviations are noticed from the results obtained from the third-order evolution equations which consist of two coupled nonlinear Schrödinger equations. © 1991 American Institute of Physics.

Journal	Data powered by TypesetEuropean Journal of Mechanics, B/Fluids
Publisher	Data powered by TypesetElsevier Ltd
ISSN	0997-7546
Open Access	No