Journal ArticleDOI
On evolution equations for a three-dimensional surface gravity wave packet in a two-layer fluid
TLDR
In this article, two coupled nonlinear partial differential equations are derived, which describe nonlinear evolution of a three-dimensional surface gravity wave packet in a two-layer fluid, including the effect of its interaction with a long wavelength surface gravitywave and an internal wave.About:
This article is published in Wave Motion.The article was published on 1986-03-01. It has received 10 citations till now. The article focuses on the topics: Nonlinear system & Modulational instability.read more
Citations
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Journal ArticleDOI
A fourth-order evolution equation for deep water surface gravity waves in the presence of wind blowing over water
A. K. Dhar,K. P. Das +1 more
TL;DR: In this article, the stability of a train of nonlinear surface gravity waves in deep water in the presence of wind blowing over water is considered, and an evolution equation is derived for the wave envelope that is correct to fourth order in the wave steepness.
Journal ArticleDOI
Recovery of the elastic parameters of a layered half-space
Paul Sacks,Wolliam Symes +1 more
TL;DR: In this paper, the authors studied the problem of recovering the elastic parameters of a layered half-space from single component measurements of reflected waves, and applied it to reflection seismology.
Journal ArticleDOI
Fourth order nonlinear evolution equations for gravity-capillary waves in the presence of a thin thermocline in deep water
Suma Debsarma,K. P. Das +1 more
TL;DR: In this article, the stability and instability regions of a uniform gravity-capillary wave train are identified and expressions for the maximum growth rate of instability and the wavenumber at marginal stability are obtained.
Journal ArticleDOI
Fourth-order nonlinear evolution equations for surface gravity waves in the presence of a thin thermocline
Sudebi Bhattacharyya,K. P. Das +1 more
TL;DR: In this article, two coupled nonlinear evolution equations correct to fourth order in wave steepness are derived for a three-dimensional wave packet in the presence of a thin thermocline.
References
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Journal ArticleDOI
The disintegration of wave trains on deep water Part 1. Theory
T. Brooke Benjamin,J. E. Feir +1 more
TL;DR: In this paper, a theoretical analysis of the stability of periodic wave trains to small disturbances in the form of a pair of side-band modes is presented, where the wave train becomes highly irregular far from its origin, even when the departures from periodicity are scarcely detectable at the start.
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On three-dimensional packets of surface waves
A. Davey,Keith Stewartson +1 more
TL;DR: In this article, the authors used the method of multiple scales to derive the two coupled nonlinear partial differential equations which describe the evolution of a three-dimensional wavepacket of wavenumber k on water of finite depth.
Journal ArticleDOI
An exact theory of nonlinear waves on a Lagrangian-mean flow
TL;DR: In this article, an exact and very general Lagrangian-mean description of the back effect of oscillatory disturbances upon the mean state is given, which applies to any problem whose governing equations are given in the usual Eulerian form, and irrespective of whether spatial, temporal, ensemble, or two-timing averages are appropriate.
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On two-dimensional packets of capillary-gravity waves
TL;DR: In this article, the Stokes capillary-gravity wave train is studied and the evolution of a packet is described by two partial differential equations: the nonlinear Schroedinger equation with a forcing term and a linear equation, which is of either elliptic or hyperbolic type depending on whether the group velocity of the capillary gravity wave is less than or greater than the velocity of long gravity waves.
Journal ArticleDOI
Non-linear dispersion of water waves
TL;DR: In this article, the type of the differential equations for wave-train parameters (local amplitude, wave-number, etc.) is established, and the equations are hyperbolic or elliptic according to whether k 0 is less than or greater than 1.36.