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Modulation of Gravity Waves with Shear in Water
Author(s) -
Baumstein Anatoly I.
Publication year - 1998
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00081
Subject(s) - amplitude , shear (geology) , physics , mechanics , gravity wave , nonlinear system , instability , classical mechanics , infinitesimal , wave propagation , geology , mathematical analysis , mathematics , optics , quantum mechanics , petrology
The effect of water shear on the stability of infinitesimal perturbations (in the form of side bands) to a finite‐amplitude gravity wave is investigated both numerically and analytically. The shear is modeled by a piecewise‐linear velocity profile. Nonlinear cubic Schrödinger equation for the wave envelope of a slowly varying wave train is derived. It is shown that depending on the direction of propagation (along or against the shear) of the finite‐amplitude waves, the effect of shear on the stability is substantially different. In most cases, however, the shear strength increase first enhances, but later suppresses, the instability.