The two‐dimensional stability of periodic and solitary wave trains on a water surface over arbitrary depth
作者:
E. Infeld,
J. Ziemkiewicz,
G. Rowlands,
期刊:
Physics of Fluids(00319171)
(AIP Available online 1987)
卷期:
Volume 30,
issue 8
页码: 2330-2338
ISSN:0031-9171
年代: 1987
DOI:10.1063/1.866123
出版商: AIP
数据来源: AIP
摘要:
The two‐surface dimensional dynamics of a periodically or soliton‐shaped modulated wave train on a water surface is investigated, using the Davey–Stewartson model. The depthhis taken to be uniform. The results obtained are twofold: the general behavior of the Benjamin–Feir (BF) instability is found for an arbitrary stationary envelope profile, thus generalizing Hayes’ analysis for uniform wave trains, and a new ‘‘Kdegeneracy’’ instability is found. The instability is always limited to ∼45° around the direction of propagation of the basic wave train and this critical angle decreases as the modulation becomes stronger. The new instability covers a narrow range of acute angles for 2&pgr;h/&lgr;≤1.363, where &lgr; is the wavelength of the carrier wave, and all angles for 2&pgr;h/&lgr;≥1.363. Thus our results add new significance to the famous critical number 1.363. A simple explanation of how the new instability comes about concludes the paper. Agreement with previous work is demonstrated.
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