Crest instabilities of gravity waves. Part 2. Matching and asymptotic analysis

Autor:	M. J. H. Fox, R. P. Cleaver, Michael S. Longuet-Higgins
Rok vydání:	1994
Předmět:	Physics Subharmonic function Mechanical Engineering Mechanics Condensed Matter Physics Conservative vector field Instability Physics::Fluid Dynamics Classical mechanics Flow (mathematics) Mechanics of Materials Fluid dynamics Crest Asymptote Asymptotic expansion
Zdroj:	Journal of Fluid Mechanics. 259:333-344
ISSN:	1469-7645 0022-1120
DOI:	10.1017/s0022112094000169
Popis:	In a previous study (Longuet-Higgins & Cleaver 1994) we calculated the stability of the flow near the crest of a steep, irrotational wave, the ‘almost-highest’ wave, considered as an isolated wave crest. In the present paper we consider the modification of this inner flow when it is matched to the flow in the rest of the wave, and obtain the normal-mode perturbations of the modified inner flow. It is found that there is just one exponentially growing mode. Its rate of growth β is a decreasing function of the matching parameter ε and hence a decreasing function of the wave steepness ak. When compared numerically to the rates of growth of the lowest superharmonic instability in a deep-water wave as calculated by Tanaka (1983) it is found that the present theory provides a satisfactory asymptote to the previously calculated values of the growth rate. This suggests that the instability of the lowest superharmonic is essentially due to the flow near the crest of the wave.
Databáze:	OpenAIRE
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