Three-dimensional instabilities of periodic gravity waves in shallow water
article
A linear stability analysis of finite-amplitude periodic progressive gravity waves on
water of finite depth has extended existing results to steeper waves and shallower
water. Some new types of instability are found for shallow water. When the water
depth decreases, higher-order resonances lead to the dominant instabilities. In contrast
with the deep water case, we have found that in shallow water the dominant
instabilities are usually associated with resonant interactions between five, six, seven
and eight waves. For small steepness, dominant instabilities are quasi two-dimensional.
For moderate and large steepness, the dominant instabilities are three-dimensional
and phased-locked with the unperturbed nonlinear wave. At the margin of instability
diagrams, these results suggest the existence of new bifurcated three-dimensional
steady waves.
water of finite depth has extended existing results to steeper waves and shallower
water. Some new types of instability are found for shallow water. When the water
depth decreases, higher-order resonances lead to the dominant instabilities. In contrast
with the deep water case, we have found that in shallow water the dominant
instabilities are usually associated with resonant interactions between five, six, seven
and eight waves. For small steepness, dominant instabilities are quasi two-dimensional.
For moderate and large steepness, the dominant instabilities are three-dimensional
and phased-locked with the unperturbed nonlinear wave. At the margin of instability
diagrams, these results suggest the existence of new bifurcated three-dimensional
steady waves.
TNO Identifier
223261
Source
Journal of Fluid Mechanics, 561, pp. 471-437.
Pages
471-437
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