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- W3181692912 abstract "In this paper, we examine the formation of small capillary waves (parasitic ripples) on the surface of steep steadily-travelling gravity waves. Previously, authors have developed ad-hoc analytical procedures for describing the formation of such parasitic ripples in potential flows; however, it has not been clear whether the small-surface tension limit is well-posed -- that is, whether it is possible for an appropriate travelling gravity-capillary wave to be continuously deformed to the classic Stokes wave in the limit of vanishing surface tension. The work of Chen & Saffman (1980) had suggested smooth continuation was not possible. In this paper, we numerically explore the low surface tension limit of the steep gravity-capillary travelling-wave problem. Our results allow for a classification of the bifurcation structure that arises, and serve to unify a number of previous numerical studies. Crucially, we demonstrate that different choices of solution amplitude can lead to subtle restrictions on the continuation procedure; the use of wave energy as an amplitude condition allows solution branches to be continuously deformed to the zero surface tension limit." @default.
- W3181692912 created "2021-07-19" @default.
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- W3181692912 date "2021-07-09" @default.
- W3181692912 modified "2023-10-09" @default.
- W3181692912 title "On the structure of steady parasitic gravity-capillary waves in the small surface tension limit" @default.
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- W3181692912 doi "https://doi.org/10.1017/jfm.2021.514" @default.
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