Parasitic capillary waves on small-amplitude gravity waves with a linear shear current

Document Type

Article

Publication Date

11-1-2021

Abstract

This paper describes a numerical investigation of ripples generated on the front face of deep-water gravity waves progressing on a vertically sheared current with the linearly changing horizontal velocity distribution, namely parasitic capillary waves with a linear shear current. A method of fully nonlinear computation using conformal mapping of the flow domain onto the lower half of a complex plane enables us to obtain highly accurate solutions for this phenomenon with the wide range of parameters. Numerical examples demonstrated that, in the presence of a linear shear current, the curvature of surface of underlying gravity waves depends on the shear strength, the wave energy can be transferred from gravity waves to capillary waves and parasitic capillary waves can be generated even if the wave amplitude is very small. In addition, it is shown that an approximate model valid for small-amplitude gravity waves in a linear shear current can reasonably well reproduce the generation of parasitic capillary waves.

Identifier

85119618696 (Scopus)

Publication Title

Journal of Marine Science and Engineering

External Full Text Location

https://doi.org/10.3390/jmse9111217

e-ISSN

20771312

Issue

11

Volume

9

Grant

2021H1D3A2A01082312

Fund Ref

Japan Society for the Promotion of Science

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