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Parasitic Capillary Waves on Small-Amplitude Gravity Waves with a Linear Shear Current

1
Department of Mathematics and Informatics, Ibaraki University, Mito 310-8512, Japan
2
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102-1982, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Christian Kharif
J. Mar. Sci. Eng. 2021, 9(11), 1217; https://doi.org/10.3390/jmse9111217
Received: 10 October 2021 / Revised: 29 October 2021 / Accepted: 30 October 2021 / Published: 4 November 2021
(This article belongs to the Special Issue Water Waves on Vortical Flows)
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. View Full-Text
Keywords: water waves; gravity-capillary waves; shear current; fully nonlinear computation; conformal mapping water waves; gravity-capillary waves; shear current; fully nonlinear computation; conformal mapping
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MDPI and ACS Style

Murashige, S.; Choi, W. Parasitic Capillary Waves on Small-Amplitude Gravity Waves with a Linear Shear Current. J. Mar. Sci. Eng. 2021, 9, 1217. https://doi.org/10.3390/jmse9111217

AMA Style

Murashige S, Choi W. Parasitic Capillary Waves on Small-Amplitude Gravity Waves with a Linear Shear Current. Journal of Marine Science and Engineering. 2021; 9(11):1217. https://doi.org/10.3390/jmse9111217

Chicago/Turabian Style

Murashige, Sunao, and Wooyoung Choi. 2021. "Parasitic Capillary Waves on Small-Amplitude Gravity Waves with a Linear Shear Current" Journal of Marine Science and Engineering 9, no. 11: 1217. https://doi.org/10.3390/jmse9111217

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