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Appearance and disappearance of non-symmetric progressive capillary–gravity waves of deep water

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Abstract

We report our numerical computation of non-symmetric progressive capillary–gravity waves on water of infinite depth. The problem considered here is a classical one and there have been lots of studies on symmetric wave solutions. However we know only a few about the existence of non-symmetric progressive waves. Numerically there are only the works of Zufiria (J Fluid Mech 180:371–385, 1987; J Fluid Mech 181:17–39, 1987; J Fluid Mech 191:341–372, 1987) for gravity waves on water of finite/infinite depth and capillary–gravity waves of finite depth. All of them are non-symmetric waves with six peaks in one wave length. We made a thorough investigation in the case of capillary–gravity waves of deep water in a different numerical method with a formulation different from that of Zufiria. Then we not only demonstrate the existence of non-symmetric waves with six peaks but also clarify the mechanism of their appearance/disappearance. Furthermore we obtained a new type of non-symmetric waves.

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Authors and Affiliations

  1. Department of Mathematical and Physical Sciences, Japan Women’s University, Mejirodai, Bunkyoku, Tokyo, 112-8681, Japan

    Chika Shimizu & Mayumi Shōji

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  1. Chika Shimizu
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  2. Mayumi Shōji
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Correspondence to Mayumi Shōji.

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Shimizu, C., Shōji, M. Appearance and disappearance of non-symmetric progressive capillary–gravity waves of deep water. Japan J. Indust. Appl. Math. 29, 331–353 (2012). https://doi.org/10.1007/s13160-012-0070-4

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  • DOI: https://doi.org/10.1007/s13160-012-0070-4

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