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On transient development of surface waves

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Summary

An initial value investigation into the development of two-dimensional surface waves generated by a harmonically oscillating pressure acting on the free surface of a fluid of limited, unlimited and very shallow depth is made in this paper in considerable detail. A rigorous mathematical treatment of the problem is given with the aid of integral transform technique in conjunction with asymptotic methods. The limiting behaviour of the asymptotic solution as timet tends to infinity has been given due attention. It is shown that the ultimate steady state is attained in the case of physically realisable pressure distributions. Finally, a discussion of the wave motions including the main predictions of this theory is presented in some detail. A careful consideration has also been given to examine the validity of Lighthill's prediction regarding the steady state.

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Authors and Affiliations

  1. Dept. of Appl. Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    Lokenath Debnath

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  1. Lokenath Debnath
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Debnath, L. On transient development of surface waves. Journal of Applied Mathematics and Physics (ZAMP) 19, 948–961 (1968). https://doi.org/10.1007/BF01602275

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  • DOI: https://doi.org/10.1007/BF01602275

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