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A new approach to the study of standing surface waves of finite amplitude

Ein neuer Weg zur Darstellung stehender Oberflächenwellen endlicher Amplitude

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Summary

A non-linear theory of periodic gravity waves in an incompressible inviscid liquid is presented. The problem which is found to be a singular perturbation problem is treated accordingly with considerable ease. Results for frequency, surface profile and potential function are calculated up to third order as series in powers of a parameter which is the ratio of the amplitude to wavelength. Unlike the linear theory, in this third-order theory, the frequency is found to depend on the amplitude also and decreases with increasing amplitude. The results agree with those obtained earlier by a complicated and labourious method and confirmed by experiments.

Zusammenfassung

Es wird eine nichtlineare Theorie periodischer Gravitationswellen in einer inkompressiblen reibungslosen Flüssigkeit vorgelegt. Das Problem wird als singuläres Störungsproblem behandelt. Ergebnisse für Frequenz, Wellenprofil und Potentialfunktion werden berechnet bis zu Gliedern dritter Ordnung eines Störparameters, welcher das Verhältnis von Amplitude zu Wellenlänge darstellt. Im Gegensatz zur linearen Theorie hängt die Frequenz in der nichtlinearen Theorie von der Amplitude ab und nimmt ab mit zunehmender Amplitude.

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References

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Authors and Affiliations

  1. Department of Applied Mechanics and Aeronautics, Indian Institute of Technology, Madras 36, India

    N. R. Rajappa

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  1. N. R. Rajappa
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Rajappa, N.R. A new approach to the study of standing surface waves of finite amplitude. Acta Mechanica 9, 130–136 (1970). https://doi.org/10.1007/BF01176615

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  • DOI: https://doi.org/10.1007/BF01176615

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