Asymptotic analysis of surface waves due to high-frequency disturbances

Nikolay Kuznetsov; Vladimir Gilelevich Maz'ya

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1997)

  • Volume: 8, Issue: 1, page 5-29
  • ISSN: 1120-6330

Abstract

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The present paper is devoted to the asymptotic analysis of the linear unsteady surface waves. We study two problems concerned with high-frequency surface and submerged disturbances. The two-scale asymptotic series are obtained for the velocity potential. The principal terms in the asymptotics of some hydrodynamical characteristics of the wave motion (the free surface elevation, the energy, etc.) are described.

How to cite

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Kuznetsov, Nikolay, and Maz'ya, Vladimir Gilelevich. "Asymptotic analysis of surface waves due to high-frequency disturbances." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 8.1 (1997): 5-29. <http://eudml.org/doc/244100>.

@article{Kuznetsov1997,
abstract = {The present paper is devoted to the asymptotic analysis of the linear unsteady surface waves. We study two problems concerned with high-frequency surface and submerged disturbances. The two-scale asymptotic series are obtained for the velocity potential. The principal terms in the asymptotics of some hydrodynamical characteristics of the wave motion (the free surface elevation, the energy, etc.) are described.},
author = {Kuznetsov, Nikolay, Maz'ya, Vladimir Gilelevich},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Surface waves theory; Asymptotic expansions; Cauchy-Poisson problem; Two-scaled asymptotic series; two-scale asymptotic series; velocity potential; free surface elevation; energy},
language = {eng},
month = {4},
number = {1},
pages = {5-29},
publisher = {Accademia Nazionale dei Lincei},
title = {Asymptotic analysis of surface waves due to high-frequency disturbances},
url = {http://eudml.org/doc/244100},
volume = {8},
year = {1997},
}

TY - JOUR
AU - Kuznetsov, Nikolay
AU - Maz'ya, Vladimir Gilelevich
TI - Asymptotic analysis of surface waves due to high-frequency disturbances
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1997/4//
PB - Accademia Nazionale dei Lincei
VL - 8
IS - 1
SP - 5
EP - 29
AB - The present paper is devoted to the asymptotic analysis of the linear unsteady surface waves. We study two problems concerned with high-frequency surface and submerged disturbances. The two-scale asymptotic series are obtained for the velocity potential. The principal terms in the asymptotics of some hydrodynamical characteristics of the wave motion (the free surface elevation, the energy, etc.) are described.
LA - eng
KW - Surface waves theory; Asymptotic expansions; Cauchy-Poisson problem; Two-scaled asymptotic series; two-scale asymptotic series; velocity potential; free surface elevation; energy
UR - http://eudml.org/doc/244100
ER -

References

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  1. FRIEDMAN, A. - SHINBROT, M., The initial value problem for the linearized equation of water waves, I. J. Math. Mech., 17, 1967, 107-180. Zbl0148.35402MR214932
  2. FRIEDMAN, A. - SHINBROT, M., The initial value problem for the linearized equation of water waves, II. J. Math. Mech., 18, 1969, 1177-1194. Zbl0193.27401MR273223
  3. GARIPOV, R. M., On the linear theory of gravity waves: the theorem of existence and uniqueness. Arch. Rat. Mech. Anal., 24, 1967, 352-362. Zbl0149.45603MR211669
  4. GRADSHTEIN, I. S. - RYZHIK, I. M., Tables of Integrals, Sums, Series and Products. Fizmatgiz, Moscow1962 (in Russian). 
  5. HAMDACHE, K., Forward speed motions of a submerged body. The Cauchy problem. Math. Meth. Appl. Sci., 6, 1984, 371-392. Zbl0568.35059MR761499DOI10.1002/mma.1670060123
  6. NEWMAN, J. N., The theory of ship motions. Adv. Appl. Mech., 18, 1978, 221-283. MR564896
  7. SRETENSKIY, L. N., The Theory of Wave Motions of a Fluid. Nauka, Moscow1977 (in Russian). 
  8. STOKER, J. J., Water Waves. Interscience, New York1957. Zbl0078.40805
  9. WEHAUSEN, J. V. - LAITONE, E. V., Surface waves. Handbuch der Physik, Springer-Verlag, Berlin, 9, I960, 446-778. MR119656
  10. WHITTAKER, E. T. - WATSON, G. N., A Course of Modem Analysis. University Press, Cambridge1927. JFM53.0180.04

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