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Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2013, Volume 98, Issue 4, Pages 265–269
DOI: https://doi.org/10.7868/S0370274X1316011X (Mi jetpl3503) 		 
This article is cited in 12 scientific papers (total in 12 papers)

NONLINEAR DYNAMICS

Universal power law for the energy spectrum of breaking Riemann waves

D. E. Pelinovskyab, E. N. Pelinovskycbd, E. A. Kartashovad, T. G. Talipovacb, A. Giniyatullinb

a McMaster University
b Nizhny Novgorod State Technical University
c Institute of Applied Physics, Russian Academy of Sciences, Nizhnii Novgorod
d Johannes Kepler University Linz
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DOI: https://doi.org/10.7868/S0370274X1316011X
Abstract: The universal power law for the spectrum of one-dimensional breaking Riemann waves is justified for the simple wave equation. The spectrum of spatial amplitudes at the breaking time $t = t_b$ has an asymptotic decay of $k^{-4/3}$, with corresponding energy spectrum decaying as $k^{-8/3}$. This spectrum is formed by the singularity of the form $(x-x_b)^{1/3}$ in the wave shape at the breaking time. This result remains valid for arbitrary nonlinear wave speed. In addition, we demonstrate numerically that the universal power law is observed for long time in the range of small wave numbers if small dissipation or dispersion is accounted in the viscous Burgers or Korteweg–de Vries equations.
Received: 21.06.2013
Revised: 09.07.2013
English version:
Journal of Experimental and Theoretical Physics Letters, 2013, Volume 98, Issue 4, Pages 237–241
DOI: https://doi.org/10.1134/S0021364013170116
Bibliographic databases:
Document Type: Article
Language: English
Citation: D. E. Pelinovsky, E. N. Pelinovsky, E. A. Kartashova, T. G. Talipova, A. Giniyatullin, “Universal power law for the energy spectrum of breaking Riemann waves”, Pis'ma v Zh. Èksper. Teoret. Fiz., 98:4 (2013), 265–269; JETP Letters, 98:4 (2013), 237–241
Citation in format AMSBIB
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