Singularities and spectral asymptotics of a random nonlinearwave in a nondispersive system

Gurbatov, S.N.; Rudenko, O.V.; Tyurina, A.V.

Авторы: Gurbatov S.N., Rudenko O.V., Tyurina A.V.
Журнал: Wave Motion
Том: 95
Номер: 102519
Год издания: 2020
Издательство: Elsevier BV
Местоположение издательства: Netherlands
Первая страница: 1
Последняя страница: 15
DOI: 10.1016/j.wavemoti.2020.102519
Аннотация: In this paper, we study the propagation of high-intensity acoustic noise in free spaceand in waveguide systems. A mathematical model generalizing the Burgers equation isused. It describes the nonlinear wave evolution inside tubes of variable cross-section,as well as in ray tubes, if the geometric approximation for heterogeneous media isused. The generalized equation transforms to the common Burgers equation with adissipative parameter, known as the ‘‘Reynolds–Goldberg number’’. In our model, thisnumber depends on the distance travelled by the wave. With a zero ‘‘viscous’’ dissipativeterm, the model reduces to the Riemann (or Hopf) equation. Its solution presents thefield by an implicit function. The spectral form of this solution makes it possible to deriveexplicit expressions for both dynamic and statistical characteristics of intense waves. Theuse of a spectral approach allowed us to describe the high-intensity noise in media withzero and finite viscosity. Applicability conditions of these solutions are defined. Since thephase matching is fulfilled for any triplet of interacting spectral components, there isan avalanche-like increase in the number of harmonics and the formation of shocks.The relationship between these discontinuities and other singularities and the high-frequency asymptotic of intense noise is studied. The possibility is shown to enhancenonlinear effects in waveguide systems during the evolution of noise.© 2020Published by Elsevier
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Singularities and spectral asymptotics of a random nonlinearwave in a nondispersive systemстатья

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