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Probability analysis of random plane waves in gas dynamics

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Abstract

A statistical analysis is made of random nonlinear plane waves in a gas with polytropic exponent γ = 3 by reduction of the original problem to an auxiliary Cauchy boundary-value problem for a system of stochastic ordinary differential equations. The probability distribution is found for the velocity and density of the gas in the case when at the initial time the gas density is constant and the velocity field Gaussian and statistically homogeneous. It is noted that there exists a finite time of statistical nonlinear interaction of colliding waves during which the probability distribution of the velocity and density of the gas can be essentially non-Gaussian.

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Authors and Affiliations

  1. Gor'kii

    A. I. Saichev

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  1. A. I. Saichev
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Translated from Izvesitya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–104, September–October, 1982.

I thank A. N. Malakhov and S. N. Gurbatov for helpful discussions.

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Saichev, A.I. Probability analysis of random plane waves in gas dynamics. Fluid Dyn 17, 735–739 (1982). https://doi.org/10.1007/BF01090155

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  • DOI: https://doi.org/10.1007/BF01090155

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