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Self-preservation of large-scale structures in a nonlinear viscous medium described by the Burgers equation

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Abstract

We use the asymptotic solution of the one-dimensional Burgers equation to study the self-preservation of large-scale random structures. We show that in the process of their evolution, large-scale structures remain stable against small-scale perturbations for the case of a continuous initial spectrum with a spectral index smaller than unity. We study both analytically and numerically the correlation coefficient of a large-scale structure and of the same structure with a high-frequency perturbation and show that with the passage of time the coefficient tends to unity. Using the asymptotic formulas of the theory of random excursion of stochastic processes, we study the statistical properties of the perturbing field and find that the effect of high-frequency perturbations is equivalent to the introduction of effective viscosity.

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Authors and Affiliations

  1. N. I. Lobachevskii Nizhnii Novgorod State University, 603000, Nizhnii Novgorod, Russia

    S. N. Gurbatov & G. V. Pasmanik

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  1. S. N. Gurbatov
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  2. G. V. Pasmanik
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Zh. Éksp. Teor. Fiz. 115, 564–583 (February 1999)

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Gurbatov, S.N., Pasmanik, G.V. Self-preservation of large-scale structures in a nonlinear viscous medium described by the Burgers equation. J. Exp. Theor. Phys. 88, 309–319 (1999). https://doi.org/10.1134/1.558798

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