Abstract
Wave processes are studied within the framework of a turbulence model that describes the reaction-diffusion processes in physicochemical hydrodynamics [{xc1}–{xc5}]. For certain parameters of the equation, exact analytical traveling-wave solutions in the form of kinks are obtained. In the general case, the wave processes can be analyzed using numerical simulation. It is confirmed that for a zero dispersion coefficient the nonlinear wave processes are disordered. It is established that when the dispersion terms are taken into account, as for the Kuramoto-Sivashinsky equation, periodic structures develop in the system starting from a certain threshold dispersion-coefficient value.
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Original Russian Text © N.A. Kudryashov, A.V. Migita, 2007, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2007, Vol. 42, No. 3, pp. 145–154.
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Kudryashov, N.A., Migita, A.V. Periodic structures developing with account for dispersion in a turbulence model. Fluid Dyn 42, 463–471 (2007). https://doi.org/10.1134/S0015462807030143
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DOI: https://doi.org/10.1134/S0015462807030143