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Evolution of weak noise and regular waves on dissipative shock fronts described by the Burgers model
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
Lobachevsky State University of Nizhni Novgorod, RUS.
Lobachevsky State University of Nizhni Novgorod, RUS.
2018 (English)In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 82, p. 20-29Article in journal (Refereed) Published
Abstract [en]

The interaction of weak noise and regular signals with a shock wave having a finite width is studied in the framework of the Burgers equation model. The temporal realization of the random process located behind the front approaches it at supersonic speed. In the process of moving to the front, the intensity of noise decreases and the correlation time increases. In the central region of the shock front, noise reveals non-trivial behaviour. For large acoustic Reynolds numbers the average intensity can increase and reach a maximum value at a definite distance. The behaviour of statistical characteristics is studied using linearized Burgers equation with variable coefficients reducible to an autonomous equation. This model allows one to take into account not only the finite width of the front, but the attenuation and diverse character of initial profiles and spectra as well. Analytical solutions of this equation are derived. Interaction of regular signals of complex shape with the front is studied by numerical methods. Some illustrative examples of ongoing processes are given. Among possible applications, the controlling the spectra of signals, in particular, noise suppression by irradiating it with shocks or sawtooth waves can be mentioned. © 2018 Elsevier B.V.

Place, publisher, year, edition, pages
Elsevier B.V. , 2018. Vol. 82, p. 20-29
Keywords [en]
Burgers equation, Dissipation, Noise, Nonlinearity, Shock front, Control nonlinearities, Energy dissipation, Numerical methods, Partial differential equations, Random processes, Reynolds number, Autonomous equations, Burgers equations, Noise suppression, Shock fronts, Statistical characteristics, Variable coefficients, Shock waves, numerical model, shock wave
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Other Mathematics
Identifiers
URN: urn:nbn:se:bth-16903DOI: 10.1016/j.wavemoti.2018.06.007ISI: 000444790500003Scopus ID: 2-s2.0-85050081319OAI: oai:DiVA.org:bth-16903DiVA, id: diva2:1240156
Available from: 2018-08-20 Created: 2018-08-20 Last updated: 2018-10-04Bibliographically approved

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Rudenko, Oleg

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