Three-Wave Interactions between Disturbances in a Supersonic Boundary Layer
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e-Wave Interactions between Disturbances in a Supersonic Boundary Layer S. A. Gaponova,* and N. M. Terekhovaa,** a
Khristianovich Institute of Theoretical and Applied Mechanics of Russian Academy of Sciences, Institutskaya ul. 4/1, Novosibirsk, 630090 Russia *e-mail: [email protected] **e-mail: [email protected] Received December 5, 2019; revised March 3, 2020; accepted March 3, 2020
Abstract—The interaction between vortex disturbances (Tollmien—Schlichting waves) in the supersonic boundary layer on an impermeable surface is studied within the framework of the weakly nonlinear stability theory. The first level of the nonlinear interaction, namely, that in three-wave resonance systems, is investigated. The main features of the interaction in unit triplets consisting of plane and three-dimensional components, are considered, whereupon the group mutual influence (the joint realization of several simple triplets) is studied. The streamwise dynamics of the disturbances of two types, controlled and natural, are modeled. The possibility of energy redistribution is these wave systems in the case of the nonlinear interaction between the constituting wave packets is studied. The resonance interactions are shown to be adequate to the actual nonlinear processes at the earlier transition stages. Keywords: supersonic boundary layer, three-wave resonance systems, vortex disturbances DOI: 10.1134/S0015462820050067
The mathematical apparatus developed in the section of mechanics associated with the study of laminar-turbulent transitions in subsonic flows [1] can be applied to an investigation of high-velocity flows. In recent years, the in-depth study of several methods of disturbance evolution in compressible supersonic boundary layers has been performed. The studies concerned with the mathematical modeling can be subdivided into two groups. The first group develops the methods of direct numerical integration of systems of equations in partial derivatives [2–5]. Inherent in this approach are difficulties related with the processing of large bodies of data, whose plausibility is not always obvious, and the physical interpretation of the results obtained. Because of this, for example, in reviewing the publications on the numerical modeling of laminar-turbulent transition in boundary layers at high Mach numbers [5], neither generalizing conclusions on the nonlinear interaction between disturbances have been done. Despite a certain popularity of this approach, it is the methods of the second group developed within the framework of perturbation theory (for mean characteristics and small oscillations) that turned out much more effective in modeling the nonlinear processes. The investigations in the nonlinear domain are preformed basing on the study of interactions in threewave systems (triads or triplets). The physical validation of this modeling lies in an analysis of the evolution of a single wave in the force field of the two other waves realized under the condition of the synchronization between the disturbance phases, which mak
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