2002/07/09 by A. Perelomova, Anna Perelomova, Sergey Leble +3
Earth and Planetary Sciences · Engineering · Materials Science · Physics and Astronomy · #Acoustic Wave Phenomena Research #Atmospheric and Oceanic Physics (physics.ao-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Ultrasound and Cavitation Phenomena #Underwater Acoustics Research #physics.ao-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.physics/0207036
15 pages
arxiv created 2002/07/09 · openalex publication_date 2002/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The general hydro-thermodynamic system of equations in 2+1 dimensions with arbitrary equations of state (Taylor series approximation) is split to eigen modes: Tollmienn-Schlichting (TS) wave and two acoustic ones. A mode definition is realized via local relation equations, extracted from the linearization of the general system over boundary layer flow. Each such connection defines the subspace and the corresponding projector. So the division is performed locally and could help in initial (or boundary) problems formulation. The general nonlinearity account determines the specific form of interaction between acoustic and vortical boundary layer perturbation fields. After the next projecting to a subspace of Orr-Sommerfeld equation solution for the TS wave and the corresponding procedure for acoustics, the equations go to one-dimensional system that describes evolution along the basic stream. A new mechanism of nonlinear resonance excitation of the TS wave by sound is proposed and modelled via four-wave interaction. Subjectclass: Primary 35Q30 ; Secondary 76F70, 35Q72; Keywords: keywords fluid mechanics, boundary layer, projector to eigen modes, Tollmien-Schlichting waves, acoustic waves, nonlinear resonance, N-wave system.