On Tollmien-Schlichting Wave Generation by Sound
It is well known that acoustic disturbances incident upon the boundary layer may cause Tollmien-Schlichting waves. An intense generation of these waves is observed in local inhomogeneities of the flow . To investigate this phenomenon we shall consider a two-dimensional gas flow about a flat plate directed along a free-stream flow (fig.1). The free-stream velocity U∞ is taken to be subsonic with M < 1. Introduce cartesian coordinates x′, y′ aligning their origin with the plate leading edge and orienting x′ along the plate surface. Denote velocity vector components in this coordinate system by u′ and v′, density by p′, and viscosity coefficient by μ′ . Let the gas under consideration have an adiabatic constant r and its thermodynamic state be described by the Clapeyron equation.
KeywordsBoundary Layer Roughness Surface Plate Surface Slip Condition Boundary Layer Equation
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- 1.Kachanov, Yu.S.; Kozlov, V.V.; Levchenko, V.Ya. Turbulence initiation in a boundary layer. Novosibirsk, Nauka, 1982 (in Russian).Google Scholar
- 2.Ruban, A.I.; Sychev, V.V. Asymptotic theory of laminar boundary layer separation in incompressible fluid. Uspekhi Mekhaniki“, 1979, v.2, N 2 (in Russian).Google Scholar
- 3.Smith, F.T. On the non-parallel flow stability of the Blasius boundary layer. Proc.Roy.Soc. London, Ser.A, 1979, vol.366, N 1724.Google Scholar
- 4.Zhuk V.I.; Ryzhov, O.S. Free interaction and boundary layer stability in incompressible fluid. Dokl.Akad.Nauk SSSR, 1980, v.253, N 6 (in Russian).Google Scholar
- 5.Stewartson, K. On laminar boundary layers near corners. Quart.J.Mech.Appl.Math., 1970, v.23, pt.2.Google Scholar
- 6.Bogdanova, E.V.; Ryzhov, O.S. On oscillations induced by a harmonic oscillator in Poiseuille flow. Dokl.Akad.Nauk SSSR, 1981, v.257, N 4 (in Russian).Google Scholar
- 7.Terentiev, E.D. Linear problem of a vibrator in a subsonic boundary layer. Prikl. MM, 1981, v.45, vyp.6 (in Russian).Google Scholar