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Journal of Applied Mechanics and Technical Physics

2002 year, number 1

Generation of the tollmien-schlichting wave in a supersonic boundary layer by two sinusoidal acoustic waves

G. V. Petrov
Institute of Theoretical and Applied Mechanics,
Siberian Division, Russian Academy of Sciences, Novosibirsk 630090


The problem is solved using parabolized
equations of stability for three-
dimensional perturbations of a
compressible boundary layer on a flat
plate. Nonlinearity is taken into
account by quadratic terms that are most
significant in estimates of the viscous
critical layer of the stability theory.
These terms are determined by the total
field of two acoustic perturbations, and
the equations become linear and
inhomogeneous. The calculations are
performed for one acoustic wave being
stationary in the reference system
fitted to the plate for Mach numbers
M=2;5. Solutions are presented, which
are identified very accurately with
Tollmien-Schlichting waves at a rather
large distance from the plate edge.