Longitudinal structures in boundary layers and their resonance nature

Abstract

On the basis of resonance theory the possibility of the longitudinal structures generation was fixed in the compressible boundary layer by an external vorticity. It takes place under a condition when parameters of externally vortex wave become the close to parameters of Eigen stationary perturbations of a boundary layer. Researches are conducted as in case of subsonic numbers of the Mach, and in case of a supersonic flow at M=2. Data of the resonance theory agree with direct calculations of an interaction external vorticity with boundary layer satisfactorily. Parameters of two-dimensional stationary perturbations of a subsonic boundary layer completely match with data of Grosch C. E., Jackson T. L., Kapila A. K. (1992). In particular, the infinite set of Eigen functions is installed, which are damped by a power law of the longitudinal coordinate, x−λk. Researches of three-dimensional perturbations showed, that the damping degree of perturbations down a flow depends on a wave number in the lateral direction poorly. However, there are the optimal values of the wave number in the lateral direction, in which perturbations damped down by a stream the most poorly. If in case of subsonic speeds decrements of perturbations of the first mode doesn’t depend neither on a Reynolds number, nor on value of a lateral wave number, then in case of M=2 the nature of a perturbations reduction on longitudinal coordinate depends both on a wave number, and on a Reynolds number.