Convergence of locally self-similar solutions to exact numerical solutions of boundary layer equations for a plate

This paper considers a possibility of using locally self-similar solutions for a stationary boundary layer in linear stability problems. The solutions, obtained at various boundary conditions for a vibrationally excited gas, are compared with finite-difference calculations of the corresponding flows. An initial system of equations for a plane boundary layer of the vibrationally excited gas is derived from complete equations of two-temperature relaxation aerodynamics. Relaxation of vibrational modes of gas molecules is described in the framework of the Landau–Teller equation. Transfer coefficients depend on the static flow temperature. In a complete problem statement, the flows are calculated using the Crank–Nicolson finite-difference scheme. In all the considered cases, it is shown that the locally self-similar velocity and temperature profiles converge to the corresponding profiles for a fully developed boundary-layer flow calculated in a finite-difference formulation. The obtained results justify the use of locally self-similar solutions in problems of the linear stability theory for boundary-layer flows of a vibrationally excited gas.