On the parabolization of equations for the propagation of small disturbances in two-dimensional boundary layers

Abstract

The work is devoted to modeling the disturbance propagation in viscous incompressible laminar boundary layers, using linearized equations for disturbance amplitudes. Along with the numerical model based on original linearized equations, the article considers three models based on equations derived from the original ones by neglecting the streamwise pressure gradient, or the streamwise viscous terms, or both. The models are compared numerically by the example of generation and propagation of disturbances in the boundary layer over a slightly concave plate. Conclusions are drawn about the feasibility of the same simplified models to adequately simulate both Tollmien–Schlichting waves and Görtler vortices in a range of practically important parameters.