Further solutions for laminar boundary layers with cross flows driven by boundary motion

Abstract

Laminar boundary layers with cross flows driven by transverse plate motions are considered. In each case, the cross flows are generated either by uniform plate motion or by transverse uniform shear. The three streamwise laminar boundary layers studied are the two-dimensional wall jet, the Blasius boundary layer flow with streamwise uniform plate motion, and uniform shear flow over a plate with streamwise stretching plate motion. In each case, a coordinate decomposition reduces the governing equations to a primary ordinary differential equation for the streamwise flow and a secondary linear equation coupled to the primary solution describing the fully developed cross flow. The one-parameter family of Blasius and uniform shear flow solutions, dependent on the streamwise wall motion parameter \(\lambda \), have dual solutions, and previous studies have shown that the upper branches of these dual solutions are stable, while the lower branches are unstable. This limits the range of admissible solutions for the new cross flows studied here.