Effect of boundary-layer growth on stability of incompressible flat plate boundary layer with pressure gradient

Abstract

The stability of an incompressible flat plate boundary layer with pressure gradient (Hartree pressure gradient parameter β = 1.0, 0.6, 0.4, 0.2, 0, −0.1, −0.14, and −0.1988) is computed from the linearized complete small disturbance equations. The analysis is nevertheless a quasiparallel treatment because although boundary layer growth is accounted for, the disturbance wave function is correct only in a strictly parallel flow. It is found that the nonparallel flow effect has a negligible influence on the critical Reynolds number Rδ*−c for 0.4 ≤ β ≤ 1.0, but leads to a decrease in Rδ*−c in the range −0.1988 ≤ β ≤ 0.4. The V terms lead to an increase in Rδ*−c in the range 0.4 ≤ β ≤ 1.0, and to a decrease in the range −0.1988 ≤ β ≤ 0.4. The stream tube stretching term led to a decrease in Rδ*−c in the range 0.4 ≤ β ≤ 1.0, and to an increase in the range 0.4 ≥ β ≥ −0.1988. The effect of the V terms and the stream tube stretching term ∂2U/∂x∂y appear to dominate all other boundary layer growth terms; near Rδ*−c for β = −0.1988 however, the stream tube stretching term and ∂2V/∂x2 appear to be of the same order of magnitude.