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

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 R δ*−c for 0.4 ≤ β ≤ 1.0 , but leads to a decrease in R δ*−c in the range −0.1988 ≤ β ≤ 0.4 . The V terms lead to an increase in R δ*−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 R δ*−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 ∂ 2 U/∂x∂y appear to dominate all other boundary layer growth terms; near R δ*−c for β = −0.1988 however, the stream tube stretching term and ∂ 2 V/∂x 2 appear to be of the same order of magnitude.