On the Growth of Waves in Boundary Layers: a simple Approximate Solution

Abstract

The behaviour of instability waves in boundary layers is considered when the mean flow differs only slightly from a parallel flow. A solution for the instability is sought in the form of a scaled solution of the local parallel flow mode. The scaling is chosen to minimise the deviation of the solution from the full linearised equations of motion. By re-arranging the terms in the governing equation a modified Orr-Sommerfeld equation is formed to define the base solution and this then enables the scaling function to be reduced to a simple integral conservation relation.