Discontinuous velocity profiles for the Orr-Sommerfeld equation

Abstract

Simple ideas of dimensional analysis and of limiting cases are used to elucidate the stability characteristics of a steady basic parallel flow of a viscous incompressible fluid. The principal result is that the stability characteristics of a smoothly varying velocity profile for wave disturbances of small wave-number can be found by use of a discontinuous velocity profile. The boundary conditions for a disturbance at a discontinuity of the basic flow are derived, and are used to find the stability characteristics of broken-line representations of the hal-jet and jet. These findings are in agreement with previous ones.