NON-LINEAR INSTABILITY OF THE ASYMPTOTIC SUCTION VELOCITY PROFILE

Abstract

The velocity profile for fluid moving parallel to a fixed plate with uniform suction has a boundary-layer character, except that there is no variation of the flow in the direction parallel to the plate. If a small, centred disturbance is made to the flow, at a Reynolds number which is slightly super-critical, the disturbance evolves into a wave-packet, whose amplitude satisfies a non-linear Schrödinger equation. This equation is determined by using methods introduced for plane parallel-flow problems by Stewartson and Stuart (1), but with the additional features of a cross-flow velocity in the undisturbed motion, and an unbounded flow region normal to the bounding plate. The coefficients in the equation are determined numerically. It is shown that both line- and point-centred initial disturbances develop into localized bursts in a finite time.