On the motion of a flat plate at high speed in a viscous compressible fluid. I. Impulsive motion

Abstract

ABSTRACTThe effect of giving an infinite plate, immersed in a compressible fluid, an impulsive velocity U in its own plane is examined on the assumption that M = U/a0 ≫ 1 where a0 is the velocity of sound in the undisturbed fluid. To begin with the flow field is very complex but very soon after the motion has begun a shock wave moves at right angles to the plate gradually weakening and eventually degenerating into a sound wave. Attention is concentrated on the flow field when there is a distinct strong shock wave, it being assumed, and justified a posteriori, that the flow behind it may be divided into an inviscid region and a boundary layer region. The equation of the shock wave and a complete description of the flow behind it is found when log M, where ν0 is the coefficient of kinematic viscosity of the undisturbed air. An approximate method is also given to enable the solution to be joined up to Van Dyke's (10) which is valid when .