Loss of momentum in a viscous compressible fluid due to no-slip boundary condition at one or two planar walls

Abstract

The loss of fluid momentum due to friction at one or two planar walls bounding a viscous compressible fluid is studied as a function of time for the situation where the flow is due to a sudden impulse applied at a selected point in initially quiescent fluid. The no-slip condition is assumed to hold at the walls, and the initial impulse is assumed to be sufficiently small, so that the linearized Navier-Stokes equations may be used. When the initial impulse is directed parallel to the walls the time-dependent total fluid momentum is independent of compressibility and volume viscosity. For initial impulse directed perpendicular to the walls an echoing effect, corresponding to sound bouncing between the two walls, is observed.