Nonlinear streaming due to the oscillatory stretching of a sheet in a viscous fluid

Summary An elastic sheet is stretched back and forth in a viscous fluid. The problem is governed by a nondimensional parameterS which represents the relative magnitude of frequency to stretching rate. The Navier-Stokes equations are solved by matched asymptotic expansions for largeS. Due to nonlinearity there exists boundary layers ofO(S ^–1/2). The unsteady oscillatory flow contains both basic and higher harmonic oscillations. The induced steady streamlines show a saddle like flow which is different from that of acoustic streaming.With 5 Figures