Flow in a Channel With a Time-Dependent Indentation in One Wall

Abstract

Computations and flow visualization experiments have been carried out on 2-D flow in a channel, with an indentation in one wall that can move in and out. There is plane Poiseuille flow upstream and attention is focussed on the flow downstream of the indentation. Four time-courses of indentation motion are examined: I oscillation between a flush and an indented postion; II advance from flush to indented, after which it remains stationary; III retraction to flush from a steady indentation; IV small amplitude oscillation about a substantially indented position. Various values of Reynolds number, Re, and Strouhal number, St, are employed (250≤Re≤911; 0.01≤St≤0.1). The results show that (a) vorticity waves and eddies are generated in cases I and II (as in reference [11]); (b) in case II at higher experimental Re the flow does not become steady because the steady flow is unstable to a Rayleigh wave, on the shear layer bounding the main separation region, whose wavelength is significantly less than that of the vorticity wave; (c) in case III the waves that are generated at each parameter set seem to be Rayleigh waves not vorticity waves; (d) in case IV short waves give way to longer waves whose amplitude is comparable with the mean indentation height not the oscillation amplitude. Although resembling vorticity waves these do not propagate like the forced waves of case I and presumably represent a nonlinear interaction between Rayleigh waves, vorticity waves, and the very long, weak waves present even in steady flow. Further downstream, in many cases, the 2-D waves break down into turbulence via 3-D disturbances.