Boundary-layer transition problems for forced and for thermally driven gas oscillations

Abstract

The transition of the acoustic (Stokes) boundary layer from laminar to turbulent flow has been observed and also to some extent theoretically explained for forced oscillations of a gas column in a tube. The pertinent critical Reynolds number is the ratio of the particle displacement amplitude to the Stokes boundary layer thickness. For thermally driven acoustic oscillations, there seems to be no experimental evidence for the occurrence of turbulence, in “ordinary” gases that have a Prandtl number of the order 1. For gases with high thermal conductivity (i.e., with near-zero Prandtl number), theory predicts extremely high amplitudes of the second-order velocity (associated with acoustic streaming) in the thermal boundary layer. Even for very weak acoustic oscillations, this means a “shortcut to turbulence.” If the tube or channel width is reduced to the order of the thermal boundary layer thickness, then acoustic streaming effects are drastically reduced and laminar flow is to be expected.