Acoustic streaming in a waveguide with slowly varying height

Abstract

An analysis of acoustic streaming in a two-dimensional waveguide having slowly varying height is presented. Special attention is paid to waveguides with cross sections that are small compared to the acoustic and/or wall wavelength. It is shown that the dynamic behavior of the enclosed fluid can be parametrized by the values of three small parameters ε, 1/S, and 1/R, where ε is the wall slope, S is the oscillatory Strouhal number, and R is the oscillatory Reynolds number. An analytical solution describing the streaming flow is given in terms of a regular perturbation sequence in ε. Outside the boundary layer it is shown that the time averaged slip velocity is the sum of two term. The first terms is proportional to the product of the incident and reflected wave amplitudes. The second is proportional to the difference between incident and reflected acoustic intensities of the wave. It is shown that the streaming solution remains valid until εR/S2 = O(1). The results for a duct with sinusoidally varying height in the incompressible limit and waveguides with a Gaussian variation in height are given.