Measurement of Rayleigh streaming in high-amplitude standing waves using laser Doppler anemometry

Abstract

Current theories for Rayleigh streaming in a long, cylindrical pipe predict dc velocities which increase as the square of the amplitude of the first harmonic, and exhibit a parabolic radial profile. The velocity field in such a pipe, driven at one end and rigidly capped at the other, has been measured using LDA (laser Doppler anemometry) techniques. Analysis of the data produced by the LDA system can be complicated by two things: (i) the data are randomly sampled at a frequency below the Nyquist rate, resulting in a large, uneven sample spacing which is unsuitable for standard discrete Fourier transform techniques; and (ii) the dc velocity is typically two to three orders of magnitude smaller than the ac velocity, resulting in a very low signal-to-noise ratio. A robust signal processing algorithm is presented which overcomes these two obstacles, permitting fast and accurate estimates of the magnitudes, phases, and uncertainties of the velocity Fourier coefficients. The measured dc velocities agree well with the theoretical predictions when the tube is driven at low amplitudes, but deviate significantly from the theoretical predictions when the tube is driven at high amplitudes. [Work supported by ONR.]