THEORY OF ULTRASOUND DOPPLER-SPECTRA VELOCIMETRY FOR ARBITRARY BEAM AND FLOW CONFIGURATIONS.

It is shown that for velocity gradients and transverse flows the output spectrum of a pulsed Doppler system with the beam transversely oriented with respect to the flow remains symmetrical, with the edges corresponding to the maximal velocity. However, the profile becomes peaked at the center. For oblique incidence an asymmetrical spectrum is obtained and its edges are related to the maximal and minimal velocities within the measurement volume. Using the reciprocity theorem it is shown that the output spectrum is obtained by convolving the particle excitation spectrum due to monochromatic excitation, with the receiver input spectrum due to a moving monochromatic source, all this shifted to the classical Doppler frequency. It is shown that when the excitation, rather than being monochromatic, possesses an arbitrary (narrowband) spectrum, this spectrum, replicated in a prescribed manner, has to be convolved with the spectra.