Nonlinear Doppler effect and its use for bubble flow velocity measurement

The Doppler effect is a familiar phenomenon in linear acoustics. The nonlinear Doppler effect is also possible when a moving target exhibits nonlinear responses. In these cases Doppler frequency shifts arise at harmonics or combination frequencies in the scattered waves. For collinear geometry of primary beams, the nonlinear Doppler frequency shifts at the second harmonic and the combination frequencies are found to be the same as those for the linear scattering of those frequency components by the target. However, for highly, noncollinear primary beams, the difference frequency Doppler frequency shift can greatly exceed the linear one. This phenomenon is mainly studied in the present work. Experimental verification done with flowing bubbles in a tube shows good agreement with the theory. The suggested difference frequency Doppler technique can find applications in medical diagnostics of blood flow as well as in industries and in oceanology.