Scattering from crossed ultrasonic beams in the presence of turbulence

Abstract

Experimental results on the mutual scattering from two perpendicularly directed, continuous ultrasonic beams interacting in the presence of turbulence in water have been shown to produce a sum‐frequency component that radiates outside the interaction region. Measurements of spectral broadening and Doppler shift have been reported by the authors [10th ICA, Vol. 1, p. 164, Sydney (1980)]. An investigation of the scattering mechanisms suggests that scattering to lowest order is from the cubic quadrupole source term in the wave equation (the Reynolds stress tensor ρuiuj). This mechanism allows an excess acoustic density ρ = ρ1 + ρ2 to interact nonlinearly with acoustic particle velocities uiL1 + uiL1 and turbulent velocity fluctuations uiT. The theoretical results for the temporal spectrum density of the scattered sum frequency are compared with single beam scattering. The Doppler shifts of the two scattered primary waves, when added together, equal the Doppler shift of the sum frequency for each scattering angie. The prediction for the angular dependence of the sum's broadening is Δf+ ∼ sin (θ − 45°)/2. These results are in good agreement with experiment.