Nonlinear scattering of crossed ultrasonic beams in the presence of turbulence in water. I: Experiment

Abstract

Experiments are reported on the measurements of the scattered sum frequency pressure from two finite-amplitude, mutually perpendicular ultrasonic beams intersecting in the presence of turbulence. In the absence of turbulence, virtually no sum frequency pressure is observed outside the interaction region. The primary carrier beams are generated by individual 2.54-cm-diam transducer units of frequency f1=2.05 and f2=1.95 MHz, respectively. The turbulence is created by a 2.54-cm-diam submerged water jet. The scattering geometry places both of the transmitting acoustic beam axes and the stationary transducer receiving unit axis on the same plane with the jet axis. Angular measurements are performed by rotating the axes of the transmitting crossed beams (which are always perpendicular to each other) in the plane. The highly directional receiver is located outside the interaction region. Scattering angles θ1 and θ2 are measured with vertex at the interaction region from the beam axis of each respective carrier going counterclockwise to the line defined by the beam axis of the receiver. Results for the spectral broadening Δfe and Doppler shift fd of the scattered spectrum as a function of angle for each of the primaries are compared with the sum frequency component. The Doppler shifts of the scattered primaries f (1)d, f (2)d add up to give the Doppler shift of the sum frequency f (+)d at the individual scattering angles. The sum frequency broadening varies with angle as Δf (+)e∝f (+)(σv/c) sin(θ*/2), where θ* is replaced by θ1−45°, σv is an rms turbulent velocity, and f (+) is the average nonlinearly generated sum frequency. Crossed-beam scattering may be valuable as a diagnostic tool in studying turbulent flows.