Determination of turbulent vorticity by the nonlinear scattering of crossed ultrasonic beams

Abstract

The nonlinear interaction of two, mutually perpendicular crossed ultrasonic beams, overlapping in the presence of turbulence, generates a scattered sum frequency component that radiates outside the interaction region. In the absence of turbulence, virtually no scattered sum frequency component exists (outside the interaction region). A theoretical investigation is reported which relates the angular dependence of the time-dependent Doppler shift (of the scattered sum frequency) to the time-dependent velocity fluctuations of the turbulent eddies. When a second set of focused crossed beams is operated with an overlap region slightly displaced from the first set (by 1.27 mm), one can measure the vorticity using Doppler shift information from four distinct combination frequencies obtained at two different scattering angles. Experimental results are presented using continuous wave (CW) focused primary beams of frequencies f1=1.8, f2=2.0, f3=2.2 and f4=2.3 MHz (generated by concave transducer units with 15 cm focal lengths). The turbulence is generated by a submerged water jet with nozzle diameter D=0.635 cm and exit velocity ≈7 m/s. Here the interaction region is located 37D from the nozzle exit. A 4 MHz circular plane array receiving transducer detects four distinct scattered sum frequency components (at specific angles) using a spectrum analyzer to demonstrate the effect. The receiver is located 14D from the interaction region.