Nonlinear scattering of crossed focused sound beams in the presence of turbulences—Theoretical results

Abstract

A theoretical study involving the interaction of mutually perpendicular crossed continuous wave ultrasonic beams overlapping (at a common focal point) and interacting in the presence of turbulence in water leads to a prediction of the far-field radiated sum frequency pressure. Earlier experimental results [M. S. Korman and S. C. Rife, “Nonlinear Sound Scattering of Crossed Focused Beams in the Presence of Turbulence,” Proc. 13th Int. Cong. Acoust., Belgrade, Yugoslavia (1989)] measured the profile of the radiated sum frequency pressure by scanning the overlap region across the width of turbulence produced by a submerged circular water jet (Re = 8.5 × 104). In scanning, the receiver transducer unit moves fixed relative to the senders (of primary frequencies f1 = 2.05 MHz and f2 = 1.95 MHz). Pressure scans compare well with known values of the radial turbulent rms velocity profile ur (r). These results can be explained in part by modifying an existing theory [M. S. Korman and R. T. Beyer, J. Acoust. Soc. Am. 85, 611–620 (1989)] to include the effects of amplitude and phase fluctuations by turbulence on the primary beams, focusing and allowing for anisotropic turbulence. [Work supported by the Naval Academy Research Council.]