DIFFRACTING NONLINEAR ACOUSTIC BEAMS IN 3+1 DIMENSIONS WITH APPLICATIONS TO OCEANIC ACOUSTICS

The dissipative Zabolotskaya-Khokhlov equation (dZK) is the model equation appropriate to the study of a weakly nonlinear acoustic beam which is slowly diffracting through a slightly viscous medium. A number of recent analytic works have discussed the dZK equation when diffraction is in one direction only, and three computational studies have been done on the case of non-dissipative cylindrical diffraction. The present work reports a large family of fully three-dimensional similarity reductions of dZK, which are the first known, and include the first known exact solutions to the cylindrical (non-dissipative) ZK. These similarity reductions are of direct interest to the study of acoustic signals propagating through stratified media (such as the ocean), as well as more generally to previous numerical studies, and to acoustic beams in any geometry. Some applications to oceanic acoustics are discussed in detail. Of particular interest is the identification of transverse signal rotation, as a fundamental property of acoustic beams. © 1990.