Determination of the broadband spectra for saturated parametric sonars

Abstract

The determination of the propagation of a finite amplitude wave by Burger's equation is well known. Application of this solution to parametric sonars generally involves modeling a plane wave in the nearfield and a spherical wave in the farfield. The transition between these regions is not well defined and generally involves an arbitrary choice of a transition region. To avoid this requirement and to allow the solution for a broadband parametric sonar to be extended to the finite amplitude case, a model has been developed based on the approximation that the nonlinear losses in the fundamental are due entirely to the work done on the nonlinear source function. The model developed is similar in principle to that of H. Merklinger [J. Acoust. Soc. Am. 54, 1760–1761 (1973)], except that the ad hoc estimate of the nonlinear source function is replaced by an integral of the primary intensity. This solution is extended to allow for broadband source signals up to 1‐oct bandwidth. A solution is obtained for the spectrum of the total power in the primary beam, which is independent of the cross‐sectional area of the beam and is thus valid in both the nearfield and farfield.