Linear and nonlinear acoustics in the time domain: Long-range pulse propagation

Abstract

During recent years the nonlinear progressive wave equation (NPE) model has been developed as a nonlinear time domain counterpart of the linear frequency domain parabolic equation (PE) model [B. E. McDonald and W. A. Kuperman, J. Acoust. Soc. Am. 81, 1406–1417 (1987)]. It was motivated by investigation of nonlinear wave evolution, so that time domain formulation was natural. With nonlinearity absent, the NPE gives an efficient algorithm for linear broadband propagation in the time domain. (No Fourier transforms between frequency and time domains are involved.) Recent simulation results from the NPE model (given in a color movie) illustrate linear and nonlinear pulse propagation through a deep ocean convergence zone. Differences in physics between broadband linear and nonlinear propagation will be pointed out and discussed. Linear results reveal transients whose time scale as a function of range is “remembered” from the source. In corresponding nonlinear results, steepening and shock formation cause the source's time scale to be gradually “forgotten.” For the parameters of the example given, nonlinear spreading behind the shock increases the transients' time scale by roughly a factor of 3 in the farfield.