Nonlinear acoustic pulse propagation in dispersive sediments using fractional loss operators

The nonlinear progressive wave equation (NPE) is a time-domain formulation of the Euler fluid equations designed to model low-angle wave propagation using a wave-following computational domain. The wave-following frame of reference permits the simulation of long-range propagation and is useful in modeling blast wave effects in the ocean waveguide. Existing models do not take into account frequency-dependent sediment attenuation, a feature necessary for accurately describing sound propagation over, into, and out of the ocean sediment. Sediment attenuation is addressed in this work by applying lossy operators to the governing equation that are based on a fractional Laplacian. These operators accurately describe frequency-dependent attenuation and dispersion in typical ocean sediments. However, dispersion within the sediment is found to be a secondary process to absorption and effectively negligible for ranges of interest. The resulting fractional NPE is benchmarked against a Fourier-transformed parabolic equation solution for a linear case, and against the analytical Mendousse solution to Burgers' equation for the nonlinear case. The fractional NPE is then used to investigate the effects of attenuation on shock wave propagation.