Numerical Simulation of a Nonlinear Parabolic Equation for Analyzing The Perceived Loudness Statistics of Sonic Boom Wave after Propagation Through Atmospheric Turbulent Layer

Soniс boom propagation in the atmospheric turbulent layer, represented by a model of homogeneous isotropic turbulence, is investigated numerically in two-dimensional geometry using a KZK-type nonlinear parabolic equation for an inhomogeneous moving medium with relaxation. The mean value, standard deviation, and cumulative probabilities of the sonic boom amplitude, shock front steepness, and the Perceived Loudness Mark VII metric of subjective loudness of an impulse noise are analyzed at different propagation distances traveled by the sonic boom wave in the turbulent layer and for different initial amplitudes of the wave.