Nonlinear propagation of N-waves through kinematic turbulence: Statistics of peak overpressure and shock front steepness

Nonlinear propagation of short N-waves (wavelength of 1.4 cm) through a turbulent layer with outer scale of about 16 cm was simulated based on the 2D parabolic KZK-type equation. A modified von Karman spectrum was used to generate random fluctuations of wind velocity associated with the presence of turbulence. Statistics of peak overpressure and shock front steepness were analyzed for linear and various degrees of nonlinear effects in N-wave propagation. It was shown that in case of linear propagation, the turbulence mainly led to smearing the shock fronts and resulted in low probabilities of observing steepened shocks. At higher pressure level, nonlinear effects resulted in steepening of the shock fronts and hence counteracted the effects introduced by the turbulence. Due to nonlinear enhancement of focusing gain in random foci, up to twofold increase of the cumulative probability of observing highly peaked waveforms was shown for nonlinear wave propagation comparing to the linear case. However, it was a...