Linear and nonlinear propagation of high amplitude acoustic pulses through turbulent layer in air is simulated using two-dimensional KZK-type (Khokhlov-Zabolotskaya-Kuznetsov) equation. Incident acoustic field is a plane wave with symmetrical N-wave waveform. Turbulent wind velocity field with modified Von Karman spectrum represents random sound speed inhomogeneities in the propagation medium. Cumulative probabilities of observing waveforms with amplified peak overpressures and shock fronts with high steepness are collected from long realizations of acoustic field. It is shown that in linear propagation regime the turbulence leads to smearing of the shock front and cumulative probability of waveforms with high steepness has low values under 1%. In nonlinear propagation regimes nonlinear shock front steepening counteracts shock front smearing resulting in much higher values of cumulative probabilities of observing waveforms with high steepness of the shock front (up to 8 %).
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