Statistics of peak overpressure and shock steepness for linear and nonlinear N-wave propagation in a kinematic turbulence

Abstract

Linear and nonlinear propagation of high amplitude acoustic pulses through a turbulent layer in air is investigated using a two-dimensional KZK-type (Khokhlov-Zabolotskaya-Kuznetsov) equation. Initial waves are symmetrical N-waves with shock fronts of finite width. A modified von Kármán spectrum model is used to generate random wind velocity fluctuations associated with the turbulence. Physical parameters in simulations correspond to previous laboratory scale experiments where N-waves with 1.4 cm wavelength propagated through a turbulence layer with the outer scale of about 16 cm. Mean value and standard deviation of peak overpressure and shock steepness, as well as cumulative probabilities to observe amplified peak overpressure and shock steepness, are analyzed. Nonlinear propagation effects are shown to enhance pressure level in random foci for moderate initial amplitudes of N-waves thus increasing the probability to observe highly peaked waveforms. Saturation of the pressure level is observed for stronger nonlinear effects. It is shown that in the linear propagation regime, the turbulence mainly leads to the smearing of shock fronts, thus decreasing the probability to observe high values of steepness, whereas nonlinear effects dramatically increase the probability to observe steep shocks.

One‐Minute Resolution GOES‐R Observations of Lamb and Gravity Waves Triggered by the Hunga Tonga‐Hunga Ha'apai Eruptions on 15 January 2022

“…Atmospheric pressure anomalies caused by the HTHH eruption were recorded all around the globe. Laboratory measurements and numerical simulations show that acoustic waveforms propagating through the atmosphere can get strongly distorted mostly by thermal inhomogeneities and turbulent wind velocity fluctuations (Averiyanov et al., 2011; Stout, 2018; Yuldashev et al., 2017). Unlike the classic N ‐wave sonic boom, distorted waveforms can have rounded waves, several spikes, multiple shock fronts, and oscillations or even a maximum overpressure in the tail part.…”

“…For example, the peak overpressure and the rise time are difficult to evaluate in distorted waveforms found in turbulent flow. These important acoustic wave parameters can be better defined based on the first derivative of the pressure waveform (Averiyanov et al., 2011; Yuldashev et al., 2017). Analyzing P ′ allows ranking shocks by strength (steepness), separating close shocks that otherwise might be considered as one long shock, and enables detecting shocks in the tail part of the packet.…”

Characterization of topographic effects on sonic boom reflection by resolution of the Euler equations

“…Ray-tracing was thus the only method employed for farfield prediction in the second and third AIAA Sonic Boom Prediction Workshops (AIAA, 2017(AIAA, , 2020Rallabhandi and Loubeau, 2019). One-way wave equation methods are favored when propagation in a turbulent medium is examined (Blanc-Benon et al, 2002;Yuldashev et al, 2017). State-of-the-art simulations (Luquet et al, 2019;Stout and Sparrow, 2019) are now able to consider a threedimensional geometry.…”