Simulation of N-wave propagation in turbulent atmosphere using standard and wide-angle parabolic equations

Abstract

Interest to the problem of sonic boom propagation in atmosphere is growing in recent decade due to the development of new generation of supersonic business jets. Important nonlinear wave effects occur in the last kilometer above the ground where sonic boom wave interacts with turbulence of the planetary boundary layer. Focusing and defocusing of the sonic boom on random inhomogeneities of sound speed lead to fluctuations of its peak overpressure and rise time, affecting the perceived loudness. Various one-way model equations of different complexity have been developed and actively used by the research community for analyzing wave propagation in turbulent atmosphere. The basic equation is the nonlinear parabolic equation of the Khokhlov-Zabolotskaya-Kuznetsov-type, which has limitation on diffraction angles. Improvement in accuracy of the diffraction term can be reached using wide-angle formulation. Here, the simulation results for N-wave propagation through homogeneous isotropic turbulence are compared for standard and wide-angle parabolic equations of scalar type. Turbulence wind velocity fluctuations are accounted via effective sound speed. The wide-angle model is based on split-step Pade approximation of the propagation operator. The importance of taking into account large diffraction angles for N-wave propagation in atmospheric turbulence is discussed. [Work supported by RSF-18-72-00196 and ANR-10-LABX-0060/ANR-16-IDEX-0005].