Numerical analysis of linear wave propagation in the atmosphere with temperature gradient for Mach cutoff reproduction

In this paper, the compact-explicit finite difference-time domain method is applied to two-dimensional analysis of linear sound wave propagation in the atmosphere with temperature gradient in order to numerically reproduce the Mach cutoff in sonic boom propagation and predict the evanescent wave below the caustic. In order to simulate sound waves radiated from the supersonic transport in the Mach angle direction, sound source is modeled by a linear phased array. Some numerical experiments are carried out for the two-dimensional full-field model. Comparing the results by present method with the computatipnal fluid dynamics results and the nonlinear Tricomi results, it was confirmed that the formation of the Mach cutoff and the caustic are numerically reproduced with reasonable accuracy. It is found in some numerical experiments on sonic boom propagation that the linear analysis is sufficient for the analysis of evanescent waves below caustic.