Abstract
The time profiles and characteristics of sonic boom waves during propagation in a density-stratified atmosphere are calculated. It is shown that this stratification leads to a significant change in wave parameters: the wave amplitude, the characteristic distances at which the wave transformation is manifested, the width of the shock front. It is shown that the effective role of viscosity decreases when the shock wave propagates down to the earth's surface. So the width of the shock front decreases. Two methods are being developed for analytical calculation. The first one, the nonlinear geometric acoustics approximation, allows obtaining the Burgers equation with a variable viscosity to describe the wave field along the ray. Some exact solutions and asymptotic solution for low viscosity are obtained. This method is not applicable in focusing regions. The second method is based on the application of a modular nonlinearity model. Replacing the quadratic nonlinearity with a modular one allows obtaining a system of linear equations, the solution of which is possible. The difficulty lies in the correct construction of the discontinuity in the profile and subsequent stitching of solutions for different polarities. [This study was supported by the Russian Foundation for Basic Research (Project No. 20-02-00493-a).]
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