Solution of the Lossy Nonlinear Tricomi Equation Applied to Sonic Boom Focusing

Abstract

Mathematical modeling of sonic boom focusing theory has been augmented with new terms representing the influence of atmospheric loss mechanisms. The new terms account for atmospheric absorption and dispersion in the vicinity of the caustic. An additional term has been derived to include the effect of wind in the direction tangent to the caustic. A code was developed to numerically implement the newly derived lossy nonlinear Tricomi equation. A numerical validation verified the calculation of diffraction effects due to linear focusing at a fold caustic. A numerical check was also performed to verify the calculation of the nonlinear, absorption, and dispersion coupling using an analytical solution of lossy nonlinear propagation through a homogeneous medium. The numerical results showed good agreement with the analytical solutions. Comparisons were also made between predictions from the lossy nonlinear Tricomi equation code and focus-boom measurements from the Superboom Caustic Analysis and Measurement Program flight test funded by NASA. The lossy nonlinear Tricomi equation predictions also agreed well with the experimental data from the Superboom Caustic Analysis and Measurement Program flight-test measurements.