Evolution of complex waveforms Distorsion HF Shock formation Shock evolution Shock fusion BF N wave
Conclusion The dominant phenomenon in nonlinear acoustics is the dependancy of sound speed with instanteneous wave amplitude. The evolution of the temporal waveform of a signal as a function of the propagation distance is modelled at 1D by the inviscid Burgers’ equation. Poisson’s solution provides an implicit solution that maybe multivalued. Starting from an initial profile, non- linearities lead to the waveform distorsion, up to the shock formation distance. This is associated to a shift of the frequency spectrum towards high frequencies. Shocks are necessarily compression ones (to satisfy the 2nd principle of thermodynamics). They are determined according to the weak shock theory, or law of equal areas. This implies dissipation of energy, the rate of which depends on the temporal waveform of the signal. Beyond the shock formation distance, waveforms evolve rapidly towards linear profiles (simple waves) matching moving shocks. This generally implies a slow shift of the frequency spectrum towards low frequencies. An efficient way to compute any wave profile at any distance is to use the potential. For potential, the physically admissible solution (that satisfies the entropy condition) is the largest value among the multivalued ones.