Evolution of intensive acoustical noise pulses (the numerical simulation with Fast Legendre Transform Algorithm)

Igor Demin , Sergey Gurbatov , Nikolay Pronchatov-Rubtsov

The propagation of finite amplitude sound waves is of fundamental interest in nonlinear acoustics. In the simplest model of propagation in fluids these waves are described by the well-known Burgers’ equation (plane waves). In studies of nonlinear wave propagation an important problem is to find the waveform of the asymptotic wave at long time after the preparation of the initial wave or at long distance from the source emitting the wave. In case of noise-type initial disturbance, the analytical calculation the velocity field is very complicated mathematical problem. The Fast Legendre Transform Algorithm should be applied to solve the problem. In the present paper we consider the numerical simulation of evolution of complex pulses which are characterized by two scales. For such signals the generation of a low-frequency component or a non-zero mean field takes place. It has also been shown that, for a pulse with random carrier, the parameters of the asymptotic waveform depend weakly on the fine structure of the initial pulse, but that the old-age behaviour is very sensitive to the properties of the carrier.

Mots clés: nonlinear acoustics; noise pulses; numerical simulation

Domaines: Acoustique [physics.class-ph]

Igor Demin, Sergey Gurbatov, Nikolay Pronchatov-Rubtsov. Evolution of intensive acoustical noise pulses (the numerical simulation with Fast Legendre Transform Algorithm). Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810946⟩