The numerical solution of nonlinear hydrodynamic equations has been considered on the basis of the fast Legendre transform algorithm, which makes it possible to reduce substantially the number of operations as compared to standard methods. The evolution of intense acoustic pulses with noise filling has been studied numerically. Three typical envelopes are considered. Speed profiles and the probability distributions of the absolute maximum coordinate have been obtained for each of the envelopes. The generation of non-zero average speed field at large distances has been shown to occur as a result of nonlinear interactions.
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