Spectrograms of one-dimensional isotropic turbulence

Abstract

An equation for describing the evolution of the spectrogram velocity amplitudes of individual wave components placed on a finite field, the interaction of the components in which satisfies the triad rule: k = k' ± k", is proposed. The details of the energy transport along the spectrum, the decay and power supply modes are considered. In the absence of dissipation and pumping the total intensity of the system that is analogy of energy is unchanged. The results of a numerical calculation of the transition to white noise (in the absence of dissipation), the decay regimes at various Reynolds numbers, and the transition to the equilibrium state for different pumping by the large-scale components, are obtained. The results obtained correspond to known experimental data obtained for real turbulent flows. In the one-dimensional case, the correlation function and the third moment that determines the structure change in the field structure upon decay is restored.