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Integrable Turbulence
Turbulence intégrable

Dates: 6 -17 May 2019
Place: CIRM (Marseille Luminy, France)

The field of integrable turbulence has been recently introduced as a completely new chapter of turbulence theory by V. E. Zakharov, one of the creators of the standard wave turbulence theory. In wave turbulence theory, the random initial data are obtained by considering Fourier components as independent (normal) random variables. Typically, one is interested in the expectation of the square of the Fourier modes (wave spectrum) or the correlations between the various Fourier modes over large times. V. Zakharov has found that in turbulence with weak nonlinearity, the wave spectrum possesses a power law solution like the Kolmogorov spectra of fluid turbulence. In integrable systems, the wave turbulence theory fails and new concepts have been put forward. Indeed, in strongly nonlinear integrable systems, the typical excitations are solitons, therefore, in analogy with the kinetic equations of gas, one is interested in studying the statistical properties of random incoherent gas of solitons. More precisely, the goals are the statistical description of incoherent waves that are a mixture of gas of solitons and small amplitude dispersive radiation; and the determination of the probability density function for the fluctuations of the incoherent field.