Statistical properties of an equation describing fluid interfaces

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Abstract
The Kuramoto-Sivashinsky equation which describes fluid interfaces in several physical contexts is known to have chaotic solutions, displaying both space and time disorder. We have investigated numerically several statistical properties of this model. The fluctuations of a local quantity are shown to have a highly non Gaussian distribution; boundary effects and small scale intermittency phenomena are examined. The moments of the fluctuations of the space Fourier transform, which are related to the space correlation functions, are also investigated. The high order moments of large wavenumber fluctuations grow faster than the moments of a Gaussian variable; while the low wavenumber fluctuations are found to be almost Gaussian. Some finite size effects are also discussed. Similarly the fluctuations of the time Fourier transform of a local quantity have been investigated; they share most of the above mentioned property. A similar behaviour is observed in the case of the Lorenz [23] equations. Eventually we introduce correlation functions testing the time symmetry of the fluctuations and compute some of these functions. We use our numerical results to discuss energy transfer process

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