Statistics of Fourier modes in a turbulent flow

Fourier series are often used to discuss the properties of a homogeneous turbulent field. We investigate the statistics of Fourier modes of the turbulent velocity field and of a passive scalar. The statistics of individual Fourier modes is known to be Gaussian when the size of the system L is much larger that the integral (correlation) size l(0). The case where the integral size is of the order of the system size L approximately l(0), is studied by direct numerical simulations in the range 20 < or approximately = Rlambda < or approximately = 80. At a given Rlambda, we find that the probabilities of large fluctuations become larger when the wave number increases, in qualitative agreement with the notion of intermittency. As the Reynolds number increases, however, the probability density functions become closer to Gaussian, in sharp contrast with the behavior of velocity increments. We also show that in a simple model of cascade, the Fourier series decomposition is not appropriate to capture intermittency effects. Last, we discuss other issues related to our results.