Intermittency, synthetic turbulence and wavelet structure functions

Some techniques for the study of intermittency by means of wavelet transforms, are presented on an example of synthetic turbulent signal. Several features of the turbulent field, that cannot be probed looking at standard structure function scaling, become accessible in this way. The concept of a directly measurable intermittency scale, distinct from the scale of the fluctuations, is introduced. A method for optimizing the analyzing wavelets, which exploits this concept, and allows to minimize non-local contributions in scale to wavelet correlations, is described. The transition from a wavelet to a Fourier transform based description of an intermittent random field, and the possibility of using Fourier correlations to measure intermittency are discussed. Important limitations in the ability of structure functions to give a local in scale description of intermittent random fields, are observed. PACS numbers: 47.27.Jv, 02.50.Ey, 05.45.+b, 47.27.Gs Submitted to Physica D 3/27/98