Turbulence is a state of flows which is characterized by a combination of chaotic and random behaviours affecting a very large range of scales. It is governed by Navier-Stokes equations and corresponds to their solutions in the limit where the fluid viscosity becomes negligible, the nonlinearity dominant and the turbulent dissipation constant. In this regime one observes that fluctuations tend to self-organize into coherent structures which seem to have their own dynamics.

A prominent tool for multiscale decomposition are wavelets. A wavelet is a well localized oscillating smooth function, e.g. a wave packet, which is translated and dilated. The wavelet transform decomposes a flow field into scale-space contributions from which it can be reconstructed.

We will show how the wavelet transform can decompose turbulent flows into coherent and incoherent contributions presenting different statistical and dynamical properties. We will then propose a new way to analyze and predict the evolution of turbulent flows.

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The presentation will use different results obtained in collaboration with:

Kai Schneider (Universite de Provence, Marseille, France),
Naoya Okamoto, Katsunori Yoshimatsu and Yukio Kaneda (Nagoya University, Japan)

Related publications can be downloaded from the web page
http://wavelets.ens.fr