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2 Hydrodynamics of incompressible fluid in wavelet representation

We present multiscale description of hydrodynamic turbulence in incompressible fluid based on continuous wavelet transform. The wavelet transform of the velocity field is taken in L 1 norm, so that the wavelet coefficients u l (x) have the meaning of the velocity fluctuations of scale l. An extra contribution to the energy transfer from large to smaller scales is derived. It is shown that the Kolmogorov hypotheses are naturally reformulated in multiscale formalism. The multiscale perturbation theory and statistical closures are constructed.