Wavelet Transform Analysis of Turbulence

Considerable progress has been made over the last three decades in our understanding of turbulence through new developments of theory, experiment, and computation. More and more evidence has been accumulated for the physical description of turbulent motions in both two and three dimensions. Consequently, turbulence is now characterized by a remarkable degree of order even though turbulence is usually defined as disordered fluid flows. In spite of tremendous progress, there are still a number of open questions and unsolved problems. These include coherent structures and intermittency effects, singularities of the Navier-Stokes equations, non-Gaussian statistics of turbulent flows, perturbations to the small scale produced by nonisotropic, non-Gaussian, and inhomogeneous large-scale motions, and measurements and computations of small-scale turbulence. No complete theory is yet available for the problem of how the eddy structure of turbulence evolves both under the action of mean distortion and even during the mutual random interaction of eddies of different sizes or scales.