An Adaptive Wavelet Method Compared to Non-Linearly Filtered Pseudo-Spectral Methods for Two-Dimensional Turbulence

Wavelet methods have been associated with turbulence, almost since their invention, to analyze the structure and dynamics of the flow, for a recent review we refer the reader to [1]. These studies have shown that the strongest modes of the wavelet transform of a two-dimensional turbulent flow represent the coherent structures (e.g. vortices), while the weaker modes represent the unorganized background flow. Furthermore, it has been found that the coherent vortices can be well represented by only a very few wavelet modes. These observations suggest that wavelets could be an efficient basis for two-dimensional turbulent flows since the dynamics of such flows are largely controlled by their coherent vortices.