INTERNATIONAL JOURNAL OF c © 2008 Institute for Scientific NUMERICAL ANALYSIS AND MODELING Computing and Information Volume 5, Supp, Pages 64–84 WAVELETS, A NUMERICAL TOOL FOR MULTISCALE PHENOMENA: FROM TWO DIMENSIONAL TURBULENCE TO ATMOSPHERIC DATA ANALY

Abstract. Multiresolution methods, such as the wavelet decompositions, are increasingly used in physical applications where multiscale phenomena occur. We present in this paper two applications illustrating two different aspects of the wavelet theory. In the first part of this paper, we recall the bases of the wavelets theory. We describe how to use the continuous wavelet decomposition for analyzing mul-tifractal patterns. We also summarize some results about orthogonal wavelets and wavelet packets decompositions. In the second part, we show that the wavelet packet filtering can be successfully used for analyzing two-dimensional turbulent flows. This technique allows the separation of two structures: the solid rotation part of the vortices and the remaining mainly composed of vorticity filaments. These two structures are multiscale and cannot be obtained through usual filtering methods like Fourier decompositions. The first structures are responsible for the inverse transfer of energy while the second ones are responsible for the forward transfer of en