Wavelet Transforms And Their Applications To Turbulence

A general description of continuous vs discrete wavelet transform is given emphasizing their use in the study of turbulence, and diagnostic methods are described based on wavelet coefficients. Attention is given to the need for a space-scale decomposition of turbulent flows and to the principles of wavelet transform. An analyzing function must have an average that is zero to be called a wavelet, and wavelets must be mutually similar, invertible, and regular. Continuous wavelet transform is described in terms of its analysis and synthesis, and the main properties of this process include linearity, covariance by translation and dilation, energy conservation, and space-scale locality. Comparison is made to the process of discrete wavelet transform which uses quasiorthogonal wavelet frames and interpolation. Wavelet applications to turbulence reviewed in the paper encompass energy decomposition, turbulence diagnostics, space-scale anisotropy, and turbulence computing and modeling methods. (C.C.S.)