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Analysis of turbulence in the orthonormal wavelet representation. (English) Zbl 0749.76033
This paper uses orthonormal wavelet transforms rather than the more usual Fourier transforms to analyze turbulent velocity fields. The aim is to obtain a description that can exhibit both localization in wavenumber and physical space simultaneously. After reviewing wavelet theory and describing its application to the Navier-Stokes equations both on terms of continuous and discrete transforms, the author applies the wavelet analysis of the turbulent kinetic energy to both experimental and numerical data sets. Issues addressed in this new approach include attempts to describe intermittency using notions of multifractal distributions and transfer and flux amongst small scales. The author concludes that orthonormal wavelet analysis can be performed as easily as Fourier analysis, but offers potentially more physical insight.

MSC:
76F99 Turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
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