Wavelet decomposition of Taylor-Green forced-turbulence: sensitivity of the incoherent component statistics to threshold value
Abstract
We examine orthonormal wavelet decomposition of turbulent flows into what are called coherent and incoherent components by the authors of the Coherent Vortex Extraction (CVE) methodology. The CVE thresholding method de-noises a signal based on the variance of the noise, assuming the noise is Gaussian. We ask whether this assumption is valid when the method is applied to Taylor-Green turbulence. Employing Coiflet 12 and 30 wavelets, we confirm previous results showing that coherent flow reconstruction when based on a small fraction of the wavelet coefficients (the highest 1% in amplitude) yields vorticity distributions, kinetic energy spectra, and helicity spectra very close to the original data. However, we find that no wavelet amplitude threshold yields a strictly Gaussian vorticity distribution for the incoherent (noise) component. The most Gaussian incoherent flow is found for threshold values that give data compression of ~83%, much lower than that based on the CVE de-noising criterion. For all wavelet decompositions, between 20 to 99% compression (the ladder being the CVE value), the incoherent component has a vorticity distribution with significantly positive kurtosis. This is true even when the threshold is explicitly chosen to yield the most Gaussian incoherent vorticity distribution (see Figure). Finally, we confirm that the incoherent component does have a k^2 kinetic energy spectrum as reported previously in other applications of CVE, if the threshold is explicitly chosen to yield the most Gaussian incoherent vorticity distribution, but not if it is chosen based on the CVE criterion. Near Gaussianity of the incoherent vorticity thus appears to be linked with uniform energy distribution among the high wavenumber modes. Kurtosis of the x component of the incoherent vorticity as a function of compression, indicating percent of wavelet coefficients [Coiflet 12 (squares) Coiflet 30 (triangles)] contributing to incoherent flow ranging from 20 to over 99%.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2010
- Bibcode:
- 2010AGUFMNG51B1207L
- Keywords:
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- 3379 ATMOSPHERIC PROCESSES / Turbulence;
- 4490 NONLINEAR GEOPHYSICS / Turbulence