Abstract
Coherent vortices are extracted from data obtained by direct numerical simulation (DNS) of three-dimensional homogeneous isotropic turbulence performed for different Taylor microscale Reynolds numbers, ranging from Reλ=167 to 732, in order to study their role with respect to the flow intermittency. The wavelet-based extraction method assumes that coherent vortices are what remains after denoising, without requiring any template of their shape. Hypotheses are only made on the noise that, as the simplest guess, is considered to be additive, Gaussian, and white. The vorticity vector field is projected onto an orthogonal wavelet basis, and the coefficients whose moduli are larger than a given threshold are reconstructed in physical space, the threshold value depending on the enstrophy and the resolution of the field, which are both known a priori. The DNS dataset, computed with a dealiased pseudospectral method at resolutions N=2563,5123,10243, and 20483, is analyzed. It shows that, as the Reynolds number increases, the percentage of wavelet coefficients representing the coherent vortices decreases; i.e., flow intermittency increases. Although the number of degrees of freedom necessary to track the coherent vortices remains small (e.g., 2.6% of N=20483 for Reλ=732), it preserves the nonlinear dynamics of the flow. It is thus conjectured that using the wavelet representation the number of degrees of freedom to compute fully developed turbulent flows could be reduced in comparison to the standard estimation based on Kolmogorov’s theory.
Highlights
Direct numerical simulationDNSof homogeneous isotropic turbulence using Fourier spectral methods has a long tradition
A dimensional analysis based on the Kolmogorov scaling predicts N κ Re9/2, where N denotes the total number of spatial grid points
Since there has not yet been a universal definition for them, we consider the following minimal but hopefully consensual statement about them: coherent structures are not noise. Using this apophatic methodon the model of negative theologywe propose the definition: coherent structures correspond to what remains after denoising. ͑4͒ For the noise, we use the mathematical definition stating that a noise cannot be compressed in any functional basis. ͑5͒ We choose, as a first guess, the simplest possible type of noise, namely, additive, Gaussian, and whiteuncorrelatednoise. ͑6͒ Since we do not know a priori the variance of the noise, we have developed an iterative procedure27 to estimate it from the weakest wavelet coefficients. ͑7͒ Since we consider the case of homogeneous isotropic turbulence, we suppose that each component of the vector field has a similar contribution to the modulus, which is used to compute the variance
Summary
The incoherent vorticity reconstructed from most of the wavelet coefficients, whose moduli are below the threshold, corresponds to an almost uncorrelated random background flow with quasi-Gaussian one-point statistics. This technique has been extended to three-dimensional3Dflows using a vector-valued orthogonal wavelet decomposition.. This technique has been extended to three-dimensional3Dflows using a vector-valued orthogonal wavelet decomposition.18 We applied it to DNS data computed at resolution 2563 corresponding to a Taylor microscale Reynolds number Re = 150. The aim of the present paper is to apply the coherent vortex extraction algorithm to higher resolution DNS data of homogeneous isotropic turbulenceup to Re = 732͒ in order to study the influence of the Reynolds number. In Appendix B, the influence of the number of the iterations in the coherent vortex extraction method is examined
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