Coherent vortices in high resolution direct numerical simulation of homogeneous isotropic turbulence: A wavelet viewpoint

Abstract

Coherent vortices are extracted from data obtained by direct numerical simulation ͑DNS͒ of three-dimensional homogeneous isotropic turbulence performed for different Taylor microscale Reynolds numbers, ranging from Re = 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 = 256 3 , 512 3 , 1024 3 , and 2048 3 , 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 = 2048 3 for Re = 732͒, 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.

Multifractal structure of fully developed turbulence

“…Excluding these regions would cut the spectrum up to k ∼ l −1 , and the scales are easy to separate. An evidence for this second approach comes from the numerical simulations [12]: the observed 'coherent structures' with high vorticity, i.e. vortex filaments, are found to be very stable, the lifetime exceeding many times the largest-eddy turnover time.…”

“…This contradicts to the idea of cascade. In [12] it is shown that these smallscale structures are responsible for the 5/3 law. Picking them out breaks the power-law energy spectrum in the whole inertial range.…”

“…In [12] it was shown that these structures make a fundamental contribution to the observed Kolmogorov's two-thirds law, and they contain the most part of the whole enstrophy of a flow. The origin of these coherent structures is still obscure (in [6] the tendency of a flow to produce these structures was characterized as 'mysterious').…”

Wave-induced coherent turbulence structures and sediment resuspension in the nearshore of a prototype-scale sandy barrier beach

“…Cao (1997), Wu and Yang (2004), Wu and Jiang (2007)). Considerable recent work therefore focusses on the structural form of these features of flow, their role in fluid and sediment entrainment, bed shear stress generation, energy transfer and velocity asymmetry; and the influence of the space-time structure of the flow, with emphasis on oscillatory flows, and different bed roughnesses (Adrian and Marusic, 2012;Carstensen et al, 2010;Carstensen et al (2012); Grigoriadis et al, 2013;Hardy et al, 2010;Hare et al, 2014;Okamoto et al, 2007). Advanced visualisation and data analysis techniques reveal complex interactions between passing coherent energetic structures and sediments in suspension, such as particle response to turbulent fluctuations in the frequency domain (e.g.…”

Adaptive wavelet simulation of weakly compressible flow in a channel with a suddenly expanded section

“…The assessment of adaptive CVS for turbulent flows bounded by walls of complex geometries is also an important issue. In [24], it was shown that wavelet representations are more efficient than non-adaptive representations for isotropic turbulent flow, as the Reynolds number increases. It is thus expected that adaptive CVS is an attractive tool for high Reynolds number flows bounded by walls in complex geometries.…”