Coherent vorticity extraction in 3D homogeneous isotropic turbulence: influence of the Reynolds number and geometrical statistics

Abstract

The coherent vorticity extraction method (CVE) is based on the nonlinear filtering of the vorticity field projected onto an orthonormal wavelet basis made of compactly supported functions. CVE decomposes each turbulent flow realization into two orthogonal components: a coherent and an incoherent random flow. They both contribute to all scales in the inertial range, but exhibit different statistical behavior. We apply CVE to 256 3 subcubes extracted from 3D homogeneous isotropic turbulent flows at different Taylor microscale Reynolds numbers (R λ = 140, 240 and 680), computed by a direct numerical simulation (DNS) at different resolutions (N = 256 3 , 512 3 and 2048 3 ), respectively. We compare the total, coherent and incoherent vorticity fields obtained by using CVE and show that few wavelets coefficients are sufficient to represent the coherent vortices of the flows. Geometrical statistics in term of helicity are also analyzed and the λ 2 criterion is applied to the filtered flow fields.

Wavelet decomposition of forced turbulence: Applicability of the iterative Donoho-Johnstone threshold

“…The Anderson-Darling test is more robust to outliers and only values where the cumulative density function of the model Gaussian distribution had value zero or one to machine precision were omitted. Validation tests with 1024 3 Gaussianly distributed random numbers in place of the incoherent flow vorticity components confirmed with better than 99% confidence that in these test cases the hypothesis could not be dismissed. As a secondary validation criteria we confirmed that the probabilities-to-exceed in the random number cases were uniformly distributed.…”

“…The incoherent component, on the other hand, shows k 2 spectrum, with a peak at the low wave number end of the dissipative range where it joins the original flow spectrum. 2,3,9,12 These findings largely result from Coifman12 wavelet analysis of both run-down and forced turbulent flows, though the results are reported to be robust to the choice of orthogonal wavelet, excluding the Haar, 9 but not to biorthogonal decomposition. 12 Here we investigate the effectiveness of CVE when employing the Haar, Coifman12, and Coifman30 wavelets in the analysis of Taylor-Green and ABC flows.…”

“…Often that convergence is approximated by the variance after a single iteration [8][9][10] or the variance of the total vorticity itself (no iteration). 3,16 The fully iterated threshold would yield optimal de-noising if the flow vorticity were indeed composed of coherent signal and incoherent noise and if the latter were both Gaussianly distributed and spatially uncorrelated. If such were the case, one would also expect the incoherent helicity distribution to reflect random velocity and vorticity vector orientations and the incoherent kinetic energy to scale as k 2 .…”

“…The incoherent component, by contrast, typically contains less than 1% of the flow energy, shows a peak in its helicity distribution near h = 0, and exhibits a k 2 kinetic energy spectrum. 2,3 In this paper, we report on the results of wavelet analysis of two 1024 3 simulations of turbulence forced coherently at large scale, one as a Taylor-Green (TG) and the other as an Arn'old-Beltrami-Childress (ABC) flow (Eqs. (3) and (4) below).…”

“…2,3 In this paper, we report on the results of wavelet analysis of two 1024 3 simulations of turbulence forced coherently at large scale, one as a Taylor-Green (TG) and the other as an Arn'old-Beltrami-Childress (ABC) flow (Eqs. (3) and (4) below). We examine sensitivity to three different wavelets, apply threshold filtering to either the magnitude of the vorticity or the amplitudes of the individual components independently, and study compression ratios ranging from 10% to 98.7%, the later achieved when the iterative Donoho-Johnstone threshold is applied to the wavelet amplitudes of the individual vorticity components.…”