This Letter presents a wavelet technique for extracting coherent vortices from three-dimensional turbulent flows, which is applied to a homogeneous isotropic turbulent flow at resolution N = 256(3). The coherent flow is reconstructed from only 3%N wavelet coefficients that retain the vortex tubes, and 98.9% of the energy with the same k(-5/3) spectrum as the total flow. In contrast, the remaining 97%N wavelet coefficients correspond to the incoherent flow which is structureless, decorrelated, and whose effect can therefore be modeled statistically.
The coherent vortex simulation ͑CVS͒ decomposes each realization of a turbulent flow into two orthogonal components: An organized coherent flow and a random incoherent flow. They both contribute to all scales in the inertial range, but exhibit different statistical behaviors. The CVS decomposition is based on the nonlinear filtering of the vorticity field, projected onto an orthonormal wavelet basis made of compactly supported functions, and the computation of the induced velocity field using Biot-Savart's relation. We apply it to a three-dimensional homogeneous isotropic turbulent flow with a Taylor microscale Reynolds number R ϭ168, computed by direct numerical simulation at resolution Nϭ256 3 . Only 2.9%N wavelet modes correspond to the coherent flow made of vortex tubes, which contribute 99% of energy and 79% of enstrophy, and exhibit the same k Ϫ5/3 energy spectrum as the total flow. The remaining 97.1%N wavelet modes correspond to a incoherent random flow which is structureless, has an equipartition energy spectrum, and a Gaussian velocity probability distribution function ͑PDF͒. For the same flow and the same compression rate, the proper orthogonal decomposition ͑POD͒, which in this statistically homogeneous case degenerates into the Fourier basis, decomposes each flow realization into large scale and small scale flows, in a way similar to large eddy simulation ͑LES͒ filtering. It is shown that the large scale flow thus obtained does not extract the vortex tubes equally well as the coherent flow resulting from the CVS decomposition. Moreover, the small scale flow still contains coherent structures, and its velocity PDF is stretched exponential, while the incoherent flow is structureless, decorrelated, and its velocity PDF is Gaussian. Thus, modeling the effect of the incoherent flow discarded by CVS-wavelet shall be easier than modeling the effect of the small scale flow discarded by POD-Fourier or LES.
This paper assesses the potential of coherent vortex simulation (CVS) to compute three-dimensional turbulent mixing layers. CVS splits each turbulent flow realization into two orthogonal parts, one corresponding to coherent vortices which are kept, and the other to an incoherent background flow which is discarded. The CVS filter is applied to data from direct numerical simulations (DNS) of three-dimensional forced and unforced time-developing turbulent mixing layers. The coherent flow is represented by few wavelet modes, but these are sufficient to reproduce the vorticity probability distribution function and the energy spectrum out to the high-wavenumber end of the inertial range. The discarded incoherent background flow is homogeneous, small-amplitude and decorrelated. The CVS-filtering results are then compared with those obtained for the same compression ratio using Fourier low-pass filtering, as employed in large-eddy simulation (LES). Compared to the incoherent background flow of CVS filtering, the subgrid scales of LES filtering are less homogeneous, have much larger amplitude, and exhibit spatial correlations that makes modelling them a difficult challenge. Finally we present simulations of a time-developing mixing layer where the CVS filter is applied at each time step. The results show that CVS preserves the nonlinear dynamics of the flow, and that discarding the incoherent modes is sufficient to model turbulent dissipation.
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