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Coherent vortices in high resolution direct numerical simulation of homogeneous isotropic turbulence: a wavelet viewpoint. (English) Zbl 1182.76566
Summary: 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 \(Re_\lambda=167\) 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 \(N=20483\) for \(Re_\lambda=732\)), 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.

MSC:
76M28 Particle methods and lattice-gas methods
76F05 Isotropic turbulence; homogeneous turbulence
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[1] DOI: 10.1063/1.1692279 · doi:10.1063/1.1692279
[2] DOI: 10.1063/1.1693365 · Zbl 0225.76033 · doi:10.1063/1.1693365
[3] Yokokawa M., ACM/IEEE SC 2002 Conference (SC’02) (2002)
[4] DOI: 10.1063/1.1539855 · Zbl 1185.76191 · doi:10.1063/1.1539855
[5] DOI: 10.1098/rspa.1938.0032 · JFM 64.1454.02 · doi:10.1098/rspa.1938.0032
[6] DOI: 10.1017/S002211208100181X · Zbl 0476.76051 · doi:10.1017/S002211208100181X
[7] DOI: 10.1017/S0022112091001957 · Zbl 0721.76036 · doi:10.1017/S0022112091001957
[8] DOI: 10.1017/S0022112093002393 · Zbl 0800.76156 · doi:10.1017/S0022112093002393
[9] DOI: 10.1017/S0022112094003319 · Zbl 0800.76157 · doi:10.1017/S0022112094003319
[10] DOI: 10.1103/PhysRevLett.67.983 · doi:10.1103/PhysRevLett.67.983
[11] DOI: 10.1017/S0022112089002351 · Zbl 0678.76011 · doi:10.1017/S0022112089002351
[12] DOI: 10.1146/annurev.fluid.24.1.395 · doi:10.1146/annurev.fluid.24.1.395
[13] van den Berg J. C., Wavelets in Physics (1999) · Zbl 0934.76002 · doi:10.1017/CBO9780511613265
[14] Farge M., New Trends in Turbulence, Les Houches 2000 74 pp 449– (2002)
[15] Farge M., Encyclopedia of Mathematical Physics pp 408– (2006) · doi:10.1016/B0-12-512666-2/00274-1
[16] DOI: 10.1063/1.870080 · Zbl 1147.76386 · doi:10.1063/1.870080
[17] DOI: 10.2307/2337118 · doi:10.2307/2337118
[18] DOI: 10.1103/PhysRevLett.87.054501 · doi:10.1103/PhysRevLett.87.054501
[19] DOI: 10.1063/1.1736671 · Zbl 1186.76198 · doi:10.1063/1.1736671
[20] Roussel O., J. Turbul. 6 pp 11– (2005) · Zbl 1083.76519 · doi:10.1080/14685240500149831
[21] DOI: 10.1023/A:1013512726409 · Zbl 1094.76525 · doi:10.1023/A:1013512726409
[22] DOI: 10.1017/S0022112005004234 · Zbl 1086.76026 · doi:10.1017/S0022112005004234
[23] DOI: 10.1080/14685240600601061 · Zbl 1273.76331 · doi:10.1080/14685240600601061
[24] DOI: 10.1023/B:APPL.0000044408.46141.26 · Zbl 1081.76564 · doi:10.1023/B:APPL.0000044408.46141.26
[25] Mallat S., A Wavelet Tour of Signal Processing (1998) · Zbl 1125.94306
[26] Schneider K., Woods Hole Mathematics, Perspectives in Mathematics and Physics 34 pp 302– (2004) · doi:10.1142/9789812701398_0007
[27] DOI: 10.1016/j.acha.2004.10.001 · Zbl 1061.42022 · doi:10.1016/j.acha.2004.10.001
[28] Kaneda Y., J. Turbul. 7 pp 20– (2006) · doi:10.1080/14685240500256099
[29] DOI: 10.1146/annurev.fluid.29.1.435 · doi:10.1146/annurev.fluid.29.1.435
[30] DOI: 10.1063/1.1599857 · Zbl 1186.76165 · doi:10.1063/1.1599857
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