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Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence. (English) Zbl 1156.76406
Summary: We perform a multi-scale non-local geometrical analysis of the structures extracted from the enstrophy and kinetic energy dissipation-rate, instantaneous fields of a numerical database of incompressible homogeneous isotropic turbulence decaying in time obtained by DNS in a periodic box. Three different resolutions are considered: 256\(^3\), 512\(^3\) and 1024\(^3\) grid points, with \(k_{\max}\overline \eta\) approximately 1, 2 and 4, respectively, the same initial conditions and \(Re_\lambda\approx 77\). This allows a comparison of the geometry of the structures obtained for different resolutions. For the highest resolution, structures of enstrophy and dissipation evolve in a continuous distribution from blob-like and moderately stretched tube-like shapes at the large scales to highly stretched sheet-like structures at the small scales. The intermediate scales show a predominance of tube-like structures for both fields, much more pronounced for the enstrophy field. The dissipation field shows a tendency towards structures with lower curvedness than those of the enstrophy, for intermediate and small scales. The 256\(^3\) grid resolution case \(k_{\max}\overline \eta\approx 1\) was unable to detect the predominance of highly stretched sheet-like structures at the smaller scales in both fields. The same non-local methodology for the study of the geometry of structures, but without the multi-scale decomposition, is applied to two scalar fields used by existing local criteria for the eduction of tube- and sheet-like structures in turbulence, \(Q\) and \([A_{ij}]_+\), respectively, obtained from invariants of the velocity-gradient tensor and alike in the 1024\(^3\) case. This adds the non-local geometrical characterization and classification to those local criteria, assessing their validity in educing particular geometries. Finally, we introduce a new methodology for the study of proximity issues among structures of different fields, based on geometrical considerations and non-local analysis, by taking into account the spatial extent of the structures. We apply it to the four fields previously studied. Tube-like structures of \(Q\) are predominantly surrounded by sheet-like structures of \([A_{ij}]_+\), which appear at closer distances. For the enstrophy, tube-like structures at an intermediate scale are primarily surrounded by sheets of smaller scales of the enstrophy and structures of dissipation at the same and smaller scales. A secondary contribution results from tubes of enstrophy at smaller scales appearing at farther distances. Different configurations of composite structures are presented.
Reviewer: Reviewer (Berlin)

MSC:
76F65 Direct numerical and large eddy simulation of turbulence
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References:
[1] DOI: 10.1017/S0022112005004040 · Zbl 1070.76033 · doi:10.1017/S0022112005004040
[2] DOI: 10.1023/B:APPL.0000044408.46141.26 · Zbl 1081.76564 · doi:10.1023/B:APPL.0000044408.46141.26
[3] DOI: 10.1063/1.858333 · doi:10.1063/1.858333
[4] DOI: 10.1017/S0022112008001511 · Zbl 1145.76024 · doi:10.1017/S0022112008001511
[5] DOI: 10.1103/PhysRevLett.79.1253 · doi:10.1103/PhysRevLett.79.1253
[6] DOI: 10.1098/rspa.1926.0043 · doi:10.1098/rspa.1926.0043
[7] DOI: 10.1137/05064182X · Zbl 1122.65134 · doi:10.1137/05064182X
[8] Richardson, Weather Prediction by Numerical Process. (1922) · JFM 48.0629.07
[9] DOI: 10.1063/1.858441 · Zbl 0775.76078 · doi:10.1063/1.858441
[10] DOI: 10.1146/annurev.fluid.30.1.31 · Zbl 1398.76084 · doi:10.1146/annurev.fluid.30.1.31
[11] DOI: 10.1063/1.863442 · doi:10.1063/1.863442
[12] Onsager, Phys. Rev. 68 pp 286– (1945)
[13] DOI: 10.1017/S002211200800092X · Zbl 1151.76522 · doi:10.1017/S002211200800092X
[14] DOI: 10.1063/1.2771661 · Zbl 1182.76566 · doi:10.1063/1.2771661
[15] Batchelor, Proc. R. Soc. Lond. A 199 pp 238– (1949)
[16] DOI: 10.1017/S0022112098003024 · Zbl 0933.76035 · doi:10.1017/S0022112098003024
[17] DOI: 10.1063/1.866513 · doi:10.1063/1.866513
[18] DOI: 10.1017/S0022112004009802 · Zbl 1107.76328 · doi:10.1017/S0022112004009802
[19] DOI: 10.1063/1.869361 · Zbl 1185.76770 · doi:10.1063/1.869361
[20] DOI: 10.1017/S0022112091003786 · Zbl 0749.76033 · doi:10.1017/S0022112091003786
[21] DOI: 10.1063/1.863957 · Zbl 0536.76034 · doi:10.1063/1.863957
[22] Landau, Fluid Mechanics. (1959)
[23] DOI: 10.1017/S002211207400070X · Zbl 0273.76037 · doi:10.1017/S002211207400070X
[24] DOI: 10.1017/S0022112062000518 · Zbl 0112.42003 · doi:10.1017/S0022112062000518
[25] Kolmogorov, Dokl. Nauk. SSSR. 30 pp 301– (1941)
[26] Kolmogorov, Dokl. Nauk. SSSR. 32 pp 16– (1941)
[27] DOI: 10.1016/0262-8856(92)90076-F · doi:10.1016/0262-8856(92)90076-F
[28] DOI: 10.1017/S0022112085001136 · Zbl 0587.76080 · doi:10.1017/S0022112085001136
[29] DOI: 10.1017/S0022112061000974 · Zbl 0103.19903 · doi:10.1017/S0022112061000974
[30] DOI: 10.1017/S0022112093002393 · Zbl 0800.76156 · doi:10.1017/S0022112093002393
[31] DOI: 10.1063/1.858282 · doi:10.1063/1.858282
[32] DOI: 10.1038/nature01334 · doi:10.1038/nature01334
[33] DOI: 10.1017/S0022112095000462 · Zbl 0847.76007 · doi:10.1017/S0022112095000462
[34] DOI: 10.1063/1.869866 · Zbl 1147.76537 · doi:10.1063/1.869866
[35] DOI: 10.1143/JPSJ.72.983 · doi:10.1143/JPSJ.72.983
[36] DOI: 10.1017/S0022112006009128 · Zbl 1156.76405 · doi:10.1017/S0022112006009128
[37] DOI: 10.1017/S0022112094003319 · Zbl 0800.76157 · doi:10.1017/S0022112094003319
[38] DOI: 10.1063/1.2147610 · Zbl 1188.76063 · doi:10.1063/1.2147610
[39] DOI: 10.1017/S002211208100181X · Zbl 0476.76051 · doi:10.1017/S002211208100181X
[40] DOI: 10.1017/S0022112092002325 · doi:10.1017/S0022112092002325
[41] DOI: 10.1017/S0022112007009251 · Zbl 1159.76334 · doi:10.1017/S0022112007009251
[42] DOI: 10.1063/1.870348 · Zbl 1149.76561 · doi:10.1063/1.870348
[43] DOI: 10.1063/1.1410981 · Zbl 1184.76230 · doi:10.1063/1.1410981
[44] DOI: 10.1063/1.858546 · doi:10.1063/1.858546
[45] He, Phys. Rev. Lett. 81 pp 4639– (1998)
[46] DOI: 10.1103/PhysRevA.38.6287 · doi:10.1103/PhysRevA.38.6287
[47] DOI: 10.1103/PhysRevE.77.026303 · doi:10.1103/PhysRevE.77.026303
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