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Topological evolution in compressible turbulent boundary layers. (English) Zbl 1294.76175
Summary: Topological evolution of compressible turbulent boundary layers at Mach 2 is investigated by means of statistical analysis of the invariants of the velocity gradient tensor based on the direct numerical simulation database. The probability density functions of the rate of change of the invariants exhibit the -3 power-law distribution in the region of large Lagrangian derivative of the invariants in the inner and outer layers. The topological evolution is studied by conditional mean trajectories for the evolution of the invariants. The trajectories illustrate inward-spiralling orbits around and converging to the origin of the space of invariants in the outer layer, while they are repelled by the vicinity of the origin and converge towards a limit cycle in the inner layer. The compressibility effect on the mean topological evolution is studied in terms of the ’incompressible’, compressed and expanding regions. It is found that the mean evolution of flow topologies is altered by the compressibility. The evolution equations of the invariants are derived and the relevant dynamics of the mean topological evolution are analysed. The compressibility effect is mainly related to the pressure effect. The mutual-interaction terms among the invariants are the root of the clockwise spiral behaviour of the local flow topology in the space of invariants.

MSC:
76F40 Turbulent boundary layers
76F50 Compressibility effects in turbulence
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[1] Proceedings of the Summer Program (1990)
[2] DOI: 10.1063/1.857511 · doi:10.1063/1.857511
[3] DOI: 10.1017/S0022112006009244 · Zbl 1093.76510 · doi:10.1017/S0022112006009244
[4] DOI: 10.1063/1.858295 · Zbl 0754.76004 · doi:10.1063/1.858295
[5] Turbulence (1995)
[6] J. Phys. Paris 43 pp 837– (1982)
[7] DOI: 10.1017/S0022112096001802 · Zbl 0864.76036 · doi:10.1017/S0022112096001802
[8] DOI: 10.1063/1.3291070 · Zbl 1183.76191 · doi:10.1063/1.3291070
[9] DOI: 10.1063/1.1472506 · Zbl 1185.76376 · doi:10.1063/1.1472506
[10] Proceedings of the Summer Program (2010)
[11] DOI: 10.1017/S0022112010005902 · Zbl 1225.76160 · doi:10.1017/S0022112010005902
[12] An Informal Conceptual Introduction to Turbulence (2009) · Zbl 1177.76001
[13] An Introduction to Fluid Mechanics (1967)
[14] Turbulence Structure and Vortex Dynamics pp 164– (2000)
[15] DOI: 10.1007/s00348-010-1004-z · doi:10.1007/s00348-010-1004-z
[16] DOI: 10.1017/S0022112097008057 · Zbl 0908.76039 · doi:10.1017/S0022112097008057
[17] DOI: 10.1098/rspa.1938.0002 · JFM 64.1453.04 · doi:10.1098/rspa.1938.0002
[18] DOI: 10.1063/1.4757656 · Zbl 06429779 · doi:10.1063/1.4757656
[19] DOI: 10.1063/1.857730 · doi:10.1063/1.857730
[20] DOI: 10.1080/14685248.2011.633522 · Zbl 1273.76220 · doi:10.1080/14685248.2011.633522
[21] J. Fluid Mech. 439 pp 131– (2001)
[22] DOI: 10.1063/1.3005832 · Zbl 1182.76149 · doi:10.1063/1.3005832
[23] DOI: 10.1080/14685241003627760 · doi:10.1080/14685241003627760
[24] DOI: 10.1103/PhysRevLett.97.174501 · doi:10.1103/PhysRevLett.97.174501
[25] DOI: 10.1017/S0022112008004631 · Zbl 1156.76435 · doi:10.1017/S0022112008004631
[26] DOI: 10.1063/1.870101 · Zbl 1147.76360 · doi:10.1063/1.870101
[27] DOI: 10.1063/1.868323 · Zbl 0827.76031 · doi:10.1063/1.868323
[28] DOI: 10.1016/0021-9991(88)90177-5 · Zbl 0653.65072 · doi:10.1016/0021-9991(88)90177-5
[29] Homogeneous Turbulence Dynamics (2008) · Zbl 1154.76003
[30] Turbulent Flows (2000) · Zbl 0966.76002
[31] DOI: 10.1063/1.1637604 · Zbl 1186.76423 · doi:10.1063/1.1637604
[32] DOI: 10.1063/1.1804553 · Zbl 1187.76418 · doi:10.1063/1.1804553
[33] J. Fluid Mech. 613 pp 205– (2008)
[34] DOI: 10.1146/annurev.fl.19.010187.001013 · doi:10.1146/annurev.fl.19.010187.001013
[35] DOI: 10.1017/S0022112098003681 · Zbl 0965.76031 · doi:10.1017/S0022112098003681
[36] DOI: 10.1088/1742-6596/318/6/062018 · doi:10.1088/1742-6596/318/6/062018
[37] DOI: 10.1146/annurev-fluid-122109-160708 · Zbl 1299.76088 · doi:10.1146/annurev-fluid-122109-160708
[38] DOI: 10.1063/1.869179 · doi:10.1063/1.869179
[39] DOI: 10.1063/1.869752 · Zbl 1185.76767 · doi:10.1063/1.869752
[40] DOI: 10.1017/S0022112009991947 · Zbl 1183.76787 · doi:10.1017/S0022112009991947
[41] DOI: 10.1103/PhysRevE.79.016305 · doi:10.1103/PhysRevE.79.016305
[42] DOI: 10.1080/14685240802698774 · doi:10.1080/14685240802698774
[43] DOI: 10.1063/1.3541841 · Zbl 06421601 · doi:10.1063/1.3541841
[44] DOI: 10.1017/S0022112087000892 · Zbl 0616.76071 · doi:10.1017/S0022112087000892
[45] DOI: 10.1006/jcph.1996.0130 · Zbl 0877.65065 · doi:10.1006/jcph.1996.0130
[46] DOI: 10.1063/1.3475816 · Zbl 06415457 · doi:10.1063/1.3475816
[47] DOI: 10.1007/s00162-002-0084-7 · Zbl 1068.76522 · doi:10.1007/s00162-002-0084-7
[48] DOI: 10.1017/jfm.2012.212 · Zbl 1248.76085 · doi:10.1017/jfm.2012.212
[49] Phys. Fluids A 2 pp 242– (1990)
[50] DOI: 10.1017/jfm.2012.474 · Zbl 1284.76214 · doi:10.1017/jfm.2012.474
[51] DOI: 10.1080/14685240500307389 · Zbl 1273.76223 · doi:10.1080/14685240500307389
[52] DOI: 10.1017/S002211209900720X · Zbl 0985.76038 · doi:10.1017/S002211209900720X
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