×

Spectral modelling of high Reynolds number unstably stratified homogeneous turbulence. (English) Zbl 1328.76034

Summary: We study unconfined homogeneous turbulence with a destabilizing background density gradient in the Boussinesq approximation. Starting from initial isotropic turbulence, the buoyancy force induces a transient phase toward a self-similar regime accompanied by a rapid growth of kinetic energy and Reynolds number, along with the development of anisotropic structures in the flow in the direction of gravity. We model this with a two-point statistical approach using an axisymmetric eddy-damped quasi-normal Markovian (EDQNM) closure that includes buoyancy production. The model is able to match direct numerical simulations (DNS) in a parametric study showing the effect of initial Froude number and mixing intensity on the development of the flow. We further improve the model by including the stratification timescale in the characteristic relaxation time for triple correlations in the closure. It permits the computation of the long-term evolution of unstably stratified turbulence at high Reynolds number. This agrees with recent theoretical predictions concerning the self-similar dynamics and brings new insight into the spectral energy distribution and anisotropy of the flow.

MSC:

76F45 Stratification effects in turbulence
76F55 Statistical turbulence modeling
76F25 Turbulent transport, mixing
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (1961)
[2] DOI: 10.1088/1468-5248/1/1/007 · Zbl 1078.76550 · doi:10.1088/1468-5248/1/1/007
[3] DOI: 10.1063/1.868214 · Zbl 0830.76039 · doi:10.1063/1.868214
[4] DOI: 10.1017/S002211209700493X · Zbl 0891.76044 · doi:10.1017/S002211209700493X
[5] DOI: 10.1017/jfm.2011.207 · Zbl 1241.76293 · doi:10.1017/jfm.2011.207
[6] DOI: 10.1063/1.869842 · doi:10.1063/1.869842
[7] DOI: 10.1017/S0022112089001199 · Zbl 0667.76084 · doi:10.1017/S0022112089001199
[8] DOI: 10.1063/1.1688328 · Zbl 1186.76143 · doi:10.1063/1.1688328
[9] DOI: 10.1098/rspa.1950.0052 · Zbl 0038.12201 · doi:10.1098/rspa.1950.0052
[10] DOI: 10.1017/S0022112092001149 · Zbl 0743.76040 · doi:10.1017/S0022112092001149
[11] DOI: 10.1063/1.4864099 · Zbl 06485955 · doi:10.1063/1.4864099
[12] DOI: 10.1063/1.4862445 · Zbl 06485903 · doi:10.1063/1.4862445
[13] DOI: 10.1175/1520-0469(1971)028&lt;0145:APATDT&gt;2.0.CO;2 · doi:10.1175/1520-0469(1971)028<0145:APATDT>2.0.CO;2
[14] DOI: 10.1063/1.1539855 · Zbl 1185.76191 · doi:10.1063/1.1539855
[15] Zhou, Phys. Rev. E 67 (2003)
[16] DOI: 10.1063/1.1694822 · Zbl 0366.76045 · doi:10.1063/1.1694822
[17] DOI: 10.1103/RevModPhys.76.1015 · doi:10.1103/RevModPhys.76.1015
[18] Griffond, Trans. ASME: J. Fluids Engng 136 (2014)
[19] DOI: 10.1016/j.physrep.2009.04.004 · doi:10.1016/j.physrep.2009.04.004
[20] Gréa, Phys. Fluids 26 (2014) · Zbl 06486014 · doi:10.1063/1.4867893
[21] DOI: 10.1063/1.1336151 · Zbl 1184.76614 · doi:10.1063/1.1336151
[22] Gréa, Phys. Fluids 25 (2013) · Zbl 06432786 · doi:10.1063/1.4775379
[23] DOI: 10.1098/rsta.2012.0173 · Zbl 1353.76031 · doi:10.1098/rsta.2012.0173
[24] DOI: 10.1017/S0022112003004531 · Zbl 1085.76026 · doi:10.1017/S0022112003004531
[25] DOI: 10.1016/0167-2789(84)90512-8 · doi:10.1016/0167-2789(84)90512-8
[26] DOI: 10.1063/1.3054152 · Zbl 1183.76550 · doi:10.1063/1.3054152
[27] DOI: 10.1007/978-1-4020-6435-7 · doi:10.1007/978-1-4020-6435-7
[28] Batchelor, The Theory of Homogeneous Turbulence (1953) · Zbl 0053.14404
[29] DOI: 10.1023/B:EFMC.0000016610.05554.0f · doi:10.1023/B:EFMC.0000016610.05554.0f
[30] DOI: 10.1063/1.3680871 · Zbl 06424246 · doi:10.1063/1.3680871
[31] DOI: 10.1098/rspa.1949.0007 · Zbl 0036.25601 · doi:10.1098/rspa.1949.0007
[32] DOI: 10.1103/PhysRevLett.109.254501 · doi:10.1103/PhysRevLett.109.254501
[33] DOI: 10.1017/S0022112077001979 · Zbl 0369.76054 · doi:10.1017/S0022112077001979
[34] DOI: 10.1038/nphys361 · doi:10.1038/nphys361
[35] DOI: 10.1016/0167-2789(84)90510-4 · Zbl 0577.76047 · doi:10.1016/0167-2789(84)90510-4
[36] DOI: 10.1209/0295-5075/91/35001 · doi:10.1209/0295-5075/91/35001
[37] DOI: 10.1017/S0022112009992801 · Zbl 1189.76309 · doi:10.1017/S0022112009992801
[38] DOI: 10.1017/CBO9780511546099 · Zbl 1154.76003 · doi:10.1017/CBO9780511546099
[39] DOI: 10.1103/PhysRevLett.91.115001 · doi:10.1103/PhysRevLett.91.115001
[40] DOI: 10.1103/PhysRevLett.70.3051 · doi:10.1103/PhysRevLett.70.3051
[41] DOI: 10.1112/plms/s1-14.1.170 · JFM 15.0848.02 · doi:10.1112/plms/s1-14.1.170
[42] DOI: 10.1017/S0022112075003369 · Zbl 0323.76039 · doi:10.1017/S0022112075003369
[43] DOI: 10.1103/PhysRevE.81.016316 · doi:10.1103/PhysRevE.81.016316
[44] DOI: 10.1103/PhysRevLett.97.185002 · doi:10.1103/PhysRevLett.97.185002
[45] DOI: 10.1017/CBO9780511840531 · Zbl 0966.76002 · doi:10.1017/CBO9780511840531
[46] DOI: 10.1103/PhysRevLett.28.76 · doi:10.1103/PhysRevLett.28.76
[47] DOI: 10.1017/S0022112070000642 · Zbl 0191.25601 · doi:10.1017/S0022112070000642
[48] DOI: 10.1016/j.pce.2003.11.018 · doi:10.1016/j.pce.2003.11.018
[49] DOI: 10.1175/1520-0469(1964)021&lt;0099:TSONIT&gt;2.0.CO;2 · doi:10.1175/1520-0469(1964)021<0099:TSONIT>2.0.CO;2
[50] DOI: 10.1017/S0022112007008270 · Zbl 1125.76353 · doi:10.1017/S0022112007008270
[51] DOI: 10.1063/1.871025 · doi:10.1063/1.871025
[52] DOI: 10.1080/14685240500207407 · doi:10.1080/14685240500207407
[53] DOI: 10.1063/1.869331 · Zbl 1185.76740 · doi:10.1063/1.869331
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.