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Kinetic energy transfer in compressible isotropic turbulence. (English) Zbl 1419.76252
Summary: Kinetic energy transfer in compressible isotropic turbulence is studied using numerical simulations with solenoidal forcing at turbulent Mach numbers ranging from 0.4 to 1.0 and at a Taylor Reynolds number of approximately 250. The pressure dilatation plays an important role in the local conversion between kinetic energy and internal energy, but its net contribution to the average kinetic energy transfer is negligibly small, due to the cancellation between compression and expansion work. The right tail of probability density function (PDF) of the subgrid-scale (SGS) flux of kinetic energy is found to be longer at higher turbulent Mach numbers. With an increase of the turbulent Mach number, compression motions enhance the positive SGS flux, and expansion motions enhance the negative SGS flux. Average of SGS flux conditioned on the filtered velocity divergence is studied by numerical analysis and a heuristic model. The conditional average of SGS flux is shown to be proportional to the square of filtered velocity divergence in strong compression regions for turbulent Mach numbers from 0.6 to 1.0. Moreover, the antiparallel alignment between the large-scale strain and the SGS stress is observed in strong compression regions. The inter-scale transfer of solenoidal and compressible components of kinetic energy is investigated by Helmholtz decomposition. The SGS flux of solenoidal kinetic energy is insensitive to the change of turbulent Mach number, while the SGS flux of compressible kinetic energy increases drastically as the turbulent Mach number becomes larger. The compressible mode persistently absorbs energy from the solenoidal mode through nonlinear advection. The kinetic energy of the compressible mode is transferred from large scales to small scales through the compressible SGS flux, and is dissipated by viscosity at small scales.

MSC:
76F05 Isotropic turbulence; homogeneous turbulence
76F50 Compressibility effects in turbulence
76F65 Direct numerical and large eddy simulation of turbulence
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[1] Aluie, H.; Eyink, G. L., Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter, Phys. Fluids, 21, (2009) · Zbl 1183.76072
[2] Aluie, H., Compressible turbulence: the cascade and its locality, Phys. Rev. Lett., 106, (2011)
[3] Aluie, H.; Li, S.; Li, H., Conservative cascade of kinetic energy in compressible turbulence, Astrophys. J. Lett., 751, L29, (2012)
[4] Aluie, H., Scale decomposition in compressible turbulence, Physica D, 247, 54-65, (2013) · Zbl 1308.76133
[5] Anderson, B. W.; Domaradzki, J. A., A subgrid-scale model for large-eddy simulation based on the physics of interscale energy transfer in turbulence, Phys. Fluids, 24, (2012)
[6] Balsara, D. S.; Shu, C. W., Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J. Comput. Phys., 160, 405-452, (2000) · Zbl 0961.65078
[7] Benzi, R.; Biferale, L.; Fisher, R. T.; Kadanoff, L. P.; Lamb, D. Q.; Toschi, F., Intermittency and universality in fully developed inviscid and weakly compressible turbulent flows, Phys. Rev. Lett., 100, (2008)
[8] Borue, V.; Orszag, S. A., Local energy flux and subgrid-scale statistics in three-dimensional turbulence, J. Fluid Mech., 366, 1-31, (1998) · Zbl 0924.76035
[9] Cerutti, S.; Meneveau, C., Intermittency and relative scaling of subgrid-scale energy dissipation in isotropic turbulence, Phys. Fluids, 10, 928-937, (1997) · Zbl 1185.76660
[10] Cimarelli, A.; Angelis, E. D., The physics of energy transfer toward improved subgrid-scale models, Phys. Fluids, 26, (2014)
[11] Domaradzki, J. A.; Liu, W.; Brachet, M. E., An analysis of subgrid-scale interactions in numerically simulated isotropic turbulence, Phys. Fluids A, 5, 1747-1759, (1993) · Zbl 0782.76043
[12] Domaradzki, J. A.; Carati, D., A comparison of spectral sharp and smooth filters in the analysis of nonlinear interactions and energy transfer in turbulence, Phys. Fluids, 19, (2007) · Zbl 1182.76208
[13] Domaradzki, J. A.; Carati, D., An analysis of the energy transfer and the locality of nonlinear interactions in turbulence, Phys. Fluids, 19, (2007) · Zbl 1182.76209
[14] Domaradzki, J. A.; Saiki, E. M., Backscatter models for large-Eddy simulations, Theor. Comput. Fluid Dyn., 9, 75-83, (1997) · Zbl 0907.76061
[15] Domaradzki, J. A.; Teaca, B.; Carati, D., Locality properties of the energy flux in turbulence, Phys. Fluids, 21, (2009) · Zbl 1183.76185
[16] Eyink, G. L., Locality of turbulent cascades, Physica D, 207, 91-116, (2005) · Zbl 1076.76037
[17] Eyink, G. L.; Aluie, H., Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining, Phys. Fluids, 21, (2009) · Zbl 1183.76195
[18] Falkovich, G.; Fouxon, I.; Oz, Y., New relations for correlation functions in Navier-Stokes turbulence, J. Fluid Mech., 644, 465-472, (2010) · Zbl 1189.76291
[19] Ishihara, T.; Kaneda, Y.; Yokokawa, M.; Itakura, K.; Uno, A., Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics, J. Fluid Mech., 592, 335-366, (2007) · Zbl 1151.76515
[20] Jagannathan, S.; Donzis, D. A., Reynolds and Mach number scaling in solenoidally-forced compressible turbulence using high-resolution direct numerical simulations, J. Fluid Mech., 789, 669-707, (2016)
[21] Jimenez, J.; Moser, R. D., Large-eddy simulations: where are we and what can we expect?, AIAA J., 38, 605-612, (2000)
[22] Kerr, R. M.; Domaradzki, J. A.; Barbier, G., Small-scale properties of nonlinear interactions and subgrid-scale energy transfer in isotropic turbulence, Phys. Fluids, 8, 197-208, (1995) · Zbl 1027.76578
[23] Kida, S.; Orszag, S. A., Energy and spectral dynamics in decaying compressible turbulence, J. Sci. Comput., 7, 1-34, (1992) · Zbl 0758.76029
[24] Kritsuk, A. G.; Wagner, R.; Norman, M. L., Energy cascade and scaling in supersonic isothermal turbulence, J. Fluid Mech., 729, R1, (2013) · Zbl 1291.76177
[25] Lee, S.; Lele, S. K.; Moin, P., Eddy shocklets in decaying compressible turbulence, Phys. Fluids A, 3, 657-664, (1991)
[26] Lele, S. K., Compact finite difference schemes with spectral-like resolution, J. Comput. Phys., 103, 16-42, (1992) · Zbl 0759.65006
[27] Livescu, D.; Li, Z., Subgrid-scale backscatter after the shock-turbulence interaction, AIP Conf. Proc., 1793, (2017)
[28] Livescu, D.; Ryu, J., Vorticity dynamics after the shock-turbulence interaction, Shock Waves, 26, 241-251, (2016)
[29] Martin, M. P.; Piomelli, U.; Candler, G. V., Subgrid-scale models for compressible large-eddy simulations, Theor. Comput. Fluid Dyn., 13, 361-376, (2000) · Zbl 0966.76037
[30] Meneveau, C.; Katz, J., Scale-invariance and turbulence models for large-eddy simulation, Annu. Rev. Fluid Mech., 32, 1-32, (2000) · Zbl 0988.76044
[31] Miura, H.; Kida, S., Acoustic energy exchange in compressible turbulence, Phys. Fluids, 7, 1732-1742, (1995) · Zbl 1023.76557
[32] O’Brien, J.; Urzay, J.; Ihme, M.; Moin, P.; Saghafian, A., Subgrid-scale backscatter in reacting and inert supersonic hydrogenCair turbulent mixing layers, J. Fluid Mech., 743, 554-584, (2014)
[33] O’Brien, J.; Towery, C. A. Z.; Hamlington, P. E.; Ihme, M.; Poludnenko, A. Y.; Urzay, J., The cross-scale physical-space transfer of kinetic energy in turbulent premixed flames, Proc. Combust. Inst., 36, 1967-1975, (2017)
[34] Petersen, M. R.; Livescu, D., Forcing for statistically stationary compressible isotropic turbulence, Phys. Fluids, 22, (2010)
[35] Piomelli, U.; Cabot, W. H.; Moin, P.; Lee, S., Subgrid-scale backscatter in turbulent and transitional flows, Phys. Fluids A, 3, 1766-1771, (1991) · Zbl 0825.76335
[36] Pirozzoli, S.; Grasso, F., Direct numerical simulations of isotropic compressible turbulence: influence of compressibility on dynamics and structures, Phys. Fluids, 16, 4386-4407, (2004) · Zbl 1187.76418
[37] Pope, S. B., Turbulent Flows, (2000), Cambridge University Press · Zbl 0966.76002
[38] Quadros, R.; Sinha, K.; Larsson, J., Turbulent energy flux generated by shock/homogeneous-turbulence interaction, J. Fluid Mech., 796, 113-157, (2016)
[39] Ryu, J.; Livescu, D., Turbulence structure behind the shock in canonical shock-vortical turbulence interaction, J. Fluid Mech., 756, R1, (2014)
[40] Sagaut, P., Large Eddy Simulation for Incompresible Flows, (2006), Springer Science & Business Media
[41] Samtaney, R.; Pullin, D. I.; Kosovic, B., Direct numerical simulation of decaying compressible turbulence and shocklet statistics, Phys. Fluids, 13, 1415-1430, (2001) · Zbl 1184.76474
[42] Suman, S.; Girimaji, S. S., Dynamical model for velocity-gradient evolution in compressible turbulence, J. Fluid Mech., 683, 289-319, (2011) · Zbl 1241.76292
[43] Tao, B.; Katz, J.; Meneveau, C., Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements, J. Fluid Mech., 457, 35-78, (2002) · Zbl 0993.76505
[44] Tian, Y.; Jaberi, F. A.; Li, Z.; Livescu, D., Numerical study of variable density turbulence interaction with a normal shock wave, J. Fluid Mech., 829, 551-588, (2017)
[45] Towery, C. A. Z.; Poludnenko, A. Y.; Urzay, J.; O’Brien, J.; Ihme, M.; Hamlington, P. E., Spectral kinetic energy transfer in turbulent premixed reacting flows, Phys. Rev. E, 93, (2016)
[46] Wagner, R.; Falkovich, G.; Kritsuk, A. G.; Norman, M. L., Flux correlations in supersonic isothermal turbulence, J. Fluid Mech., 713, 482-490, (2012) · Zbl 1284.76213
[47] Wan, M.; Oughton, S.; Servidio, S.; Matthaeus, W. H., On the accuracy of simulations of turbulence, Phys. Plasmas, 17, (2010)
[48] Wang, J.; Gotoh, T.; Watanabe, T., Spectra and statistics in compressible isotropic turbulence, Phys. Rev. Fluids, 2, (2017)
[49] Wang, J.; Gotoh, T.; Watanabe, T., Shocklet statistics in compressible isotropic turbulence, Phys. Rev. Fluids, 2, (2017)
[50] Wang, J.; Gotoh, T.; Watanabe, T., Scaling and intermittency in compressible isotropic turbulence, Phys. Rev. Fluids, 2, (2017)
[51] Wang, J.; Shi, Y.; Wang, L.-P.; Xiao, Z.; He, X. T.; Chen, S., Effect of shocklets on the velocity gradients in highly compressible isotropic turbulence, Phys. Fluids, 23, (2011)
[52] Wang, J.; Shi, Y.; Wang, L.-P.; Xiao, Z.; He, X. T.; Chen, S., Effect of compressibility on the small scale structures in isotropic turbulence, J. Fluid Mech., 713, 588-631, (2012) · Zbl 1284.76214
[53] Wang, J.; Shi, Y.; Wang, L.-P.; Xiao, Z.; He, X. T.; Chen, S., Scaling and statistics in three-dimensional compressible turbulence, Phys. Rev. Lett., 108, (2012)
[54] Wang, J.; Wang, L.-P.; Xiao, Z.; Shi, Y.; Chen, S., A hybrid numerical simulation of isotropic compressible turbulence, J. Comput. Phys., 229, 5257-5259, (2010) · Zbl 1346.76114
[55] Wang, J.; Yang, Y.; Shi, Y.; Xiao, Z.; He, X. T.; Chen, S., Cascade of kinetic energy in three-dimensional compressible turbulence, Phys. Rev. Lett., 110, (2013)
[56] Yang, Y.; Matthaeus, W. H.; Parashar, T. N.; Haggerty, C. C.; Roytershteyn, V.; Daughton, W.; Wan, M.; Shi, Y.; Chen, S., Energy transfer, pressure tensor, and heating of kinetic plasma, Phys. Plasmas, 24, (2017)
[57] Yang, Y.; Matthaeus, W. H.; Parashar, T. N.; Wu, P.; Wan, M.; Shi, Y.; Chen, S.; Roytershteyn, V.; Daughton, W., Energy transfer channels and turbulence cascade in Vlasov-Maxwell turbulence, Phys. Rev. E, 95, (2017)
[58] Yang, Y.; Matthaeus, W. H.; Shi, Y.; Wan, M.; Chen, S., Compressibility effect on coherent structures, energy transfer, and scaling in magnetohydrodynamic turbulence, Phys. Fluids, 29, (2017)
[59] Yang, Y.; Shi, Y.; Wan, M.; Matthaeus, W. H.; Chen, S., Energy cascade and its locality in compressible magnetohydrodynamic turbulence, Phys. Rev. E, 93, (2016)
[60] Yang, Y.; Wang, J.; Shi, Y.; Xiao, Z.; He, X. T.; Chen, S., Intermittency caused by compressibility: a Lagrangian study, J. Fluid Mech., 786, R6, (2016) · Zbl 1381.76116
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