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11 - Scale-by-Scale Nonequilibrium in Turbulent Flows

from Part II - Challenges

Published online by Cambridge University Press:  31 January 2025

By
John Christos Vassilicos  and
Jean-Philippe Laval
Edited by
Fernando F. Grinstein ,
Filipe S. Pereira  and
Massimo Germano
Fernando F. Grinstein
Affiliation:
Los Alamos National Laboratory
Filipe S. Pereira
Affiliation:
Los Alamos National Laboratory
Massimo Germano
Affiliation:
Duke University, North Carolina
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Summary

The Kolmogorov scale-by-scale equilibrium cascade and concepts related to it have provided the physical basis for explicit large eddy simulation subgrid models since the mid-twentieth century. However, mounting evidence and theory have been accumulating over the past ten years for scale-by-scale nonequilibrium in a variety of turbulent flows with some new general nonequilibrium laws. One of the resulting challenges now is to translate these new nonequilibrium physics into predictive turbulence modeling.

Type
Chapter
Information
Coarse Graining Turbulence
Modeling and Data-Driven Approaches and their Applications
 , pp. 333 - 354
Publisher: Cambridge University Press
Print publication year: 2025

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References

Alves Portela, F., Papadakis, G., and Vassilicos, J. C. 2017. The turbulence cascade in the near wake of a square prism. J. Fluid Mech., 825, 315–352.CrossRefGoogle Scholar
Alves Portela, F., Papadakis, G., and Vassilicos, J. C. 2020. The role of coherent structures and inhomogeneity in near-field interscale turbulent energy transfers. J. Fluid Mech., 896, A16.CrossRefGoogle Scholar
Apostolidis, A., Laval, J.-P., and Vassilicos, J. C. 2022. Scalings of turbulence dissipation in space and time for turbulent channel flow. J. Fluid Mech., 946, A41.CrossRefGoogle Scholar
Apostolidis, A., Laval, J.-P., and Vassilicos, J. C. 2023. Turbulent cascade in fully developed turbulent channel flow. J. Fluid Mech., 967, A22.CrossRefGoogle Scholar
Bardina, J., Ferziger, J. H., and Reynolds, W. C. 1980. Improved subgrid models for Large Eddy Simulation. AIAA paper, 80, 1357.Google Scholar
Batchelor, G. K. 1953. The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Beaumard, P., Braganca, P., Cuvier, C., Steiros, K., and Vassilicos, J. C. 2023. Scale-by-scale non-equilibrium with Kolmogorov-like scalings in non-homogeneous stationary turbulence. J. Fluid Mech., 984, A35.Google Scholar
Boris, P., Grinstein, F. F., Oran, E. S., and Kolbe, R. L. 1992. New insights into large eddy simulation. Fluid Dynamics Research, 10(4–6), 199.CrossRefGoogle Scholar
Breda, M., and Buxton, O. 2018. Influence of coherent structures on the evolution of an axisymmetric turbulent jet. Phys. Fluids, 30, 035109.CrossRefGoogle Scholar
Cafiero, G., and Vassilicos, J. C. 2019. Non-equilibrium turbulence scalings and self-similarity in turbulent planar jets. Proc. R. Soc. Lond. A, 475(2225), 20190038.Google ScholarPubMed
Castro, I. 2016. Dissipative distinctions. J. Fluid Mech., 788, 1–4.CrossRefGoogle Scholar
Chen, J., and Vassilicos, J. C. 2022. Scalings of scale-by-scale turbulence energy in non-homogeneous turbulence. J. Fluid Mech., 938, A7.CrossRefGoogle Scholar
Chen, J., Cuvier, C., Foucaut, J.-M., Ostovan, Y., and Vassilicos, J. C. 2021. A turbulence dissipation inhomogeneity scaling in the wake of two side-by-side square prisms. J. Fluid Mech., 924, A4.CrossRefGoogle Scholar
Chollet, J.-P., and Lesieur, M. 1981. Parametrization of small scales of three-dimensional isotropic turbulence utilizing spectral closure. J. Atmos. Sci., 38, 2747–2757.2.0.CO;2>CrossRefGoogle Scholar
Chongsiripinyo, K., and Sarkar, S. 2020. Decay of turbulent wakes behind a disk in homogeneous and stratified fluids. J. Fluid Mech., 885, A31.CrossRefGoogle Scholar
Dairay, T., Lamballais, E., Laizet, S., and Vassilicos, J. C. 2017. Numerical dissipation vs. subgrid-scale modelling for large eddy simulation. J. Comp. Phys., 337, 252–274.Google Scholar
Domaradzki, J. A., and Saiki, E. M. 1997. A subgrid-scale model based on the estimation of unresolved scales of turbulence. Phys. Fluids A, 9, 2148–2164.Google Scholar
Frisch, U. 1995. Turbulence: The Legacy of A.N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Germano, M. 1992. Turbulence: The Filtering Approach. J. Fluid Mech., 238, 325–336.CrossRefGoogle Scholar
Germano, M. 2007a. A direct relation between the filtered subgrid stress and the second order structure function. Phys. Fluids, 19, 038102.CrossRefGoogle Scholar
Germano, M. 2007b. The elementary energy transfer between the two-point velocity mean and difference. Phys. Fluids, 19, 085105.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P., and Cabot, W. H. 1991. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A, 3, 1760–1765.CrossRefGoogle Scholar
Goto, S., and Vassilicos, J. C. 2015. Energy dissipation and flux laws for unsteady turbulence. Phys. Lett. A, 379(16–17), 1144–1148.CrossRefGoogle Scholar
Goto, S., and Vassilicos, J. C. 2016a. Local equilibrium hypothesis and Taylor’s dissipation law. Fluid Dyn. Res, 48, 021402.CrossRefGoogle Scholar
Goto, S., and Vassilicos, J. C. 2016b. Unsteady turbulence cascades. Phys. Rev. E, 94(5), 053108.CrossRefGoogle ScholarPubMed
Grinstein, F. F., Margolin, L. G., and Rider, W. J. 2007. Implicit Large Eddy Simulation. Cambridge University Press.CrossRefGoogle Scholar
Hearst, R. J., and Lavoie, P. 2014. Decay of turbulence generated by a square-fractal-element grid. J. Fluid Mech., 741, 567–584.CrossRefGoogle Scholar
Hearst, R. J., and Lavoie, P. 2015. Velocity derivative skewness in fractal-generated, non-equilibrium grid turbulence. Phys. Fluids, 071701.Google Scholar
Hearst, R. J., and Lavoie, P. 2016. Effects of multi-scale and regular grid geometries on decaying turbulence. J. Fluid Mech., 803, 528–555.CrossRefGoogle Scholar
Hill, R. J. 2001. Equations relating structure functions of all orders. J. Fluid Mech., 434, 379–388.CrossRefGoogle Scholar
Hill, R. J. 2002. Exact second-order structure-function relationships. J. Fluid Mech., 468, 317–326.CrossRefGoogle Scholar
Horiuti, K. 1993. A proper velocity scale for the modeling subgrid-scale eddy viscosities in large eddy simulation. Phys. Fluids, 5, 146.CrossRefGoogle Scholar
Horiuti, K., Yanagihara, S., and Tamaki, T. 2013. Nonequilibrium energy spectrum in the subgrid-scale one-equation model in large-eddy simulation. Phys. Fluids, 25, 125104.CrossRefGoogle Scholar
Horiuti, K., Yanagihara, S., and Tamaki, T. 2016. Nonequilibrium state in energy spectra and transfer with implications for topological transitions and SGS modeling. Fluid Dyn. Res., 48, 021409.CrossRefGoogle Scholar
Hunt, J. C. R., Philips, O. M., and Williams, D. 1991. Turbulence and Stochastic Processes: Kolmogorov’s Ideas 50 Years On. The Royal Society.Google Scholar
Isaza, J. C., Salazar, R., and Warhaft, Z. 2014. On grid-generated turbulence in the near- and far field regions. J. Fluid Mech., 753, 402–426.CrossRefGoogle Scholar
Ishihara, T., Gotoh, T., and Kaneda, Y. 2009. Study of High-Reynolds Number Isotropic Turbulence by Direct Numerical Simulation. Ann. Rev. Fluid Mech., 41, 165–180.CrossRefGoogle Scholar
Kerr, R. M., Domaradzki, J. A., and Barbier, G. 1995. Small-scale properties of nonlinear interactions and subgrid-scale energy transfer in isotropic turbulence. Phys. Fluids, 8, 197–208.Google Scholar
Keylock, C., Kida, S., and Peters, N. 2016. JSPS Supported Symposium on Interscale Transfers and Flow Topology in Equilibrium and Non-equilibrium Turbulence (Sheffield, UK, September 2014). Fluid Dyn. Res., 48(2), 020001.CrossRefGoogle Scholar
Kokkinakis, I. W., and Drikakis, D. 2015. Implicit Large Eddy Simulation of weakly-compressible turbulent channel flow. Comput. Methods Appl. Mech. Eng., 287, 229–261.CrossRefGoogle Scholar
Larssen, H. S., and Vassilicos, J. C. 2023. Spatio-temporal fluctuations of interscale and interspace energy transfer dynamics in homogeneous turbulence. J. Fluid Mech., 969, A14, 1–44.CrossRefGoogle Scholar
Leschziner, M. A. 2016. Statistical Turbulence Modelling for Fluid Dynamics – Demystified: An Introductory Text for Graduate Engineering Students. Imperial College Press.Google Scholar
Lesieur, M. 1997. Turbulence in Fluids. Kluwer.CrossRefGoogle Scholar
Lilly, D. K. 1992. A Proposed Modification of the Germano Subgrid-Scale Closure Method. Physics of Fluids A: Fluid Dynamics, 4(3), 633–634.CrossRefGoogle Scholar
Liu, F., Lu, L. P., Bos, W. J. T., and Fang, L. 2019. Assessing the nonequilibrium of decaying turbulence with reversed initial fields. Phys. Rev. Fluids, 4, 084603.CrossRefGoogle Scholar
Liu, S., Meneveau, C., and Katz, J. 1994. On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J. Fluid Mech., 275, 83–119.CrossRefGoogle Scholar
Lundgren, T. S. 2002. Kolmogorov two-thirds law by matched asymptotic expansion. Phys. Fluids, 14, 638.CrossRefGoogle Scholar
Margolin, L. G., Rider, W. J., and Grinstein, F. F. 2006. Modeling turbulent flow with implicit LES. J. Turbulence, 7, 1–27.CrossRefGoogle Scholar
Mathieu, J., and Scott, J. 2000. An Introduction to Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Meldi, M., and Sagaut, P. 2018. Investigation of anomalous very fast decay regimes in homogeneous isotropic turbulence. J. Turbulence, 19(5).CrossRefGoogle Scholar
Meldi, M., and Vassilicos, J. C. 2021. Analysis of Lundgren’s matched asymptotic expansion approach to the Karman–Howarth equation using the EDQNM turbulence closure. Phys. Rev. Fluids, 6, 064602.CrossRefGoogle Scholar
Meldi, M., Lejemble, H., and Sagaut, P. 2014. On the emergence of non-classical decay regimes in multiscale/fractal generated isotropic turbulence. J. Fluid Mech., 756, 816–843.CrossRefGoogle Scholar
Mora, D. O., Muniz Pladellorens, E., Riera Turró, P., Lagauzere, M., and Obligado, M. 2019. Energy cascades in active-grid-generated turbulent flows. Phys. Rev. Fluids, 4, 104601.CrossRefGoogle Scholar
Nagata, K., Saiki, T., Sakai, Y., Ito, Y., and Iwano, K. 2017. Effects of grid geometry on non-equilibrium dissipation in grid turbulence. Phys. Fluids, 29(1), 015102.CrossRefGoogle Scholar
Nedic, J., and Tavoularis, S. 2016. Energy dissipation scaling in uniformly sheared turbulence. Phys. Rev. E, 93, 033115.CrossRefGoogle ScholarPubMed
Nedic, J., Tavoularis, S., and Marusic, I. 2017. Dissipation scaling in constant-pressure turbulent boundary layers. Phys. Rev. Fluids, 2, 032601(R).CrossRefGoogle Scholar
Obligado, M., and Vassilicos, J. C. 2019. The non-equilibrium part of the inertial range in decaying homogeneous turbulence. Europhys. Lett., 127, 64004.CrossRefGoogle Scholar
Ortiz-Tarin, J. L., Nidhan, S., and Sarkar, S. 2021. High-Reynolds-number wake of a slender body. J. Fluid Mech., 918, A30.Google Scholar
Pope, S. B. 2000. Turbulent Flows. Cambridge University Press.Google Scholar
Rubinstein, R., and Clark, T. T. 2017. “Equilibrium” and “non-equilibrium” turbulence. Theor. App. Mech. Lett., 7(5), 301–305.Google Scholar
Sagaut, P. 2005. Large Eddy Simulation for Incompressible Flows. 3rd ed. Springer.Google Scholar
Sagaut, P., and Cambon, C. 2008. Homogeneous Turbulence Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Saunders, D. C., Britt, J. A., and Wunsch, S. 2022. Decay of the drag wake of a sphere at Reynolds number 105. Exp. Fluids, 63, 71.CrossRefGoogle Scholar
Spalart, P. 2009. Detached-Eddy Simulation. Annu. Rev. Fluid Mech., 41(1), 181–202.CrossRefGoogle Scholar
Stein, V. P., and Kaltenbach, H.-J. 2019. Non-equilibrium scaling applied to the wake evolution of a model scale wind turbine. Energies, 12(14), 2763.CrossRefGoogle Scholar
Steiros, K. 2022a. Balanced nonstationary turbulence. Phys. Rev. E, 105, 035109.CrossRefGoogle ScholarPubMed
Steiros, K. 2022b. Turbulence near initial conditions. Phys. Rev. Fluids, 7, 104607.CrossRefGoogle Scholar
Sunita, and Layek, G. C. 2021. Nonequilibrium turbulent dissipation in buoyant axisymmetric plume. Phys. Rev. Fluids, 6(104602).CrossRefGoogle Scholar
Tennekes, H., and Lumley, J. L. 1972. A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Thiesset, F., and Danaila, L. 2020. The illusion of a Kolmogorov cascade. J. Fluid Mech., 902.CrossRefGoogle Scholar
Townsend, A. A. 1976. The Structure of Turbulent Shear Flow. 2nd ed. Cambridge University Press.Google Scholar
Valente, P., and Vassilicos, J. C. 2012. Dependence of decaying homogeneous isotropic turbulence on inflow conditions. Phys. Rev. A, 376 (4), 510–514.Google Scholar
Valente, P., and Vassilicos, J. C. 2015. The energy cascade in grid-generated non-equilibrium decaying turbulence. Phys. Fluids, 27, 045103.CrossRefGoogle Scholar
Vassilicos, J. C. 2015. Dissipation in turbulent flows. Annu. Rev. Fluid Mech., 47, 95–114.CrossRefGoogle Scholar
Vela-Martín, A. 2022. Subgrid-scale models of isotropic turbulence need not produce energy backscatter. J. Fluid Mech., 937, A14.CrossRefGoogle Scholar
Waclawczyk, M., Nowak, J. L., Siebert, H., and Malinowski, S. 2022a. Detecting nonequilibrium states in atmospheric turbulence. J. Atmos. Sci., 79(10), 2757–2772.CrossRefGoogle Scholar
Waclawczyk, M., Nowak, J. L., and Malinowski, S. 2022b. Nonequilibrium dissipation scaling in atmospheric turbulence. J. Phys.: Conf. Series, 2367, 012032.Google Scholar
Watanabe, T., da Silva, C. B., and Nagata, K. 2019. Non-dimensional energy dissipation rate near the turbulent/non-turbulent interfacial layer in free shear flows and shear free turbulence. J. Fluid Mech., 875, 321–344.CrossRefGoogle Scholar
Watanabe, T., da Silva, C. B., and Nagata, K. 2020. Scale-by-scale kinetic energy budget near the turbulent/non-turbulent interface. Phys. Rev. Fluids, 5, 124610.CrossRefGoogle Scholar
Xiong, X.-L., Laima, S., and Lui, H. 2022. Novel scaling laws in the nonequilibrium turbulent wake of a rotor and a fractal plate. Phys. Fluids, 34, 065130.CrossRefGoogle Scholar
Yoshizawa, A. 1994. Nonequilibrium effect of the turbulent-energy-production process on the inertial-range energy spectrum. Phys. Rev. E, 49(5), 4065–4071.CrossRefGoogle ScholarPubMed
Zhou, Y., and Vassilicos, J. C. 2020. Energy cascade at the turbulent/nonturbulent interface. Phys. Rev. Fluid, 5(6), 064604.CrossRefGoogle Scholar

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