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Spatio-temporal intermittency of the turbulent energy cascade

  • T. Yasuda (a1) and J. C. Vassilicos (a1)

In incompressible and periodic statistically stationary turbulence, exchanges of turbulent energy across scales and space are characterised by very intense and intermittent spatio-temporal fluctuations around zero of the time-derivative term, the spatial turbulent transport of fluctuating energy and the pressure–velocity term. These fluctuations are correlated with each other and with the intense intermittent fluctuations of the interscale energy transfer rate. These correlations are caused by the sweeping effect, the link between nonlinearity and non-locality, and also relate to geometrical alignments between the two-point fluctuating pressure force difference and the two-point fluctuating velocity difference in the case of the correlation between the interscale transfer rate and the pressure–velocity term. All these processes are absent from the spatio-temporal-average picture of the turbulence cascade in statistically stationary and homogeneous turbulence.

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Alves Portela, F., Papadakis, G. & Vassilicos, J. C. 2017 The turbulence cascade in the near wake of a square prism. J. Fluid Mech. 825, 315352.
Aoyama, T., Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K. & Uno, A. 2005 Statistics of energy transfer in high-resolution direct numerical simulation of turbulence in a periodic box. J. Phys. Soc. Japan 74 (12), 32023212.
Batchelor, G. K. & Townsend, A. A. 1949 The nature of turbulent motion at large wave-numbers. Proc. R. Soc. Lond. A 199, 238255.
Cerutti, S. & Meneveau, C. 1998 Intermittency and relative scaling of subgrid-scale energy dissipation in isotropic turbulence. Phys. Fluids 10, 928937.
Cimarelli, A., Angelis, E. D., Jiménez, J. & Casciola, C. M. 2016 Cascades and wall-normal fluxes in turbulent channel flows. J. Fluid Mech. 796, 417436.
Danaila, L., Krawczynski, J. F., Thiesset, F. & Renou, B. 2012 Yaglom-like equation in axisymmetric anisotropic turbulence. Physica D 241, 216223.
Domaradzki, J. A., Liu, W. & Brachet, M. E. 1993 An analysis of subgrid-scale interactions in numerically simulated isotropic turbulence. Phys. Fluids A 5, 17471759.
Duchon, J. & Robert, R. 2000 Inertial energy dissipation for weak solutions of incompressible Euler and Navier–Stokes equations. Nonlinearity 13, 249255.
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.
Gomes-Fernandes, R., Ganapathisubramani, B. & Vassilicos, J. C. 2015 The energy cascade in near-field non-homogeneous non-isotropic turbulence. J. Fluid Mech. 771, 676705.
Goto, S. 2008 A physical mechanism of the energy cascade in homogeneous isotropic turbulence. J. Fluid Mech. 605, 355366.
Hill, R. J. 2002 Exact second-order structure-function relationships. J. Fluid Mech. 468, 317326.
Ishihara, T., Gotoh, T. & Kaneda, Y. 2009 Study of high-Reynolds number isotropic turbulence by direct numerical simulation. Annu. Rev. Fluid Mech. 41, 165180.
Kolmogorov, A. N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 8285.
Linkmann, M. F. & Morozov, A. 2015 Sudden relaminarization and lifetimes in forced isotropic turbulence. Phys. Rev. Lett. 115, 134502.
Marati, N., Casciola, C. M. & Piva, R. 2004 Energy cascade and spatial fluxes in wall turbulence. J. Fluid Mech. 521, 191215.
McComb, W. D., Linkmann, M. F., Berera, A., Yoffe, S. R. & Jankauskas, B. 2015 Self-organization and transition to turbulence in isotropic fluid motion driven by negative damping at low wavenumbers. J. Phys. A 48, 25FT01.
Piomelli, U., Cabot, W. H., Moin, P. & Lee, S. 1991 Subgrid-scale backscatter in turbulent and transitional flows. Phys. Fluids A 3, 17661771.
Togni, R., Cimarelli, A. & Angelis, E. D. 2015 Physical and scale-by-scale analysis of Rayleigh–Bénard convection. J. Fluid Mech. 782, 380404.
Tsinober, A. 2014 An Informal Introduction to Turbulence. Springer.
Valente, P. C. & Vassilicos, J. C. 2015 The energy cascade in grid-generated non-equilibrium decaying turbulence. Phys. Fluids 27, 045103.
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 120.
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