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On the emergence of non-classical decay regimes in multiscale/fractal generated isotropic turbulence

  • Marcello Meldi (a1), Hugo Lejemble (a2) and Pierre Sagaut (a3)

Abstract

The present paper addresses the issue of finding key parameters that may lead to the occurrence of non-classical decay regimes for fractal/multiscale generated grid turbulence. To this aim, a database of numerical simulations has been generated by the use of the eddy-damped quasi-normal Markovian (EDQNM) model. The turbulence production in the wake of the fractal/multiscale grid is modelled via a turbulence production term based on the forcing term developed for direct numerical simulations (DNS) purposes and the dynamics of self-similar wakes. The sensitivity of the numerical results to the simulation parameters has been investigated successively. The analysis is based on the observation of both the time evolution of the turbulent energy spectrum $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}E(k,t)$ and the decay of the flow statistical quantities, such as the turbulent kinetic energy $\mathcal{K}(t)$ and the energy dissipation rate $\varepsilon (t)$ . A satisfactory agreement with existing experimental data published by different research teams is observed. In particular, it is observed that the key parameter that governs the nature of turbulence decay is $\alpha ={d/U_{\infty }}\, {(\varepsilon (0)/\mathcal{K}(0))}={d/L(0)} \, {(\sqrt{\mathcal{K}(0)}/U_{\infty })}$ (with $d$ the bar diameter and $U_{\infty }$ the upstream uniform velocity), which measures the ratio of the time scale largest grid bar $d/U_{\infty }$ to the turbulent time scale $\mathcal{K}(0)/\varepsilon (0)$ . Two asymptotic behaviours for $\alpha \rightarrow + \infty $ and $\alpha \rightarrow 0$ are identified: (i) a fast algebraic decay law regime for rapidly decaying production terms, due to strongly modified initial kinetic energy spectrum and (ii) a real exponential decay regime associated with strong, very slowly decaying production terms. The present observations are in full agreement with conclusions drawn from recent fractal grid experiments, and it provides a physical scenario for occurrence of anomalous decay regime which encompasses previous hypotheses.

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Corresponding author

Email address for correspondence: marcellomeldi@gmail.com

References

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Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Cambon, C., Mansour, N. N. & Godeferd, F. S. 1997 Energy transfer in rotating turbulence. J. Fluid Mech. 337, 303332.
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25, 657682.
Davidson, P. A. 2011 The minimum energy decay rate in quasi-isotropic grid turbulence. Phys. Fluids 23 (8), 085108.
Discetti, S., Natale, A. & Astarita, T. 2013 Spatial filtering improved tomographic PIV. Exp. Fluids 54, 15051517.
Djenidi, L. & Tardu, S. F. 2012 On the anisotropy of a low-Reynolds-number grid turbulence. J. Fluid Mech. 702, 332353.
Ertunc, O., Ozyilmaz, N., Lienhart, H., Durst, F. & Beronov, K. 2010 Homogeneity of turbulence generated by static-grid structures. J. Fluid Mech. 654, 473500.
Eyink, G. L. & Thomson, D. J. 2000 Free decay of turbulence and breakdown of self-similarity. Phys. Fluids 12, 477479.
George, W. K. 1992 The decay of homogeneous isotropic turbulence. Phys. Fluids A 4 (7), 14921509.
George, W. K. & Wang, H. 2009 The exponential decay of homogeneous turbulence. Phys. Fluids 21 (2), 025108.
Gomes-Fernandes, R., Ganapathisubramani, B. & Vassilicos, J. C. 2012 Particle image velocimetry study of fractal-generated turbulence. J. Fluid Mech. 711, 306336.
Hearst, R. J. & Lavoie, P. 2014 Decay of turbulence generated by a square-fractal-element grid. J. Fluid Mech. 741, 567584.
Hurst, D. & Vassilicos, J. C. 2007 Scalings and decay of fractal-generated turbulence. Phys. Fluids 19, 035103.
Ishida, T., Gotoh, T. & Kaneda, Y. 2009 Study of high-Reynolds number isotropic turbulence by direct numerical simulation. Annu. Rev. Fluid Mech. 41, 165180.
Kang, H. S., Chester, S. & Meneveau, C. 2003 Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulation. J. Fluid Mech. 480, 129160.
Krogstad, P. Å. & Davidson, P. A. 2011 Freely-decaying, homogeneous turbulence generated by multi-scale grids. J. Fluid Mech. 680, 417434.
Krogstad, P. Å. & Davidson, P. A. 2012 Near-field investigation of turbulence produced by multi-scale grids. Phys. Fluids 24 (3), 035103.
Laizet, S. & Vassilicos, J. C. 2011 DNS of fractal-generated turbulence. Flow Turbul. Combust. 87, 673705.
Lesieur, M. 2008 Turbulence in Fluids, 4th edn. Springer.
Lesieur, M., Montmory, C. & Chollet, J. P. 1987 The decay of kinetic energy and temperature variance in three-dimensional isotropic turbulence. Phys. Fluids 30, 12781286.
Lesieur, M. & Schertzer, D. 1978 Self-similar decay of high Reynolds-number turbulence. J. Méc. 17 (4), 609646.
Makita, H. 1991 Realization of a large-scale turbulence field in a small wind tunnel. Fluid Dyn. Res. 8, 5364.
Mazellier, N. & Vassilicos, J. C. 2010 Turbulence without Richardson–Kolmogorov cascade. Phys. Fluids 22 (7), 075101.
Mazzi, B. & Vassilicos, J. C. 2004 Fractal-generated turbulence. J. Fluid Mech. 502, 6587.
Meldi, M. & Sagaut, P. 2012 On non-self-similar regimes in homogeneous isotropic turbulence decay. J. Fluid Mech. 711, 364393.
Meldi, M. & Sagaut, P. 2013a Further insights into self-similarity and self-preservation in freely decaying isotropic turbulence. J. Turbul. 14, 2453.
Meldi, M. & Sagaut, P. 2013b Pressure statistics in self-similar freely decaying isotropic turbulence. J. Fluid Mech. 717, R2.
Meldi, M., Sagaut, P. & Lucor, D. 2011 A stochastic view of isotropic turbulence decay. J. Fluid Mech. 668, 351362.
Meyers, J. & Meneveau, C. 2008 A functional form for the energy spectrum parametrizing Bottleneck and intermittency effects. Phys. Fluids 20 (6), 065109.
Mohamed, M. S. & LaRue, J. C. 1990 The decay power law in grid-generated turbulence. J. Fluid Mech. 219, 195214.
Moser, M. D., Rogers, M. M. & Ewing, D. W. 1998 Self-similarity of time-evolving plane wakes. J. Fluid Mech. 367, 255289.
Mydlarski, L. & Warhaft, Z. 1996 On the onset of high-Reynolds-number grid-generated wind tunnel turbulence. J. Fluid Mech. 320, 331368.
Nagata, K., Sakai, Y., Inaba, T., Suzuki, H., Terashima, O. & Suzuki, H. 2013 Turbulence structure and turbulence kinetic energy transport in multiscale/fractal-generated turbulence. Phys. Fluids 25, 065102.
Orszag, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363386.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Saffman, P. J. 1967 The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27, 581593.
Sagaut, P. & Cambon, C. 2008 Homogenous Turbulence Dynamics. Cambridge University Press.
Seoud, R. E. & Vassilicos, J. C. 2007 Dissipation and decay of fractal-generated turbulence. Phys. Fluids 19, 105108.
Skrbek, L. & Stalp, S. R. 2000 On the decay of homogeneous isotropic turbulence. Phys. Fluids 12, 19972019.
Speziale, C. G. & Bernard, P. S. 1992 The energy decay in self-preserving isotropic turbulence revisited. J. Fluid Mech. 241, 645667.
Staicu, A., Mazzi, B., Vassilicos, J. C. & Van De Water, W. 2003 Turbulent wakes of fractal objects. Phys. Rev. E 67, 066306.
Taylor, G. I. 1935 Statistical Theory of Turbulence. Proc. R. Soc. Lond. A 151, 421444.
Tchoufag, J., Sagaut, P. & Cambon, C. 2012 Spectral approach to finite Reynolds number effects on Kolmogorov’s 4/5 law in isotropic turbulence. Phys. Fluids 24 (1), 015107.
Thormann, A. & Meneveau, C. 2014 Decay of homogeneous, nearly isotropic turbulence behind active fractal grids. Phys. Fluids 26, 025112.
Valente, P. C. & Vassilicos, J. C. 2011 The decay of turbulence generated by a class of multiscale grids. J. Fluid Mech. 687, 300340.
Valente, P. C. & Vassilicos, J. C. 2012 Universal dissipation scaling for non-equilibrium turbulence. Phys. Rev. Lett. 108, 214503.
Vassilicos, J. C. 2011 An infinity of possible invariants for decaying homogeneous turbulence. Phys. Lett. A 375, 10101013.
Von Karman, T. & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. R. Soc. A 164, 192215.
Von Karman, T. & Lin, C. C. 1949 On the concept of similarity in the theory of isotropic turbulence. Rev. Mod. Phys. 21 (3), 516519.
Yeung, P. K., Donzis, D. & Sreenivasan, K. R. 2012 Dissipation, enstrophy and pressure statistics in turbulence simulations at high Reynolds numbers. J. Fluid Mech. 700, 515.
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