Spectral imbalance and the normalized dissipation rate of turbulence

Abstract

The normalized turbulent dissipation rate $C_\epsilon$ is studied in decaying and forced turbulence by direct numerical simulations, large-eddy simulations, and closure calculations. A large difference in the values of $C_\epsilon$ is observed for the two types of turbulence. This difference is found at moderate Reynolds number, and it is shown that it persists at high Reynolds number, where the value of $C_\epsilon$ becomes independent of the Reynolds number, but is still not unique. This difference can be explained by the influence of the nonlinear cascade time that introduces a spectral disequilibrium for statistically nonstationary turbulence. Phenomenological analysis yields simple analytical models that satisfactorily reproduce the numerical results. These simple spectral models also reproduce and explain the increase of $C_\epsilon$ at low Reynolds number that is observed in the simulations

Effects of helicity on dissipation in homogeneous box turbulence

“…The value of β has been measured in experiments (Sreenivasan 1984(Sreenivasan , 1998Burattini et al 2005) as well as in direct numerical simulations (DNSs) (Wang et al 1996;Kaneda et al 2003;Gotoh et al 2002;Donzis et al 2005;Bos et al 2007;Goto & Vassilicos 2009;Yeung et al 2012;McComb et al 2015;Yeung et al 2015;Ishihara et al 2016). Although the experiments differed in the flow configuration and the DNSs in the properties of the external forcing and the run time, the results are generally consistent in terms of β 1.…”

“…Since its introduction, the question remains as to whether the infinite-Reynolds-number asymptote of β is a universal quantity, i.e. whether it depends on the forces generating the turbulence and on the boundary conditions (Goto & Vassilicos 2009;Bos et al 2007). Since β is related to the Kolmogorov constant C K (Lumley 1992), the question of universality concerning β extends to the Kolmogorov constant.…”

Spectral non-equilibrium property in homogeneous isotropic turbulence and its implication in subgrid-scale modeling

“…All the three N cases show almost the same trend, illustrating the correctness of the improved Smagorinsky model in free-decaying turbulence. Note that under some definitions the free-decaying turbulence may be considered as non-equilibrium [14], but using our definition in this paper, it is equilibrium due to the balance of energy transfer in the inertial range. For the performance of the R cases, as already addressed in Ref.…”

“…Some researchers define non-equilibrium as the imbalance between the maximum non-linear energy transfer http://dx.doi.org/10.1016/j.physleta.2015.05.029 0375-9601/© 2015 Elsevier B.V. All rights reserved. and the dissipation [8,[12][13][14], for example the free-decaying turbulence is regarded as non-equilibrium under this definition. Another definition of non-equilibrium may be found from Townsend [15] and Bradshaw [16] in the studies of wall turbulence: in the governing equation of turbulence energy, if the productive terms and the dissipative terms are statistically equilibrium, the turbulent flow is defined to be "equilibrium"; otherwise it is "non-equilibrium".…”

Spectral imbalance in the inertial range dynamics of decaying rotating turbulence

“…However, for non-stationary flows the balance Π(k) = ε is yet to be observed -a fact that is usually attributed either to the data being at insufficiently high Reynolds numbers (i.e. a low Reynolds number effect [7,14]) or, contrastingly, a consequence of the delay in cascading the energy down to the small-scales (a lag which increases with the Reynolds number [11,[15][16][17][18]). …”