Emergence of universal scaling in isotropic turbulence.

Universal properties of turbulence have been associated traditionally with very high Reynolds numbers, but recent work has shown that the onset of the power laws in derivative statistics occurs at modest microscale Reynolds numbers of the order of 10, with the corresponding exponents being consistent with those for the inertial range structure functions at very high Reynolds numbers. In this paper we use well-resolved direct numerical simulations of homogeneous and isotropic turbulence to establish this result for a range of initial conditions with different forcing mechanisms. We also show that the moments of transverse velocity gradients possess larger scaling exponents than those of the longitudinal moments, confirming past results that the former are more intermittent than the latter.

Laws of turbulence decay from direct numerical simulations.

Inspection of available data on the decay exponent for the kinetic energy of homogeneous and isotropic turbulence (HIT) shows that it varies by as much as 100%. Measurements and simulations often show no correspondence with theoretical arguments, which are themselves varied. This situation is unsatisfactory given that HIT is a building block of turbulence theory and modelling. We take recourse to a large base of direct numerical simulations and study decaying HIT for a variety of initial conditions. We show that the Kolmogorov decay exponent and the Birkhoff-Saffman decay are both observed, albeit approximately, for long periods of time if the initial conditions are appropriately arranged. We also present, for both cases, other turbulent statistics such as the velocity derivative skewness, energy spectra and dissipation, and show that the decay and growth laws are approximately as expected theoretically, though the wavenumber spectrum near the origin begins to change relatively quickly, suggesting that the invariants do not strictly exist. We comment briefly on why the decay exponent has varied so widely in past experiments and simulations. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.

Comparison of intermolecular energy transfer from vibrationally excited benzene in mixed nitrogen-benzene baths at 140 K and 300 K.

Gas phase intermolecular energy transfer (IET) is a fundamental component of accurately explaining the behavior of gas phase systems in which the internal energy of particular modes of molecules is greatly out of equilibrium. In this work, chemical dynamics simulations of mixed benzene/N2 baths with one highly vibrationally excited benzene molecule (Bz*) are compared to experimental results at 140 K. Two mixed bath models are considered. In one, the bath consists of 190 N2 and 10 Bz, whereas in the other bath, 396 N2 and 4 Bz are utilized. The results are compared to results from 300 K simulations and experiments, revealing that Bz*-Bz vibration-vibration IET efficiency increased at low temperatures consistent with longer lived "chattering" collisions at lower temperatures. In the simulations, at the Bz* excitation energy of 150 kcal/mol, the averaged energy transferred per collision, ⟨ΔEc⟩, for Bz*-Bz collisions is found to be ∼2.4 times larger in 140 K than in 300 K bath, whereas this value is ∼1.3 times lower for Bz*-N2 collisions. The overall ⟨ΔEc⟩, for all collisions, is found to be almost two times larger at 140 K compared to the one obtained from the 300 K bath. Such an enhancement of IET efficiency at 140 K is qualitatively consistent with the experimental observation. However, the possible reasons for not attaining a quantitative agreement are discussed. These results imply that the bath temperature and molecular composition as well as the magnitude of vibrational energy of a highly vibrationally excited molecule can shift the overall timescale of rethermalization.

Solenoidal Scaling Laws for Compressible Mixing.

Mixing of passive scalars in compressible turbulence does not obey the same classical Reynolds number scaling as its incompressible counterpart. We first show from a large database of direct numerical simulations that even the solenoidal part of the velocity field fails to follow the classical incompressible scaling when the forcing includes a substantial dilatational component. Though the dilatational effects on the flow remain significant, our main results are that both the solenoidal energy spectrum and the passive scalar spectrum assume incompressible forms, and that the scalar gradient essentially aligns with the most compressive eigenvalue of the solenoidal part, provided that only the solenoidal components are consistently used for scaling. A slight refinement of this statement is also pointed out.

Small-scale universality in fluid turbulence.

Turbulent flows in nature and technology possess a range of scales. The largest scales carry the memory of the physical system in which a flow is embedded. One challenge is to unravel the universal statistical properties that all turbulent flows share despite their different large-scale driving mechanisms or their particular flow geometries. In the present work, we study three turbulent flows of systematically increasing complexity. These are homogeneous and isotropic turbulence in a periodic box, turbulent shear flow between two parallel walls, and thermal convection in a closed cylindrical container. They are computed by highly resolved direct numerical simulations of the governing dynamical equations. We use these simulation data to establish two fundamental results: (i) at Reynolds numbers Re ∼ 10(2) the fluctuations of the velocity derivatives pass through a transition from nearly Gaussian (or slightly sub-Gaussian) to intermittent behavior that is characteristic of fully developed high Reynolds number turbulence, and (ii) beyond the transition point, the statistics of the rate of energy dissipation in all three flows obey the same Reynolds number power laws derived for homogeneous turbulence. These results allow us to claim universality of small scales even at low Reynolds numbers. Our results shed new light on the notion of when the turbulence is fully developed at the small scales without relying on the existence of an extended inertial range.