K. R. Sreenivasan

The multifractal nature of turbulent energy dissipation

The intermittency of the rate of turbulent energy dissipation e is investigated experimentally, with special emphasis on its scale-similar facets. This is done using a general formulation in terms of multifractals, and by interpreting measurements in that light. The concept of multiplicative processes in turbulence is (heuristically) shown to lead to multifractal distributions, whose formalism is described in some detail. To prepare proper ground for the interpretation of experimental results, a variety of cascade models is reviewed and their physical contents are analysed qualitatively. Point-probe measurements of e are made in several laboratory flows and in the atmospheric surface layer, using Taylors frozen-flow hypothesis. The multifractal spectrum f (α) of e is measured using different averaging techniques, and the results are shown to be in essential agreement among themselves and with our earlier ones. Also, long data sets obtained in two laboratory flows are used to obtain the latent part of the f (α) curve, confirming Mandelbrots idea that it can in principle be obtained from linear cuts through a three-dimensional distribution. The tails of distributions of box-averaged dissipation are found to be of the square-root exponential type, and the implications of this finding for the f (α) distribution are discussed. A comparison of the results to a variety of cascade models shows that binomial models give the simplest possible mechanism that reproduces most of the observations. Generalizations to multinomial models are discussed.

On the universality of the Kolmogorov constant

All known data are collected on the Kolmogorov constant in one‐dimensional spectral formula for the inertial range. For large enough microscale Reynolds numbers, the data (despite much scatter) support the notion of a ‘‘universal’’ constant that is independent of the flow as well as the Reynolds number, with a numerical value of about 0.5. In particular, it is difficult to discern support for a recent claim that the constant is Reynolds number dependent even at high Reynolds numbers.

Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues

Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of research in recent years. Many challenges remain in theory, scaling, physical understanding, experimental techniques, and numerical simulations. In this paper we distill the salient advances of recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the principal model parameters such as the von Karman “constant,” the parametrization of roughness effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that may provide answers to these questions, notably the improvement of measuring techniques and the construction of new facilities, are identified. We also highlight aspects where differences of opinion persist, with the expectation that this discussion might mark the beginning of their resolution.

Turbulent convection at very high Rayleigh numbers

Turbulent convection occurs when the Rayleigh number (Ra)—which quantifies the relative magnitude of thermal driving to dissipative forces in the fluid motion—becomes sufficiently high. Although many theoretical and experimental studies of turbulent convection exist, the basic properties of heat transport remain unclear. One important question concerns the existence of an asymptotic regime that is supposed to occur at very high Ra. Theory predicts that in such a state the Nusselt number (Nu), representing the global heat transport, should scale as Nu ∝ Raβ with β = 1/2. Here we investigate thermal transport over eleven orders of magnitude of the Rayleigh number (106 ≤ Ra ≤ 10 17), using cryogenic helium gas as the working fluid. Our data, over the entire range of Ra, can be described to the lowest order by a single power-law with scaling exponent β close to 0.31. In particular, we find no evidence for a transition to the Ra1/2 regime. We also study the variation of internal temperature fluctuations with Ra, and probe velocity statistics indirectly.

The fractal facets of turbulence

On montre que plusieurs aspects de la turbulence peuvent etre decrits par des fractales et que leurs dimensions fractales peuvent etre mesurees

On Local Isotropy of Passive Scalars in Turbulent Shear Flows

An assessment of local isotropy and universality in high-Reynolds-number turbulent flows is presented. The emphasis is on the behaviour of passive scalar fields advected by turbulence, but a brief review of the relevant facts is given for the turbulent motion itself. Experiments suggest that local isotropy is not a natural concept for scalars in shear flows, except, perhaps, at such extreme Reynolds numbers that are of no practical relevance on Earth. Yet some type of scaling exists even at moderate Reynolds numbers. The relation between these two observations is a theme of this paper.

Relaminarization of fluid flows

The mechanisms of the relaminarization of turbulent flows are investigated with a view to establishing any general principles that might govern them. Three basic archetypes of reverting flows are considered: the dissipative type, the absorptive type, and the Richardson type exemplified by a turbulent boundary layer subjected to severe acceleration. A number of other different reverting flows are then considered in the light of the analysis of these archetypes, including radial Poiseuille flow, convex boundary layers, flows reverting by rotation, injection, and suction, as well as heated horizontal and vertical gas flows. Magnetohydrodynamic duct flows are also examined. Applications of flow reversion for turbulence control are discussed.

The passive scalar spectrum and the Obukhov–Corrsin constant

It is pointed out that, for microscale Reynolds numbers less than about 1000, the passive scalar spectrum in turbulent shear flows is less steep than anticipated and that the Obukhov–Corrsin constant can be defined only if the microscale Reynolds number exceeds this value. In flows where the large‐scale velocity field is essentially isotropic (as in grid turbulence), the expected 5/3 scaling is observed even at modest Reynolds numbers. All known data on the Obukhov–Corrsin constant are collected. The support for the notion of a ‘‘universal’’ constant is shown to be reasonable. Its value is about 0.4.

On the scaling of the turbulence energy dissipation rate

From an examination of all data to date on the dissipation of turbulent energy in grid turbulence, it is concluded that, for square‐mesh configuration, the ratio of the time scale characteristic of dissipation rate to that characteristic of energy‐containing eddies is a constant independent of Reynolds number, for microscale Reynolds numbers in excess of about 50. Insufficient data available for other grid configurations suggest a possibility that the ratio could assume different numerical values for different configurations. This persistent effect of initial conditions on the time scale ratio is further illustrated by reference to the jet‐grid data of Gad‐el‐Hak and Corrsin.

Superfluid helium: visualization of quantized vortices.

When liquid helium is cooled to below its phase transition at 2.172 K, vortices appear with cores that are only ångströms in diameter, about which the fluid circulates with quantized angular momentum. Here we generate small particles of solid hydrogen that can be used to image the cores of quantized vortices in their three-dimensional environment of liquid helium. This technique enables the geometry and interactions of these vortices to be observed directly.