Measurement of the scaling of the dissipation at high Reynolds numbers

Second order structure functions for higher powers of turbulent velocity

We experimentally study the temporal second-order structure functions for integer powers of turbulent fluid velocity fluctuations [Formula: see text], in three dimensional (3D) and two dimensional (2D) turbulence. Here [Formula: see text] is a composite time-series constructed by averaging the concurrent time-series ([Formula: see text]) sampled at N spatially distributed Eulerian points. The N  =  1 case has been extensively studied for velocity fluctuations (m  =  1) and to a lesser extent for m  >  1. The averaging method in case of N  >  1 diverges from the Kolmogorov framework and has not been studied because fluctuations in [Formula: see text] are expected to smooth with increasing N leaving behind uninteresting large-scale mean flow information, but we find this is not so. We report the evolution of scaling exponents [Formula: see text] for [Formula: see text] in going from a single (N  =  1) to a spatial average over several Eulerian points ([Formula: see text]). Our 3D experiments in a tank with rotating jets at the floor show [Formula: see text] for all m-values in agreement with prior results and evolves to an asymptotic value of [Formula: see text]. The evolution of [Formula: see text] follows the functional form [Formula: see text], where [Formula: see text] points is the only fit parameter representing the convergence rate constant. Results for the 2D experiments conducted in a gravity assisted soap film in the enstrophy cascade regime are in sharp contrast with their 3D counterparts. Firstly [Formula: see text] varies polynomially with m and asymptotes to a constant value at m  =  5. Secondly, the evolution of [Formula: see text] is logarithmic [Formula: see text], where A and B are fit parameters and eventually deviates at large N and asymptotes to [Formula: see text] for all m. The starkly different convergence forms (exponential in 3D versus logarithmic in 2D) may be interpreted as a signature of inter-scale couplings in the respective turbulent flows by decomposing the two-point correlator for [Formula: see text] into a self-correlation and cross-correlation term. In addition to aiding in the theoretical development, the results may also have implications for determination of resolution in 2D turbulence experiments and simulations, wind energy and atmospheric boundary layer turbulence.

Dissipation, intermittency, and singularities in incompressible turbulent flows

We examine the connection between the singularities or quasisingularities in the solutions of the incompressible Navier-Stokes equation (INSE) and the local energy transfer and dissipation, in order to explore in detail how the former contributes to the phenomenon of intermittency. We do so by analyzing the velocity fields (a) measured in the experiments on the turbulent von Kármán swirling flow at high Reynolds numbers and (b) obtained from the direct numerical simulations of the INSE at a moderate resolution. To compute the local interscale energy transfer and viscous dissipation in experimental and supporting numerical data, we use the weak solution formulation generalization of the Kármán-Howarth-Monin equation. In the presence of a singularity in the velocity field, this formulation yields a nonzero dissipation (inertial dissipation) in the limit of an infinite resolution. Moreover, at finite resolutions, it provides an expression for local interscale energy transfers down to the scale where the energy is dissipated by viscosity. In the presence of a quasisingularity that is regularized by viscosity, the formulation provides the contribution to the viscous dissipation due to the presence of the quasisingularity. Therefore, our formulation provides a concrete support to the general multifractal description of the intermittency. We present the maps and statistics of the interscale energy transfer and show that the extreme events of this transfer govern the intermittency corrections and are compatible with a refined similarity hypothesis based on this transfer. We characterize the probability distribution functions of these extreme events via generalized Pareto distribution analysis and find that the widths of the tails are compatible with a similarity of the second kind. Finally, we make a connection between the topological and the statistical properties of the extreme events of the interscale energy transfer field and its multifractal properties.

Wake-Driven Dynamics of Finite-Sized Buoyant Spheres in Turbulence

Particles suspended in turbulent flows are affected by the turbulence and at the same time act back on the flow. The resulting coupling can give rise to rich variability in their dynamics. Here we report experimental results from an investigation of finite-sized buoyant spheres in turbulence. We find that even a marginal reduction in the particle's density from that of the fluid can result in strong modification of its dynamics. In contrast to classical spatial filtering arguments and predictions of particle models, we find that the particle acceleration variance increases with size. We trace this reversed trend back to the growing contribution from wake-induced forces, unaccounted for in current particle models in turbulence. Our findings highlight the need for improved multiphysics based models that account for particle wake effects for a faithful representation of buoyant-sphere dynamics in turbulence.

Superfluid high REynolds von Kármán experiment

The Superfluid High REynolds von Kármán experiment facility exploits the capacities of a high cooling power refrigerator (400 W at 1.8 K) for a large dimension von Kármán flow (inner diameter 0.78 m), which can work with gaseous or subcooled liquid (He-I or He-II) from room temperature down to 1.6 K. The flow is produced between two counter-rotating or co-rotating disks. The large size of the experiment allows exploration of ultra high Reynolds numbers based on Taylor microscale and rms velocity [S. B. Pope, Turbulent Flows (Cambridge University Press, 2000)] (Rλ > 10000) or resolution of the dissipative scale for lower Re. This article presents the design and first performance of this apparatus. Measurements carried out in the first runs of the facility address the global flow behavior: calorimetric measurement of the dissipation, torque and velocity measurements on the two turbines. Moreover first local measurements (micro-Pitot, hot wire,…) have been installed and are presented.

Tracking the dynamics of translation and absolute orientation of a sphere in a turbulent flow

We study the six-dimensional dynamics--position and orientation--of a large sphere advected by a turbulent flow. The movement of the sphere is recorded with two high-speed cameras. Its orientation is tracked using a novel, efficient algorithm; it is based on the identification of possible orientation "candidates" at each time step, with the dynamics later obtained from maximization of a likelihood function. Analysis of the resulting linear and angular velocities and accelerations reveal a surprising intermittency for an object whose size lies in the inertial range, close to the integral scale of the underlying turbulent flow.

Passive scalar intermittency in low temperature helium flows

We report new measurements of mixing of passive temperature field in a turbulent flow. The use of low temperature helium gas allows us to span a range of microscale Reynolds number, R(lambda), from 100 to 650. The exponents xi(n) of the temperature structure functions </straight theta(x+r)-straight theta(x)/(n)> approximately r(xi(n)) are shown to saturate to xi(infinity) approximately 1.45+/-0.1 for the highest orders, n approximately 10. This saturation is a signature of statistics dominated by frontlike structures, the cliffs. Statistics of the cliffs' characteristics are performed, particularly their widths are shown to scale as the Kolmogorov length scale.

Periodically kicked turbulence

Periodically kicked turbulence is theoretically analyzed within a mean-field theory. For large enough kicking strength A and kicking frequency f the Reynolds number grows exponentially and then runs into some saturation. The saturation level Re(sat) can be calculated analytically; different regimes can be observed. For large enough Re we find Re(sat) approximately Af, but intermittency can modify this scaling law. We suggest an experimental realization of periodically kicked turbulence to study the different regimes we theoretically predict and thus to better understand the effect of forcing on fully developed turbulence.