Lagrangian view of time irreversibility of fluid turbulence

A turbulent flow is maintained by an external supply of kinetic energy, which is eventually dissipated into heat at steep velocity gradients. The scale at which energy is supplied greatly differs from the scale at which energy is dissipated, the more so as the turbulent intensity (the Reynolds number) is larger. The resulting energy flux over the range of scales, intermediate between energy injection and dissipation, acts as a source of time irreversibility. As it is now possible to follow accurately fluid particles in a turbulent flow field, both from laboratory experiments and from numerical simulations, a natural question arises: how do we detect time irreversibility from these Lagrangian data? Here we discuss recent results concerning this problem. For Lagrangian statistics involving more than one fluid particle, the distance between fluid particles introduces an intrinsic length scale into the problem. The evolution of quantities dependent on the relative motion between these fluid particles, including the kinetic energy in the relative motion, or the configuration of an initially isotropic structure can be related to the equal-time correlation functions of the velocity field, and is therefore sensitive to the energy flux through scales, hence to the irreversibility of the flow. In contrast, for single-particle Lagrangian statistics, the most often studied velocity structure functions cannot distinguish the "arrow of time." Recent observations from experimental and numerical simulation data, however, show that the change of kinetic energy following the particle motion, is sensitive to time-reversal. We end the survey with a brief discussion of the implication of this line of work.Comment: accepted for publication in Science China - Physics, Mechanics & Astronom

Evolution of geometric structures in intense turbulence

We report measurements of the evolution of lines, planes, and volumes in an intensely turbulent laboratory flow using high-speed particle tracking. We find that the classical characteristic time scale of an eddy at the initial scale of the object considered is the natural time scale for the subsequent evolution. The initial separation may only be neglected if this time scale is much smaller than the largest turbulence time scale, implying extremely high turbulence levels.Comment: 10 pages, 6 figures, added more detail

A Finite Element Study of the Contact Stiffness of Homogenous Materials and Thin Films

The applicability of the stiffness equation S=2Era to elastic and elastic-plastic homogeneous materials and thin films on substrates is studied by finite element techniques. It is found that the stiffness equation works well in all these materials provided that a correction factor β is included. For elastic homogenous materials, the correction factor is examined for different friction conditions, Poisson’s ratios, and indenter cone angles. In the case of elastic-plastic indentation with a 70.3° cone, the correction factor is very close to that for elastic indentation of a matching conical hole, which provides a convenient way to model the effects of plasticity. Nanoindentation measurements using the stiffness equation for film/substrate systems may be affected by the substrate properties. To address this issue, a new equation describing the relationship between the effective compliance and the elastic properties of the film and the substrate for flat cylindrical punch indentation is derived. To apply this to conical indentation, it is shown that an effective film thickness should be used in the new relation to account for the geometry difference between a conical indenter and a flat punch. Finite element analysis (FEA) is used to obtain a simple equation which can be used to determine the effective film thickness, which is independent of the elastic properties of the films and substrates for compliant films on stiff substrates. The applicability of the new relation is examined by comparing it to FEA of elastic-plastic indentation by a cone. The new relation is also compared to Yu’s approximate analytical solution to determine which is more accurate for obtaining the true contact radius from the measured stiffness. Although Yu’s solution applies to a broader range of materials, the new relation has distinct advantages in that it can be written in a simple algebraic form

Where do small, weakly inertial particles go in a turbulent flow?

We report experimental results on the dynamics of heavy particles of the size of the Kolmogorov-scale in a fully developed turbulent flow. The mixed Eulerian structure function of two-particle velocity and acceleration difference vectors was observed to increase significantly with particle inertia for identical flow conditions. We show that this increase is related to a preferential alignment between these dynamical quantities. With increasing particle density the probability for those two vectors to be collinear was observed to grow. We show that these results are consistent with the preferential sampling of strain-dominated regions by inertial particles.Comment: 8 pages, 4 figures, accepted for publication JFM (fast-track

Time-symmetry breaking in turbulence

In three-dimensional turbulent flows, the flux of energy from large to small scales breaks time symmetry. We show here that this irreversibility can be quantified by following the relative motion of several Lagrangian tracers. We find by analytical calculation, numerical analysis and experimental observation that the existence of the energy flux implies that, at short times, two particles separate temporally slower forwards than backwards, and the difference between forward and backward dispersion grows as $t^3$. We also find the geometric deformation of material volumes, surrogated by four points spanning an initially regular tetrahedron, to show sensitivity to the time-reversal with an effect growing linearly in $t$. We associate this with the structure of the strain rate in the flow.Comment: 5 pages, 4 figure