The full set of velocity derivatives, $\partial u_{i}/\partial x_{j}$, is measured experimentally in a Lagrangian way in quasi-homogeneous isotropic turbulence. This is achieved by applying the three-dimensional particle tracking velocimetry (3D-PTV) technique to an electromagnetically forced flow with $\hbox{\it Re}_{\lambda}\,{\thickapprox}\,50$. Checks based on precise kinematic relations show that the technique presented measures the velocity derivatives with good accuracy. In a study on vorticity, characteristic properties of turbulent flows known from direct numerical simulations are reproduced. These are the positive skewness of the intermediate eigenvalue of the rate of strain tensor, $s_{ij}$, $\langle \Lambda_{2}\rangle \,{>}\,0$, the predominance of vortex stretching over vortex compression, $\langle \omega_{i}\omega_{j}s_{ij}\rangle \,{>}\,0$ and the predominant alignment of vorticity, ${\bm \omega}$, with the intermediate principal axis of strain, ${\bm \lambda}_{2}$. Results on the evolution in time of material lines, ${\bm l}$, compared to vortex lines, ${\bm \omega}$, are presented. They show that the nonlinear interaction of vorticity with the surrounding flow assists viscosity in maintaining this predominant ${\bm \lambda}_{2}$-alignment of vorticity. Lagrangian measurements of enstrophy budget terms suggest that there is no pointwise balancing of production and viscous reduction of enstrophy and that the role played by viscosity is of great importance.

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R 2 120:740. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. ParisiFrisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

In this Letter we present results from particle tracking velocimetry and direct numerical simulation that are congruent with the existence of a laminar superlayer, as proposed in the pioneering work of Corrsin and Kistler (NACA, Technical Report No. 1244, 1955). We find that the local superlayer velocity is dominated by a viscous component and its magnitude is comparable to the characteristic velocity of the smallest scales of motion. This slow viscous process involves a large surface area so that the global rate of turbulence spreading is set by the largest scales of motion. These findings are important for a better understanding of mixing of mass and momentum in a variety of flows where thin layers of shear exist. Examples are boundary layers, clouds, planetary atmospheres, and oceans.

From particle tracking velocimetry we present an experimental measure of the ratio between backwards and forwards relative dispersion in an intermediate Reynolds number turbulent flow. Lack of time-reversal symmetry implies that their ratio may be different from 1. From a stochastic model, this has recently been studied by Sawford et al [Phys. Fluids 17, 095109 (2005)] giving ratios between 5 and 20. We find a value of approximately 2 and discuss it in the context of the characteristics of the rate of strain tensor s(ij). An analysis of a direct numerical simulation by Biferale et al [Phys. Rev. Lett. 93, 064502 (2004) and Phys. Fluids 17, 021701 (2004)] gives the same result.

We report an analysis of small-scale enstrophy ω 2 and rate of strain s 2 dynamics in the proximity of the turbulent/non-turbulent interface in a flow without strong mean shear. The techniques used are three-dimensional particle tracking (3D-PTV), allowing the field of velocity derivatives to be measured and followed in a Lagrangian manner, and direct numerical simulations (DNS). In both experiment and simulation the Taylor-microscale Reynolds number is Re λ = 50. The results are based on the Lagrangian viewpoint with the main focus on flow particle tracers crossing the turbulent/non-turbulent interface. This approach allowed a direct investigation of the key physical processes underlying the entrainment phenomenon and revealed the role of small-scale non-local, inviscid and viscous processes. We found that the entrainment mechanism is initiated by self-amplification of s 2 through the combined effect of strain production and pressure-strain interaction. This process is followed by a sharp change of ω 2 induced mostly by production due to viscous effects. The influence of inviscid production is initially small but gradually increasing, whereas viscous production changes abruptly towards the destruction of ω 2 . Finally, shortly after the crossing of the turbulent/non-turbulent interface, production and dissipation of both enstrophy and strain reach a balance. The characteristic time scale of the described processes is the Kolmogorov time scale, τ η . Locally, the characteristic velocity of the fluid relative to the turbulent/non-turbulent interface is the Kolmogorov velocity, u η .

In this article, we present an experimental setup and data processing schemes for 3D scanning particle tracking velocimetry (SPTV), which expands on the classical 3D particle tracking velocimetry (PTV) through changes in the illumination, image acquisition and analysis. 3D PTV is a flexible flow measurement technique based on the processing of stereoscopic images of flow tracer particles. The technique allows obtaining Lagrangian flow information directly from measured 3D trajectories of individual particles. While for a classical PTV the entire region of interest is simultaneously illuminated and recorded, in SPTV the flow field is recorded by sequential tomographic high-speed imaging of the region of interest. The advantage of the presented method is a considerable increase in maximum feasible seeding density. Results are shown for an experiment in homogenous turbulence and compared with PTV. SPTV yielded an average 3,500 tracked particles per time step, which implies a significant enhancement of the spatial resolution for Lagrangian flow measurements.

We present an experimental investigation of entrainment and the dynamics near the turbulent/non-turbulent interface in a dense gravity current. The main goal of the study is to investigate changes in the interfacial physics due to the presence of stratification and to examine their impact on the entrainment rate. To this end, three-dimensional data sets of the density and the velocity fields are obtained through a combined scanning particle tracking velocimetry/laser-induced fluorescence approach for two different stratification levels with inflow Richardson numbers of Ri 0 = 0.23 and Ri 0 = 0.46, respectively, at a Reynolds number around Re 0 = 3700. An analysis conditioned on the instantaneous position of the turbulent/non-turbulent interface as defined by a threshold on enstrophy reveals an interfacial region that is in many aspects independent of the initial level of stratification. This is reflected most prominently in matching peaks of the gradient Richardson number Ri g ≈ 0.1 located approximately 10η from the position of the interface inside the turbulent region, where η = (ν 3 / ) 1/4 is the Kolmogorov scale, and ν and denote the kinematic viscosity and the rate of turbulent dissipation, respectively. A possible explanation for this finding is offered in terms of a cyclic evolution in the interaction of stratification and shear involving the buildup of density and velocity gradients through inviscid amplification and their subsequent depletion through molecular effects and pressure. In accordance with the close agreement of the interfacial properties for the two cases, no significant differences were found for the local entrainment velocity, v n (defined as the propagation velocity of an enstrophy isosurface relative to the fluid), at different initial stratification levels. Moreover, we find that the baroclinic torque does not contribute significantly to the local entrainment velocity. Comparing results for the surface area of the convoluted interface to estimates from fractal scaling theory, we identify differences in the interface geometry as the major factor in the reduction of the entrainment rate due to density stratification.

We report an experimental analysis of the local entrainment velocity in the self-similar region of a turbulent jet. Particle tracking velocimetry is performed to determine the position of the convoluted, instantaneous turbulent/non-turbulent interface and to compute velocity and velocity derivatives in the proximity of the interface. We find that the local entrainment velocity is mostly governed by a viscous component and that its magnitude depends on the local shape of the interface. It is illustrated that local entrainment is faster for surface elements concave towards the turbulent region. A closer analysis of the plane spanned by mean and Gaussian curvature reveals that depending on the surface shape, different small-scale mechanisms are dominant for the local entrainment process, namely, viscous diffusion for concave shapes and vortex stretching for convex shapes. Key quantities influencing viscous diffusion and vortex stretching in the entrainment process are identified. It is illustrated that the viscous advancement of the interface into the non-turbulent region mostly depends on the shape of the enstrophy profile normal to the interface. The inviscid contribution is intimately related to the alignment of vorticity with the eigenvectors of the rate of strain tensor. Finally, the analysis substantiates that the convolution of the instantaneous interface is driven by the advection of the underlying fluid together with a contribution from the local entrainment velocity, with the advection velocity being the governing part.