The work reported below is a first of its kind study of the properties of turbulent flow without strong mean shear in a Newtonian fluid in proximity of the turbulent/non-turbulent interface, with emphasis on the small scale aspects. The main tools used are a three-dimensional particle tracking system (3D-PTV) allowing to measure and follow in a Lagrangian manner the field of velocity derivatives and direct numerical simulations (DNS). The comparison of flow properties in the turbulent (A), intermediate (B) and non-turbulent (C) regions in the proximity of the interface allows for direct observation of the key physical processes underlying the entrainment phenomenon. The differences between small scale strain and enstrophy are striking and point to the definite scenario of turbulent entrainment via the viscous forces originating in strain.

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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.

The evolution of material lines, $l$, and vorticity, $\omega$, is investigated experimentally through three-dimensional particle-tracking velocimetry (3D-PTV) in quasi-homogeneous isotropic turbulence at $Re_{\lambda }\,{=}\,50$. Through 3D-PTV data the full set of velocity derivatives, $\partial u_{i}/\partial x_{j}$, is accessible. This allows us to monitor the evolution of various turbulent quantities along fluid particle trajectories. The main emphasis of the present work is on the physical mechanisms that govern the Lagrangian evolution of $l$ and $\omega$ and the essential differences inherent in these two processes. For example, we show that vortex stretching is smaller than material lines stretching, i.e. $\langle\omega_{i}\omega_{j}s_{ij}/\omega^{2}\rangle \,{<}\,\langle l_{i}l_{j}s_{ij}/l^{2}\rangle$, and expand on how this issue is closely related to the predominant alignment of $\omega$ and the intermediate principal strain eigenvector $\lambda_{2}$ of the rate of strain tensor, $s_{ij}$. By focusing on Lagrangian quantities we discern whether these alignments are driven and maintained mainly by vorticity or by strain. In this context, the tilting of $\omega$ and the rotation of the eigenframe $\lambda_{i}$ of the rate of strain tensor $s_{ij}$ are investigated systematically conditioned on different magnitudes of strain, $s^{2}$, and enstrophy, $\omega^{2}$. Further, we infer that viscosity contributes through the term $\nu\omega_{i}\nabla^2\omega_{i}$ to ${\rm D}\omega^{2}/{\rm D}t$, whereas ${\rm D}l^{2}/{\rm D}t$ has no diffusive term. This difference plays a key role in defining the mutual orientation between $\omega$ and $\lambda_{i}$. Viscosity thus contributes significantly to the difference in growth rates of $\langle\omega_{i}\omega_{j}s_{ij}\rangle$ and $\langle l_{i}l_{j}s_{ij}\rangle$.