A Lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation

We report an analysis of small-scale enstrophy ω² and rate of strain s² 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_χ = 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 s² through the combined effect of strain production and pressure - strain interaction. This process is followed by a sharp change of ω² 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 τ². 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.