Markus Holzner

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 Reλ = 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 ω2. 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, τη. Locally, the characteristic velocity of the fluid relative to the turbulent/non-turbulent interface is the Kolmogorov velocity, uη.

Small-scale aspects of flows in proximity of the turbulent/nonturbulent interface

The work reported below is the first of its kind to study the properties of turbulent flow without strong mean shear in a Newtonian fluid in proximity of the turbulent/nonturbulent interface, with emphasis on the small-scale aspects. The main tools used are a three-dimensional particle tracking system allowing one to measure and follow in a Lagrangian manner the field of velocity derivatives and direct numerical simulations. The comparison of flow properties in the turbulent (A), intermediate (B), and nonturbulent (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.

Elasto-inertial turbulence

Turbulence is ubiquitous in nature, yet even for the case of ordinary Newtonian fluids like water, our understanding of this phenomenon is limited. Many liquids of practical importance are more complicated (e.g., blood, polymer melts, paints), however; they exhibit elastic as well as viscous characteristics, and the relation between stress and strain is nonlinear. We demonstrate here for a model system of such complex fluids that at high shear rates, turbulence is not simply modified as previously believed but is suppressed and replaced by a different type of disordered motion, elasto-inertial turbulence. Elasto-inertial turbulence is found to occur at much lower Reynolds numbers than Newtonian turbulence, and the dynamical properties differ significantly. The friction scaling observed coincides with the so-called “maximum drag reduction” asymptote, which is exhibited by a wide range of viscoelastic fluids.

The turbulence boundary of a temporal jet

We examine the structure of the turbulence boundary of a temporal plane jet at

Investigations on the local entrainment velocity in a turbulent jet

Re=5000

Expanding the Q – R space to three dimensions

using statistics conditioned on the enstrophy. The data is obtained by direct numerical simulation and threshold values span 24 orders of magnitude, ranging from essentially irrotational fluid outside the jet to fully turbulent fluid in the jet core. We use two independent estimators for the local entrainment velocity

Mapping mean and fluctuating velocities by Bayesian multipoint MR velocity encoding-validation against 3D particle tracking velocimetry

v_n

Acceleration, pressure and related quantities in the proximity of the turbulent/non-turbulent interface

based on the enstrophy budget. The data show clear evidence for the existence of a viscous superlayer (VSL) that envelopes the turbulence. The VSL is a nearly one-dimensional layer with low surface curvature. We find that both its area and viscous transport velocity adjust to the imposed rate so that the integral entrainment flux is independent of threshold, although low-Reynolds-number effects play a role for the case under consideration. This threshold independence is consistent with the inviscid nature of the integral rate of entrainment. A theoretical model of the VSL is developed that is in reasonably good agreement with the data and predicts that the contribution of viscous transport and dissipation to interface propagation have magnitude

On the accuracy of viscous and turbulent loss quantification in stenotic aortic flow using phase-contrast MRI.

2 v_n

High-Resolution Measurements of Turbulent Flow Close to the Sediment–Water Interface Using a Bistatic Acoustic Profiler

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