Jacob Berg

Lagrangian multi-particle statistics

Combined measurements of the Lagrangian evolution of particle constellations and the coarse-grained velocity derivative tensor ∂ũ i /∂ x j are presented. The data are obtained from three-dimensional particle tracking measurements in a quasi isotropic turbulent flow at an intermediate Reynolds number. Particle constellations are followed for as long as one integral time and for several Batchelor times. We suggest a method to obtain ∂ũ i /∂ x j from velocity measurements at discrete points. Based on an analytical result and on a sensitivity analysis, both presented here, we estimate the accuracy for filtered strain, ᵴ 2, and enstrophy, 2, at around 30%. The accuracy improves with higher tracer seeding density and with smaller filter scale Δ. We obtain good scaling with t* = √2r 2/15S 2(r) for filtered strain and vorticity and present filtered R–Q invariant maps with the typical ‘tear drop’ shape that is known from velocity gradients at viscous scales. Lagrangian results are given for the growth of particle ...

Experimental investigation of Lagrangian structure functions in turbulence.

Lagrangian properties obtained from a particle tracking velocimetry experiment in a turbulent flow at intermediate Reynolds number are presented. Accurate sampling of particle trajectories is essential in order to obtain the Lagrangian structure functions and to measure intermittency at small temporal scales. The finiteness of the measurement volume can bias the results significantly. We present a robust way to overcome this obstacle. Despite no fully developed inertial range, we observe strong intermittency at the scale of dissipation. The multifractal model is only partially able to reproduce the results.

The Correlation Between Velocity and Acceleration in Turbulence

This relation seems also fulfilled in real turbulent flows [3, 2, 4]. The Eulerian velocity–acceleration structure function 〈δv · δa〉, where δv = v(x+r)−v(x) and likewise for a, can be shown theoretically to be −2ε independent of r = |r| in the inertial subrange. This is true for homogeneous, stationary turbulence, where the body forces act on larger scales, as well as for locally homogeneous flows. For real flows and for Direct Numerical Simulation (DNS) the relation

Turbulent Pair Dispersion: A PTV Experiment

Particle Tracking Velocimetry (PTV) is an experimental technique used to obtain Lagrangian statistics in a turbulent flow[1, 2, 3]. Compared to the more widely used Particle Image Velocimetry (PIV) we track fluid elements in time and space and hence dispersion between more than one fluid element (particle hereinafter) can be observed. Dispersion of such particles is related to many applications and is governing the spreading of pollutants, combustion and prey-predator encounters in a turbulent sea, etc. In this paper we will focus on dispersion of two particles in a homogeneous and isotropic turbulent flow and present some preliminary results. Dispersion of two particles in the inertial subrange where viscous effects can be neglected is described by the Richardson-Obukhov law [4],