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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 20: Symposium SYGP: Stochastic Dynamics of Growth Processes in Biological and Social Systems

SOE 20.2: Hauptvortrag

Donnerstag, 3. April 2014, 15:30–16:00, HSZ 02

Fractal clustering of inertial particles in random velocity fields — •Bernhard Mehlig and Kristian Gustavsson — Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden

Independent particles suspended in incompressible turbulent or randomly mixing flows may cluster together even though incompressible flows exhibit no sinks. This is an inertial effect: inertia allows the particles to detach from the flow. Distinct mechanisms have been invoked to explain clustering in incompressible flows. The two most common ones are "preferential concentration" and "multiplicative amplification". Preferential concentration refers to the tendency of heavy particles to avoid vortical regions of the flow. Multiplicative amplification, by contrast, explains clustering in terms of the logarithmic amplification of the sequence of many small kicks that the suspended particles experience.

In order to quantify the relative importance of the two mechanisms it is necessary to compute the fluctuations of the flow-velocity gradients that the particles experience as they move through the flow. We show how this can be achieved systematically by means of perturbation expansions that recursively take into account how the flow affects the actual particle trajectory. We analyse the statistics of particle- and flow-velocity gradients as seen by the particles. Based on these results we show that in random velocity fields multiplicative amplification has a much stronger effect than preferential concentration, except at very small Stokes numbers. We discuss the implications of these findings for particles suspended in turbulent flows.