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TUT: Tutorials

TUT 2: Stochastic Processes from Financial Risk to Dynamics in Biology and Physics (joint session SOE/TUT/DY)

TUT 2.1: Tutorium

Sonntag, 15. März 2020, 16:00–16:50, HSZ 03

Stochastic models for particles in turbulence — •Bernhard Mehlig — Department of Physics, University of Gothenburg, Sweden

The subject of this tutorial is the dynamics of heavy particles in turbulence, such as water droplets in the turbulent air of a cumulus cloud, dust grains in the turbulent gas around a growing star, or motile micro-organisms in the turbulent ocean. The analysis of such highly non-linear and multi-scale problems poses formidable challenges, because any description of the dynamics must refer to the turbulent fluctuations that the particles experience as they move through the fluid. Experiments resolving the particle dynamics have only recently become possible, and direct numerical simulations of such systems are still immensely difficult.

In this tutorial I explain how to understand the fundamental mechanisms determining the dynamics of particles in turbulence in terms of statistical models that account for the symmetries and statistics of the turbulent flow. Using simple examples I illustrate how to solve such models with diffusion approximations, highlighting an analogy with Kramers' escape problem. I discuss the limitations of the approach, and summarise recent progress. I conclude by discussing open questions, arguing that the approach outlined provides a unique opportunity to make significant progress regarding this challenging and important problem.