Different approaches for understanding instabilities: from linear stability to the emergence of coherence in turbulence.

by Cristobal Arratia (Nordita)

Tuesday 24 Jan 2017, 13:30 → 14:30 Europe/Stockholm

112:028

Fluid mechanics offers rich and often surprising dynamics despite having well established governing equations for almost two centuries. As such, it has historically been a fruitful ground for the development of methodologies and discovery of phenomena of importance for more general complex systems. Here I will present a selection of recent results on hydrodynamic instabilities which provide new insights on well studied (and sometimes left unresolved) problems. The instabilities involve shear flow, vortex shedding and a free surface turbulent flow. The results are obtained on a variety of models which allow the introduction of a few simple yet powerful approaches. The models will be presented in an order of roughly increasing mathematical complexity, from linear autonomous and non-autonomous to non-linear stochastic systems, passing through spatially extended and self-consistent quasi-linear models. It is thus expected that the presentation will provide a broad view of recent developments on hydrodynamic instabilities. To finalize, we shall build up on some of the presented models to show how it might be becoming possible to predict the appearance of coherent structures in turbulent flows.