Condensed Matter Seminar: Condensate, fluctuations and symmetries - a tale of 2D turbulence

Abstract:

Earths jet streams, Jupiters Great Red Spot and its zonal winds are all examples of persistent large scale ows, whose dynamics is to a good approximation two-dimensional. These ows are also highly turbulent, and the interaction between the turbulence and these coherent structures remains poorly understood. Apart from its geophysical relevance, 2D turbulence is a rich and beautiful fundamental system|where turbulence takes a counter-intuitive role. Indeed, in 2D, energy is transferred to progressively larger scales, which can terminate in the self organization of the turbulence into a large scale coherent structure, a so called condensate, on top of small scale uctuations. 

I will describe a recent theoretical framework in which the pro le of this coherent mean flow can be obtained, along with the mean momentum ux of the uctuations. I will explain how and when the relation between the two can be deduced from dimensional analysis and symmetry considerations, and how it can be derived. Finally, I will show that, to leading order, the velocity two-point correlation function solves a scale invariant advection equation. The solution determines the average energy of the uctuations, but does not contribute at this order to the momentum ux, due to parity + time reversal symmetry. Using analytic expressions for the solutions, matched to data from extensive numerical simulations, it is then possible to determine the main characteristics of the average energy. This is the rst-ever self-consistent theory of turbulence-flow interaction. 

Event Organizer: Prof. Alexander Gerber