91ÊÓƵ

Condensate, fluctuations and symmetries — a tale of 2D turbulence

Earth's jet streams, Jupiters Great Red Spot and its zonal winds are all examples of persistent large scale flows,ÌýÌýwhose dynamics is to a good approximation two-dimensional.ÌýThese flows are also highly turbulent, and the interactionÌýÌýbetween the turbulence and these coherent structures remainsÌýpoorly understood.ÌýApart from its geophysical relevance,ÌýÌý2Dturbulence is a rich and beautiful fundamental system — where turbulence takesÌýa counter-intuitive role.Indeed, inÌý2D,Ìýenergy is transferred to progressively larger scales, which can terminate in the self organizationÌýof the turbulence into aÌýlarge scale coherent structure,Ìýa so calledÌýcondensate, on top of small scale fluctuations.

I will describe a recent theoretical framework in which the profile of this coherent mean flow can be obtained,Ìýalong withÌýthe mean momentum flux of the fluctuations.ÌýI will explain how and when the relation between the two can be deducedÌýfrom dimensional analysis and symmetry considerations,Ìýand how it can be derived.ÌýFinally, I will show that, to leadingÌýorder, the velocity two-point correlation function solves a scale invariantÌýadvectionÌýequation.ÌýThe solution determines theÌýaverage energy of the fluctuations,Ìýbut does not contribute at this order to the momentum flux, due to parity + time reversalÌýsymmetry.ÌýUsing analytic expressions for the solutions, matched to data from extensive numerical simulations,Ìýit is thenÌýpossible to determine the main characteristics of the average energy.ÌýThis is the first-ever self-consistent theory ofÌýturbulence-flow interaction.