Abstract

I shall review symmetry aspects of turbulent inverse cascades in fluid mechanics, optics and plasma physics. Inverse cascades are generally scale invariant in distinction from most direct cascades. It has been recently discovered that in many cases scale scale invariance can be promoted to a more general and powerful conformal invariance. Namely, two-dimensional isolines of different fields (vorticity, temperature) belong to the remarkable class of curves called Schramm-Loewner evolution (SLE). I shall briefly review the properties of such curves. That discovery brings unexpected connections between fluid mechanics, mathematics (SLE was a subject of the recent Fields medal), theory of critical phenomena and quantum field theory. I then describe the appearance of spectral condensates (modes coherent across the whole system) due to inverse cascades. I briefly discuss the possible role of condensates in atmospheric physics, including the controversy on the energy flux at meso-scales. I shall describe initial findings on how condensates break symmetries established in inverse cascades.