# math colloquium

### Event Description:

Title: Folding in fluids and Magnetohydrodynamics

Abstract:

The formation of the coherent vortical structures in the form of thin pancakes for three-dimensional flows and quasi-shocks of the vorticity in two-dimensional turbulence is studied at the high Reynolds regime when, in the leading order, the development of such structures can be described within the Euler equations for ideal incompressible fluids. Numerically and analytically on the base of the vortex line representation we show that compression of such structures and respectively increase of their amplitudes are possible due to the compressibility of the vorticity in the 3D case and of the di-vorticity field which is curl of vorticity for 2D geometry. It is demonstrated that, in both cases, this growth has an exponential behavior and can be considered as folding (analog of breaking) for the divergence-free fields of both vorticity and di-vorticity. At high amplitudes this process in 3D has a self-similar behavior connected the maximal vorticity and the pancake width by the relation of the universal type: maximal vorticity is proportional to the pancake width in power (-2/3). For the 2D turbulence numerically it is shown that maximal di-vorticity depends on the quasi-shock thickness according to the same power law, that indicates also in favor of folding for the di-vorticity field. Appearance of the 2/3-law in fluids is a consequence of frozenness for both vorticity and di-vorticity fields. In this talk we consider also the problem of generation of strong magnetic fields in MHD due to the folding mechanism. On our opinion, the formation of magnetic filaments

in the convective zone of the Sun can be explained by this mechanism.

At the end of this talk we discuss the role of folding structures in the formation of the Kolmogorov spectrum in 3D and the Kraichnan spectrum for two-dimensional turbulence.

Bio: Evgenii A. Kuznetsov is the member of Russian Academy of Siences. Focus of his research is in nonlinear waves, plasma and hydrodynamics.

### Event Contact

**Contact Name: **Pavel Lushnikov