### Speaker

Prof.
Michal Hnatič
(Department of Theoretical Physics and Astrophysics, Faculty of Science, P.J. Safarik University, Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research)

### Description

Non- perturbative Renormalization Group ( NPRG ) technique is applied to a stochastical model of non-conserved scalar order parameter near its critical point, subject to turbulent advection .
The compressible advecting flow is modelled by a random Gaussian velocity field with zero mean and correlation function $\langle \upsilon_j \, \upsilon_i \rangle \sim
(P_{j i}^{\perp} + \alpha P_{j i}^{\parallel})/k^{d+\zeta}$. Depending on the relations between the parameters $ \zeta, \alpha$ and the space dimensionality $d$, the model reveals several types of scaling regimes. Some of them are well known (model $A$ of equilibrium critical dynamics and
linear passive scalar field advected by a random turbulent flow), but there is a new nonequilibrium regime (universality class) associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram ($d, \zeta$) of possible scaling regimes in system. The physical point $d=3,
\zeta=4/3$ corresponding to three-dimensional fully developed Kolmogorov's turbulence where critical fluctuations are irrelevant, is stable for $\alpha \lesssim 2.26$. Otherwise, in the case of ``strong compressibility'' $\alpha \gtrsim 2.26$, the critical fluctuations of the order parameter become
relevant for tree-dimensional turbulence. Estimations of critical exponents for each scaling regimes are presented.

### Primary author

Prof.
Michal Hnatič
(Department of Theoretical Physics and Astrophysics, Faculty of Science, P.J. Safarik University, Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research)

### Co-authors

Dr
G Nalimov
(Saint Petersburg State University)
Dr
G. Kalagov
(Department of Theoretical Physics and Astrophysics, Faculty of Science, P.J. Safarik University)