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)
