Turbulent mixing of a critical fluid: The non-perturbative renormalization

Hnatič, Michal; Kalagov, Georgii; Nalimov, M. Yu.

doi:10.1016/j.nuclphysb.2017.10.024

Cited by 7 publications

(8 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, it would be interesting to study the problem (2.4) with the functional RG. Furthermore, recently, the functional RG was applied to a similar problem, namely, to the model A of equilibrium critical dynamics under influence of the turbulent motion of the environment described by the Kraichnan's rapid change model [52]. Surprisingly enough, the obtained results are in a full agreement with the one-loop perturbative results [45].…”

Section: Discussionmentioning

confidence: 58%

“…As such, one may hope that in the present case the one-loop approximation may serve as an adequate qualitative estimate. In support of this assumption, one can mention a recent study of the turbulence effects on the critical behaviour, where the use of the functional RG [52] provided a very detailed confirmation of the one-loop perturbative results derived earlier in [45]. It is also worth mentioning that, for the Kraichnan's model of turbulent advection, the functional renormalization group [53] reproduces the first-order results for the anomalous exponents derived some twenty-five years earlier within various perturbative approaches [54].…”

Section: The New Nontrivial Fixed Pointmentioning

confidence: 87%

See 1 more Smart Citation

The Kardar–Parisi–Zhang model of a random kinetic growth: effects of a randomly moving medium

Antonov¹,

Kakin²,

Lebedev³

2019

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The effects of a randomly moving environment on a randomly growing interface are studied by the field theoretic renormalization group analysis. The kinetic growth of an interface (kinetic roughening) is described by the Kardar-Parisi-Zhang stochastic differential equation while the velocity field of the moving medium is modelled by the Navier-Stokes equation with an external random force. It is found that the large-scale, long-time (infrared) asymptotic behavior of the system is divided into four nonequilibrium universality classes related to the four types of the renormalization group equations fixed points. In addition to the previously established regimes of asymptotic behavior (ordinary diffusion, ordinary kinetic growth process, and passively advected scalar field), a new nontrivial regime is found. The fixed point coordinates, their regions of stability and the critical dimensions related to the critical exponents (e.g. roughness exponent) are calculated to the first order of the expansion in ε = 2 − d where d is a space dimension (one-loop approximation) or exactly. The new regime possesses a feature typical to the the Kardar-Parisi-Zhang model: the fixed point corresponding to the regime cannot be reached from a physical starting point. Thus, physical interpretation is elusive.

show abstract

Section: Discussionmentioning

confidence: 58%

Section: The New Nontrivial Fixed Pointmentioning

confidence: 87%

The Kardar–Parisi–Zhang model of a random kinetic growth: effects of a randomly moving medium

Antonov¹,

Kakin²,

Lebedev³

2019

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…It is possible that the crossed contribution (75) turns out to be proportional to the uncrossed one (73), and thus vanishes, at least in some specific wave-vector configurations, but we have not been able to prove it. If this were case, this would imply that there is no intermittency in the direct cascade of 2D turbulence at equal times.…”

Section: A Logarithmic Corrections Assuming No Intermittencymentioning

confidence: 82%

Stationary, isotropic and homogeneous two-dimensional turbulence: a first non-perturbative renormalization group approach

Tarpin¹,

Canet²,

Pagani³

et al. 2019

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We study the statistical properties of stationary, isotropic and homogeneous turbulence in twodimensional (2D) flows, focusing on the direct cascade, that is on wave-numbers large compared to the integral scale, where both energy and enstrophy are provided to the fluid. Our starting point is the 2D Navier-Stokes equation in the presence of a stochastic forcing, or more precisely the associated field theory. We unveil two extended symmetries of the Navier-Stokes (NS) action which were not identified yet, one related to time-dependent (or time-gauged) shifts of the response fields and existing in both 2D and 3D, and the other to time-gauged rotations and specific to 2D flows. We derive the corresponding Ward identities, and exploit them within the non-perturbative renormalization group formalism, and the large wave-number expansion scheme developed in [Phys.Fluids 30, 055102 (2018)]. We consider the flow equation for a generalized n-point correlation function, and calculate its leading order term in the large wave-number expansion. At this order, the resulting flow equation can be closed exactly. We solve the fixed point equation for the 2-point function, which yields its explicit time dependence, for both small and large time delays in the stationary turbulent state. On the other hand, at equal times, the leading order term vanishes, so we compute the next-to-leading order term. We find that the flow equations for simultaneous npoint correlation functions are not fully constrained by the set of extended symmetries, and discuss the consequences. * leonie.canet@grenoble.cnrs.fr forcing [16][17][18]. We refer the reader to reviews on 2D turbulence for a more exhaustive account [1, 2,8,19].However, the complete characterization of the statistical properties of 2D turbulence remains a fundamental quest. In particular, the previous results concentrate on the structure functions, which are equal-time quantities, but the time dependence of velocity or vorticity correlations is also of fundamental interest. In this respect, recent theoretical works have shown that the time dependence of correlation (and response) functions could be calculated within the Non-Perturbative (also named functional) Renormalisation Group (NPRG) formalism [20,21]. This framework allows one to compute statistical properties of turbulence from "first principles", in the sense that it is based on the forced NS equation and does not require phenomenological inputs [22]. It was exploited in 3D to obtain the exact time dependence of n-point generalized velocity correlation functions at leading order at large wave-numbers at non-equal times [21]. The case of equal times is much more involved and its complete analysis in 3D is still lacking.The purpose of this paper is to use the NPRG formalism to investigate 2D turbulence.The outcome is three-fold. We identify two new extended symmetries of the 2D NS action and derive the associated Ward identities. At leading order in wave-numbers, we show that the flow equation for a generic n-point correlation functi...

show abstract

“…The field theory of fields Φ(x) ∈ L 2 (R d+1 ) determined by the action functional (3) is UV divergent [14,17]. To derive quantitative predictions for correlation functions the theory should be renormalized using the standard method of ǫ-expansion, used in quantum field theory and the theory of phase transitions [13,23]. The difference from standard quantum field theory renormalization consists in the role of ǫ: in hydrodynamic theory it turns to be the spectral parameter of the stirring force rather than the deviation from the dimension of the space-time.…”

Section: Quantum Field Theory Approach To Statistical Hydrodynamicsmentioning

confidence: 99%

Renormalization of viscosity in wavelet-based model of turbulence

2018

View full text Add to dashboard Cite

Statistical theory of turbulence in viscid incompressible fluid, described by the Navier-Stokes equation driven by random force, is reformulated in terms of scale-dependent fields ua(x), defined as wavelet-coefficients of the velocity field u taken at point x with the resolution a. Applying quantum field theory approach of stochastic hydrodynamics to the generating functional of random fields ua(x), we have shown the velocity field correlators ua 1 (x1) . . . ua n (xn) to be finite by construction for the random stirring force acting at prescribed large scale L. The study is performed in d = 3 dimension. Since there are no divergences, regularization is not required, and the renormalization group invariance becomes merely a symmetry that relates velocity fluctuations of different scales in terms of the Kolmogorov-Richardson picture of turbulence development. The integration over the scale arguments is performed from the external scale L down to the observation scale A, which lies in Kolmogorov range l ≪ A ≪ L. Our oversimplified model is full dissipative: interaction between scales is provided only locally by the gradient vertex (u∇)u, neglecting any effects or parity violation that might be responsible for energy backscatter. The corrections to viscosity and the pair velocity correlator are calculated in one-loop approximation. This gives the dependence of turbulent viscosity on observation scale and describes the scale dependence of the velocity field correlations.

show abstract

Turbulent mixing of a critical fluid: The non-perturbative renormalization

Cited by 7 publications

References 24 publications

The Kardar–Parisi–Zhang model of a random kinetic growth: effects of a randomly moving medium

The Kardar–Parisi–Zhang model of a random kinetic growth: effects of a randomly moving medium

Stationary, isotropic and homogeneous two-dimensional turbulence: a first non-perturbative renormalization group approach

Renormalization of viscosity in wavelet-based model of turbulence

Contact Info

Product

Resources

About