Anomalous exponents in the rapid-change model of the passive scalar advection in the order ${\epsilon }^3$

Abstract

Field theoretic renormalization group is applied to the Kraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance $<\mathbf{v}(t,\mathbf{x})\mathbf{v}(t^{\prime },\mathbf{x})>-<\mathbf{v}(t,\mathbf{x})\mathbf{v}(t^{\prime },{\mathbf{x}}^{\prime })>\propto \delta (t-t^{\prime })|\mathbf{x}-{\mathbf{x}}^{\prime }{|}^{\epsilon }$. Inertial-range anomalous exponents, related to the scaling dimensions of tensor composite operators built of the scalar gradients, are calculated to the order ${\epsilon }^3$ of the $\epsilon$ expansion. The nature and the convergence of the $\epsilon$ expansion in the models of turbulence is are briefly discussed.

4 pages; REVTeX source with 3 postscript figures

Cited by in corpus (26)

• Particles and fields in fluid turbulence
• Fully developed isotropic turbulence: nonperturbative renormalization group formalism and fixed point solution
• Turbulence with Pressure: Anomalous Scaling of a Passive Vector Field
• Calculation of the anomalous exponents in the rapid-change model of passive scalar advection to order ${\epsilon }^3$
• Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: Two-loop approximation
• Anomalous scaling of a passive scalar advected by the Navier--Stokes velocity field: Two-loop approximation
• Anomalous scaling, nonlocality and anisotropy in a model of the passively advected vector field
• Pressure and intermittency in passive vector turbulence
• Functional renormalisation group for turbulence
• Passive advection of a vector field: Anisotropy, finite correlation time, exact solution and logarithmic corrections to ordinary scaling
• Influence of helicity on anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: Two-loop approximation
• Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: Effects of strong compressibility and large-scale anisotropy
• Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field
• Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time and uniaxial small-scale anisotropy
• Anomalous scaling in magnetohydrodynamic turbulence: Effects of anisotropy and compressibility in the kinematic approximation
• Functional Renormalization Group approach to the Kraichnan model
• Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models
• Anomalous scaling of a passive vector field in $d$ dimensions: Higher-order structure functions
• Turbulent compressible fluid: renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields
• Influence of helicity on scaling regimes in the extended Kraichnan model
• Compressible advection of a passive scalar: Two-loop scaling regimes
• Anomalous scaling in two and three dimensions for a passive vector field advected by a turbulent flow
• Eulerian spatio-temporal correlations in passive scalar turbulence
• Helical turbulent Prandtl number in the $A$ model of passive advection: Two loop approximation
• Spatio-temporal correlation functions in scalar turbulence from functional renormalization group
• Renormalization Group in the Problem of Active Scalar Advection