# A new approach to turbulent transport of a mean scalar

@article{Blackman2003ANA, title={A new approach to turbulent transport of a mean scalar}, author={Eric G. Blackman and George B. Field}, journal={Physics of Fluids}, year={2003}, volume={15}, pages={3251-3254} }

We develop a simple mean field approach to the transport of a passive scalar for which the fundamental equation is a second order differential equation in the transported quantity, not a first order equation. Triple correlations are included, as they must be for any realistic description of turbulence. No correlation time enters the theory, only an eddy turnover time. The approach is simpler than standard approaches which incorporate triple correlations, but more realistic than Gaussian or… Expand

#### 23 Citations

Turbulent front speed in the Fisher equation: dependence on Damköhler number.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2011

By comparing with direct numerical simulations, it is found that the effective correlation time is much shorter than for nonreacting flows, and the nonlinearity of the reaction term is found to make the front speed slightly faster. Expand

Strong nonlocality variations in a spherical mean-field dynamo

- Physics
- 2018

To explain the large-scale magnetic field of the Sun and other bodies, mean-field dynamo theory is commonly applied where one solves the averaged equations for the mean magnetic field. However, the… Expand

A model of the entropy flux and Reynolds stress in turbulent convection

- Physics
- 2010

We propose a closure model for the transport of entropy and momentum in astrophysical turbulence, intended for application to rotating stellar convective regions. Our closure model is first presented… Expand

Turbulent diffusion with rotation or magnetic fields

- Physics
- 2009

The turbulent diffusion tensor describing the evolution of the mean concentration of a passive scalar is investigated for non-helically forced turbulence in the presence of rotation or a magnetic… Expand

Non-Fickian diffusion and tau approximation from numerical turbulence

- Physics
- 2004

Evidence for non-Fickian diffusion of a passive scalar is presented using direct simulations of homogeneous isotropic turbulence. The results compare favorably with an explicitly time-dependent… Expand

Advances in Theory and Simulations of Large-Scale Dynamos

- Physics
- 2009

Recent analytical and computational advances in the theory of large-scale dynamos are reviewed. The importance of the magnetic helicity constraint is apparent even without invoking mean-field theory.… Expand

Mean-field closure parameters for passive scalar turbulence

- Physics
- 2011

Direct numerical simulations (DNSs) of isotropically forced homogeneous stationary turbulence with an imposed passive scalar concentration gradient are compared with an analytical closure model whi… Expand

Stellar mixing length theory with entropy rain

- Physics
- 2015

The effects of a non-gradient flux term originating from the motion of convective elements with entropy perturbations of either sign are investigated and incorporated into a modified version of… Expand

Influence of a coronal envelope as a free boundary to global convective dynamo simulations

- Physics
- 2015

We explore the effects of an outer stably stratified coronal envelope on rotating turbulent convection, differential rotation, and large-scale dynamo action in spherical wedge models of the Sun. We… Expand

#### References

SHOWING 1-10 OF 21 REFERENCES

New dynamical mean-field dynamo theory and closure approach.

- Physics, Medicine
- Physical review letters
- 2002

We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, E. We show that the difference… Expand

Mean-field theory for a passive scalar advected by a turbulent velocity field with a random renewal time.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2001

The important role of the statistics of the field of Lagrangian trajectories in turbulent transport of a passive scalar, in a random velocity field with a finite correlation time, is demonstrated. Expand

Analytical theories of turbulence

- Physics
- 1970

This paper surveys the current state of analytical attempts at a theory of turbulence. The formulation of the problem in terms of moments is discussed. The difficulty posed by the closure problem is… Expand

A hyperbolic equation for turbulent diffusion

- Mathematics
- 2000

A hyperbolic equation, analogous to the telegrapher's equation in one dimension, is introduced to describe turbulent diffusion of a passive additive in a turbulent flow. The predictions of this… Expand

Mathematical models with exact renormalization for turbulent transport

- Mathematics, Physics
- 1990

AbstractThe advection-diffusion of a passive scalar by incompressible velocity fields which admit a statistical description and involve a continuous range of excited spatial and/or temporal scales is… Expand

Particles and fields in fluid turbulence

- Physics
- 2001

The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to… Expand

Nonlinear α-Effect in Dynamo Theory

- Physics
- 1999

The standard two-scale theory of the dynamo coefficient α in incompressible isotropic helical MHD turbulence is extended to include nonlinear effects of , the large-scale magnetic field. We express α… Expand

Self-excitation of a nonlinear scalar field in a random medium.

- Physics, Medicine
- Proceedings of the National Academy of Sciences of the United States of America
- 1987

The evolution in time of a scalar field under the influence of a random potential and diffusion is discussed: high, persistent peaks of the field exist against the background of a smooth field distribution and these widely spaced peaks may make a major contribution to the average characteristics ofThe field. Expand

The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence

- Physics
- 2000

A numerical model of isotropic homogeneous turbulence with helical forcing is investigated. The resulting flow, which is essentially the prototype of the α2 dynamo of mean field dynamo theory,… Expand

A non‐Fickian diffusion equation

- Physics
- 1991

A non‐Fickian diffusion equation, which differs from the usual (Fickian) diffusion equation by having an additional, second‐order derivative term in time, is considered to describe the dynamics of a… Expand