Large-distance and long-time properties of a randomly stirred fluid

  title={Large-distance and long-time properties of a randomly stirred fluid},
  author={Dieter Forster and David R. Nelson and Michael J. Stephen},
  journal={Physical Review A},
Dynamic renormalization-group methods are used to study the large-distance, long-time behavior of velocity correlations generated by the Navier-Stokes equations for a randomly stirred, incompressible fluid. Different models are defined, corresponding to a variety of Gaussian random forces. One of the models describes a fluid near thermal equilibrium, and gives rise to the usual long-time tail phenomena. Apart from simplifying the derivation of the latter, our methods clearly establish their… 

Figures from this paper

Renormalization-group analysis for the infrared properties of a randomly stirred binary fluid

We study the large-scale long-time properties of turbulent motion in a symmetric miscible binary fluid, driven by random stirring fields with correlations and corresponding to the modified

Renormalization of viscosity in wavelet-based model of turbulence

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 $\mathbf{u}_a(x)$,

Long time, large scale properties of the noisy driven-diffusion equation

We study the driven-diffusion equation, describing the dynamics of density fluctuations δρ(x→, t) in powders or traffic flows. We have performed quite detailed numerical simulations of this equation

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

The effects of a randomly moving environment on a randomly growing interface are studied by the field theoretic renormalization group. The kinetic roughening of an interface is described by the

Universal Reynolds Number of Transition and Derivation of Turbulent Models

Renormalization or coarse-graining applied to basic equations governing multi -scale phenomena, leading to effective equations for large-scale properties is often called model-building. Unlike fluids

Effects of mixing and stirring on the critical behaviour

Stochastic dynamics of a nonconserved scalar order parameter near its critical point, subject to random stirring and mixing, is studied using the field-theoretic renormalization group. The stirring

Field theory of the inverse cascade in two-dimensional turbulence.

  • J. Mayo
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
The zero-friction fluctuation-dissipation theorem (FDT) is derived from a generalized time-reversal symmetry and implies zero anomalous dimension for the velocity even when friction is present, so the Kolmogorov scaling of the inverse cascade cannot be explained by any RG fixed point.

Dynamics of three-dimensional turbulence from Navier-Stokes equations

〈(δru)〉, which acts as the coupling constant for scale-toscale interactions. This description can be generalized by introducing “structure functions” of order n, Sn = 〈(δru) 〉, which allow one to

Random interface growth in a random environment: Renormalization group analysis of a simple model

We study the effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modeled by the well-known

Comments on the quasi-normal Markovian approximation for fully-developed turbulence

In a recent paper, Tatsumi, Kida & Mizushima (1978) have made a numerical study of the quasi-normal Markovian (QNM) equation for homogeneous isotropic incompressible turbulence at Reynolds numbers R