Fluctuating hydrodynamics and turbulence in a rotating fluid: Universal properties

Details Fluctuating hydrodynamics and turbulence in a rotating fluid: Universal properties Fluctuating hydrodynamics and turbulence in a rotating fluid: Universal properties

2011-12-23

arxiv.org/abs/1112.5520v1

Physics

Condensed Matter

Statistical Mechanics

24 pages in preprint format; accepted for publication in Phys. Rev. E (2011)

Scientific paper

We analyze the statistical properties of three-dimensional ($3d$) turbulence in a rotating fluid. To this end we introduce a generating functional to study the statistical properties of the velocity field $\bf v$. We obtain the master equation from the Navier-Stokes equation in a rotating frame and thence a set of exact hierarchical equations for the velocity structure functions for arbitrary angular velocity $\mathbf \Omega$. In particular we obtain the {\em differential forms} for the analogs of the well-known von Karman-Howarth relation for $3d$ fluid turbulence. We examine their behavior in the limit of large rotation. Our results clearly suggest dissimilar statistical behavior and scaling along directions parallel and perpendicular to $\mathbf \Omega$. The hierarchical relations yield strong evidence that the nature of the flows for large rotation is not identical to pure two-dimensional flows. To complement these results, by using an effective model in the small-$\Omega$ limit, within a one-loop approximation, we show that the equal-time correlation of the velocity components parallel to $\mathbf \Omega$ displays Kolmogorov scaling $q^{-5/3}$, where as for all other components, the equal-time correlators scale as $q^{-3}$ in the inertial range where $\bf q$ is a wavevector in $3d$. Our results are generally testable in experiments and/or direct numerical simulations of the Navier-Stokes equation in a rotating frame.

Affiliated with

Also associated with

No associations

Rating

Fluctuating hydrodynamics and turbulence in a rotating fluid: Universal properties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fluctuating hydrodynamics and turbulence in a rotating fluid: Universal properties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fluctuating hydrodynamics and turbulence in a rotating fluid: Universal properties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-191950