Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-11-15
Physics
Condensed Matter
Statistical Mechanics
16 pages, 6 figures
Scientific paper
Dynamic renormalization group (RG) methods were originally used by Forster, Nelson and Stephen (FNS) to study the large-scale behaviour of randomly-stirred, incompressible fluids governed by the Navier-Stokes equations. Similar calculations using a variety of methods have been performed since, but have led to a discrepancy in results. In this paper, we carefully re-examine in $d$-dimensions the approaches used to calculate the renormalized viscosity increment and, by including an additional constraint which is neglected in many procedures, conclude that the original result of FNS is correct. By explicitly using step functions to control the domain of integration, we calculate a non-zero correction caused by boundary terms which cannot be ignored. We then go on to analyze how the noise renormalization, absent in many approaches, contributes an ${\mathcal O}(k^2)$ correction to the force autocorrelation and show conditions for this to be taken as a renormalization of the noise coefficient. Following this, we discuss the applicability of this RG procedure to the calculation of the inertial range properties of fluid turbulence.
Berera Arjun
Yoffe Samuel
No associations
LandOfFree
Re-examination of the infra-red properties of randomly stirred hydrodynamics 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 Re-examination of the infra-red properties of randomly stirred hydrodynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Re-examination of the infra-red properties of randomly stirred hydrodynamics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-299540