TY - JOUR
T1 - Reexamination of the infrared properties of randomly stirred hydrodynamics
AU - Berera, A.
AU - Yoffe, S.R.
N1 - Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2010/12
Y1 - 2010/12
N2 - Dynamic renormalization-group (RG) methods were originally used by Forster, Nelson, and Stephen (FNS) to study the large-scale behavior of randomly stirred incompressible fluids governed by the Navier-Stokes equations. Similar calculations using a variety of methods have been performed but have led to a discrepancy in results. In this paper, we carefully reexamine 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 nonzero correction caused by boundary terms which cannot be ignored. We then go on to analyze how the noise renormalization, which is absent in many approaches, contributes an O (k2) 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.
AB - Dynamic renormalization-group (RG) methods were originally used by Forster, Nelson, and Stephen (FNS) to study the large-scale behavior of randomly stirred incompressible fluids governed by the Navier-Stokes equations. Similar calculations using a variety of methods have been performed but have led to a discrepancy in results. In this paper, we carefully reexamine 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 nonzero correction caused by boundary terms which cannot be ignored. We then go on to analyze how the noise renormalization, which is absent in many approaches, contributes an O (k2) 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.
UR - http://www.scopus.com/inward/record.url?scp=78651392220&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.82.066304
DO - 10.1103/PhysRevE.82.066304
M3 - Article
AN - SCOPUS:78651392220
SN - 1539-3755
VL - 82
JO - Physical Review E
JF - Physical Review E
IS - 6
M1 - 066304
ER -