Reexamination of the infrared properties of randomly stirred hydrodynamics

A. Berera, S. R. Yoffe

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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(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.
LanguageEnglish
Article number066304
Number of pages12
JournalPhysical Review E
Volume82
Issue number6
DOIs
Publication statusPublished - 3 Dec 2010

Fingerprint

Renormalization
Renormalization Group
Hydrodynamics
Infrared
hydrodynamics
Calculate
step functions
Step function
renormalization group methods
incompressible fluids
Autocorrelation
Incompressible Fluid
Navier-Stokes equation
Increment
autocorrelation
Discrepancy
Turbulence
Viscosity
Navier-Stokes Equations
turbulence

Keywords

  • incompressible fluids
  • Navier-Stokes equation
  • renormalized viscosity
  • infrared properties
  • stirred hydrodynamics

Cite this

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Reexamination of the infrared properties of randomly stirred hydrodynamics. / Berera, A.; Yoffe, S. R.

In: Physical Review E, Vol. 82, No. 6, 066304, 03.12.2010.

Research output: Contribution to journalArticle

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AU - Yoffe, S. R.

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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(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.

KW - incompressible fluids

KW - Navier-Stokes equation

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KW - infrared properties

KW - stirred hydrodynamics

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