### Abstract

Original language | English |
---|---|

Article number | 066304 |

Number of pages | 12 |

Journal | Physical Review E |

Volume | 82 |

Issue number | 6 |

DOIs | |

Publication status | Published - 3 Dec 2010 |

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### Keywords

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

### Cite this

*Physical Review E*,

*82*(6), [066304]. https://doi.org/10.1103/PhysRevE.82.066304

}

*Physical Review E*, vol. 82, no. 6, 066304. https://doi.org/10.1103/PhysRevE.82.066304

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Reexamination of the infrared properties of randomly stirred hydrodynamics

AU - Berera, A.

AU - Yoffe, S. R.

PY - 2010/12/3

Y1 - 2010/12/3

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(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.

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

KW - renormalized viscosity

KW - infrared properties

KW - stirred hydrodynamics

U2 - 10.1103/PhysRevE.82.066304

DO - 10.1103/PhysRevE.82.066304

M3 - Article

VL - 82

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 6

M1 - 066304

ER -