### Abstract

The Reynolds-averaged Navier-Stokes (RANS)-equation for constant property Newtonian fluids is an exact, albeit unclosed, first-order moment equation for the mean velocity field. The RANS-equation and the Reynolds-averaged continuity equation together with a model for the Reynolds stress provide a set of closed equations that govern the behavior of the mean velocity and mean pressure fields. In this turbulent mixing and beyond (TMB) paper, the key ideas related to a recently developed universal closure for the normalized Reynolds (NR)-stress are reviewed. The new approach relates the NR-stress to four characteristic time scales: a turbulent time scale, a viscous time scale, a time scale related to the mean field velocity gradient and a time scale associated with a rigid body frame-of-reference. The theory stems from an analysis of the Navier-Stokes equation and is formulated as a universal non-negative mapping of the NR-stress into itself. Consequently, all solutions of the NR-stress equation are non-negative dyadic-valued linear operators regardless of the class of benchmark flows used to determine closure parameters. The new closure model predicts that the Coriolis acceleration causes an anisotropic re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity in rotating homogeneous decay.

Original language | English (US) |
---|---|

Article number | 014052 |

Journal | Physica Scripta |

Volume | 88 |

Issue number | T155 |

DOIs | |

State | Published - Jul 2013 |

### Profile

### ASJC Scopus subject areas

- Condensed Matter Physics
- Atomic and Molecular Physics, and Optics
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Physica Scripta*,

*88*(T155), [014052]. DOI: 10.1088/0031-8949/2013/T155/014052

**The URAPS closure for the normalized Reynolds stress.** / Koppula, Karuna S.; Muthu, Satish; Bénard, André; Petty, Charles A.

Research output: Contribution to journal › Article

*Physica Scripta*, vol 88, no. T155, 014052. DOI: 10.1088/0031-8949/2013/T155/014052

}

TY - JOUR

T1 - The URAPS closure for the normalized Reynolds stress

AU - Koppula,Karuna S.

AU - Muthu,Satish

AU - Bénard,André

AU - Petty,Charles A.

PY - 2013/7

Y1 - 2013/7

N2 - The Reynolds-averaged Navier-Stokes (RANS)-equation for constant property Newtonian fluids is an exact, albeit unclosed, first-order moment equation for the mean velocity field. The RANS-equation and the Reynolds-averaged continuity equation together with a model for the Reynolds stress provide a set of closed equations that govern the behavior of the mean velocity and mean pressure fields. In this turbulent mixing and beyond (TMB) paper, the key ideas related to a recently developed universal closure for the normalized Reynolds (NR)-stress are reviewed. The new approach relates the NR-stress to four characteristic time scales: a turbulent time scale, a viscous time scale, a time scale related to the mean field velocity gradient and a time scale associated with a rigid body frame-of-reference. The theory stems from an analysis of the Navier-Stokes equation and is formulated as a universal non-negative mapping of the NR-stress into itself. Consequently, all solutions of the NR-stress equation are non-negative dyadic-valued linear operators regardless of the class of benchmark flows used to determine closure parameters. The new closure model predicts that the Coriolis acceleration causes an anisotropic re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity in rotating homogeneous decay.

AB - The Reynolds-averaged Navier-Stokes (RANS)-equation for constant property Newtonian fluids is an exact, albeit unclosed, first-order moment equation for the mean velocity field. The RANS-equation and the Reynolds-averaged continuity equation together with a model for the Reynolds stress provide a set of closed equations that govern the behavior of the mean velocity and mean pressure fields. In this turbulent mixing and beyond (TMB) paper, the key ideas related to a recently developed universal closure for the normalized Reynolds (NR)-stress are reviewed. The new approach relates the NR-stress to four characteristic time scales: a turbulent time scale, a viscous time scale, a time scale related to the mean field velocity gradient and a time scale associated with a rigid body frame-of-reference. The theory stems from an analysis of the Navier-Stokes equation and is formulated as a universal non-negative mapping of the NR-stress into itself. Consequently, all solutions of the NR-stress equation are non-negative dyadic-valued linear operators regardless of the class of benchmark flows used to determine closure parameters. The new closure model predicts that the Coriolis acceleration causes an anisotropic re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity in rotating homogeneous decay.

UR - http://www.scopus.com/inward/record.url?scp=84880342721&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880342721&partnerID=8YFLogxK

U2 - 10.1088/0031-8949/2013/T155/014052

DO - 10.1088/0031-8949/2013/T155/014052

M3 - Article

VL - 88

JO - Physica Scripta

T2 - Physica Scripta

JF - Physica Scripta

SN - 0031-8949

IS - T155

M1 - 014052

ER -