### Abstract

An algebraic preclosure theory for the Reynolds stress 〈u′u′〉 is developed based on a smoothing approximation which compares the space-time relaxation of a convective-diffusive Green's function with the space-time relaxation of turbulent correlations. The formal preclosure theory relates the Reynolds stress to three distinct statistical properties of the flow: (1) a relaxation time τ_{R} associated with the temporal structure of the turbulence; (2) the spatial gradient of the mean field; and (3) a prestress correlation related to fluctuations in the instantaneous Reynolds stress and the pressure field. Closure occurs by using an isotropic model for the prestress. For simple shear flows, the theory predicts the existence of a nonzero primary normal stress difference and an eddy viscosity coefficient which depends on the temporal relaxation of the turbulent structure and a characteristic time scale associated with the mean field. The asymptotic state of homogeneously sheared turbulence shows that τ_{R}S ∼ 1, where S represents the mean shear rate. The Reynolds stress model and a set of recalibrated k-∈ transport equations predict that the relaxation of homogeneously sheared turbulence to an asymptotic state requires development distances larger than 20 ×〈u_{z}〉(0)/S, a theoretical result consistent with experimental observations.

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

Pages (from-to) | 645-653 |

Number of pages | 9 |

Journal | Physics of Fluids |

Volume | 10 |

Issue number | 3 |

State | Published - Mar 1998 |

### Profile

### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes
- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*10*(3), 645-653.

**An algebraic preclosure theory for the Reynolds stress.** / Parks, S. M.; Weispfennig, K.; Petty, C. A.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol 10, no. 3, pp. 645-653.

}

TY - JOUR

T1 - An algebraic preclosure theory for the Reynolds stress

AU - Parks,S. M.

AU - Weispfennig,K.

AU - Petty,C. A.

PY - 1998/3

Y1 - 1998/3

N2 - An algebraic preclosure theory for the Reynolds stress 〈u′u′〉 is developed based on a smoothing approximation which compares the space-time relaxation of a convective-diffusive Green's function with the space-time relaxation of turbulent correlations. The formal preclosure theory relates the Reynolds stress to three distinct statistical properties of the flow: (1) a relaxation time τR associated with the temporal structure of the turbulence; (2) the spatial gradient of the mean field; and (3) a prestress correlation related to fluctuations in the instantaneous Reynolds stress and the pressure field. Closure occurs by using an isotropic model for the prestress. For simple shear flows, the theory predicts the existence of a nonzero primary normal stress difference and an eddy viscosity coefficient which depends on the temporal relaxation of the turbulent structure and a characteristic time scale associated with the mean field. The asymptotic state of homogeneously sheared turbulence shows that τRS ∼ 1, where S represents the mean shear rate. The Reynolds stress model and a set of recalibrated k-∈ transport equations predict that the relaxation of homogeneously sheared turbulence to an asymptotic state requires development distances larger than 20 ×〈uz〉(0)/S, a theoretical result consistent with experimental observations.

AB - An algebraic preclosure theory for the Reynolds stress 〈u′u′〉 is developed based on a smoothing approximation which compares the space-time relaxation of a convective-diffusive Green's function with the space-time relaxation of turbulent correlations. The formal preclosure theory relates the Reynolds stress to three distinct statistical properties of the flow: (1) a relaxation time τR associated with the temporal structure of the turbulence; (2) the spatial gradient of the mean field; and (3) a prestress correlation related to fluctuations in the instantaneous Reynolds stress and the pressure field. Closure occurs by using an isotropic model for the prestress. For simple shear flows, the theory predicts the existence of a nonzero primary normal stress difference and an eddy viscosity coefficient which depends on the temporal relaxation of the turbulent structure and a characteristic time scale associated with the mean field. The asymptotic state of homogeneously sheared turbulence shows that τRS ∼ 1, where S represents the mean shear rate. The Reynolds stress model and a set of recalibrated k-∈ transport equations predict that the relaxation of homogeneously sheared turbulence to an asymptotic state requires development distances larger than 20 ×〈uz〉(0)/S, a theoretical result consistent with experimental observations.

UR - http://www.scopus.com/inward/record.url?scp=0004527598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0004527598&partnerID=8YFLogxK

M3 - Article

VL - 10

SP - 645

EP - 653

JO - Physics of Fluids

T2 - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 3

ER -