An algebraic preclosure theory for the Reynolds stress

S. M. Parks, K. Weispfennig, C. A. Petty

Research output: Contribution to journalArticle

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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 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.

LanguageEnglish (US)
Pages645-653
Number of pages9
JournalPhysics of Fluids
Volume10
Issue number3
StatePublished - Mar 1998

Profile

Reynolds stress
relaxation time
Relaxation time
turbulence
Turbulence
eddy viscosity
pressure distribution
shear flow
smoothing
closures
Shear flow
Green's functions
Green's function
Shear deformation
shear
gradients
Viscosity
coefficients
approximation

ASJC Scopus subject areas

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

Cite this

Parks, S. M., Weispfennig, K., & Petty, C. A. (1998). An algebraic preclosure theory for the Reynolds stress. Physics of Fluids, 10(3), 645-653.

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

In: Physics of Fluids, Vol. 10, No. 3, 03.1998, p. 645-653.

Research output: Contribution to journalArticle

Parks, SM, Weispfennig, K & Petty, CA 1998, 'An algebraic preclosure theory for the Reynolds stress' Physics of Fluids, vol 10, no. 3, pp. 645-653.
Parks, S. M. ; Weispfennig, K. ; Petty, C. A./ An algebraic preclosure theory for the Reynolds stress. In: Physics of Fluids. 1998 ; Vol. 10, No. 3. pp. 645-653
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