The URAPS closure for the normalized Reynolds stress

Karuna S. Koppula, Satish Muthu, André Bénard, Charles A. Petty

Research output: Contribution to journalArticle

  • 1 Citations

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.

LanguageEnglish (US)
Article number014052
JournalPhysica Scripta
Volume88
Issue numberT155
DOIs
StatePublished - Jul 2013

Profile

Reynolds Stress
Reynolds stress
closures
Closure
Time Scales
Reynolds Equation
Navier-Stokes equation
Navier-Stokes Equations
Mean Field
velocity distribution
Non-negative
Turbulent Mixing
linear operators
Moment Equations
dyadics
turbulent mixing
Newtonian fluids
Continuity Equation
continuity equation
Newtonian Fluid

ASJC Scopus subject areas

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

Cite this

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

In: Physica Scripta, Vol. 88, No. T155, 014052, 07.2013.

Research output: Contribution to journalArticle

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