Exploration of the Cusp Behavior of the RNG Eddy Viscosity Near the Cutoff Wavenumber

Abstract

The renormalization group (RNG) theory has been used to derive the cutoff-dependent subgrid eddy viscosity (Yakhot and Orszag, 1986). Here, the possibility of deriving the cusp for wavenumbers near the cutoff is investigated. It is explained why the cusp does not appear at lowest order in the RNG analysis of the Navier Stokes equations, and why previously proposed derivations of the cusp using RNG lead to mathematically or physically unreasonable results. However, the cusp may be derived from the lowest-order RNG equation for the energy spectrum using the RNG eddy damping. This energy equation is equivalent to the EDQNM model energy equation with a theoretically derived Kolmogorov constant. Renormalization group theory, Eddy viscosity, Vorticity equation.

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Document Details

Document Type
Technical Report
Publication Date
Dec 31, 1991
Accession Number
ADA271107

Entities

People

  • D. Carati
  • F. Waleffe
  • L. M. Smith

Organizations

  • Princeton University

Tags

DTIC Thesaurus Topics

  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Elimination
  • Equations
  • Frequency
  • Invariance
  • Large Eddy Simulation
  • Linearity
  • Mechanical Properties
  • Navier Stokes Equations
  • Physics
  • Reynolds Number
  • Spectra
  • Turbulence
  • Two Dimensional
  • Viscosity

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Mechanics and Fluid Dynamics.