Spectral and hyper eddy viscosity in high-Reynolds-number turbulence


Journal Article

For the purpose of studying the spectral properties of energy transfer between large and small scales in high-Reynolds-number turbulence, we measure the longitudinal subgrid-scale (SGS) dissipation spectrum, defined as the co-spectrum of the SGS stress and filtered strain-rate tensors. An array of four closely spaced X-wire probes enables us to approximate a two-dimensional box filter by averaging over different probe locations (cross-stream filtering) and in time (streamwise filtering using Taylor's hypothesis). We analyse data taken at the centreline of a cylinder wake at Reynolds numbers up to R(λ) ~ 450. Using the assumption of local isotropy, the longitudinal SGS stress and filtered strain-rate co-spectrum is transformed into a radial co-spectrum, which allows us to evaluate the spectral eddy viscosity, v(k,k(Δ)). In agreement with classical two-point closure predictions, for graded filters, the spectral eddy viscosity deduced from the box-filtered data decreases near the filter wavenumber k(Δ). When using a spectral cutoff filter in the streamwise direction (with a box-filter in the cross-stream direction) a cusp behaviour near the filter scale is observed. In physical space, certain features of a wavenumber-dependent eddy viscosity can be approximated by a combination of a regular and a hyper-viscosity term. A hyper-viscous term is also suggested from considering equilibrium between production and SGS dissipation of resolved enstrophy. Assuming local isotropy, the dimensionless coefficient of the hyper-viscous term can be related to the skewness coefficient of filtered velocity gradients. The skewness is measured from the X-wire array and from direct numerical simulation of isotropic turbulence. The results show that the hyper-viscosity coefficient is negative for graded filters and positive for spectral filters. These trends are in agreement with the spectral eddy viscosity measured directly from the SGS stress-strain rate co-spectrum. The results provide significant support, now at high Reynolds numbers, for the ability of classical two-point closures to predict general trends of mean energy transfer in locally isotropic turbulence.

Full Text

Duke Authors

Cited Authors

  • Cerutti, S; Meneveau, C; Knio, OM

Published Date

  • January 1, 2000

Published In

Volume / Issue

  • 421 /

Start / End Page

  • 307 - 338

International Standard Serial Number (ISSN)

  • 0022-1120

Digital Object Identifier (DOI)

  • 10.1017/S0022112000001671

Citation Source

  • Scopus