On the magnitude of the subgrid scale eddy coefficient

Three-dimensional numerical integrations capable of resolving the energy containing motions at large Reynolds number have tested the nonlinear eddy-viscosity formulation in the two cases when the turbulence is generated by mean shear or by thermal instability. The proportionality constant suggested by Lilly is found to be applicable in the latter case, but a smaller value is found necessary in the presence of mean shear. Spectra of calculated velocity components are shown to deviate from a k5/3 law, as k approaches the grid cutoff wavenumber, in a manner consistent with the application of Reynolds-averaging over grid volumes.

[1]  P. Lax,et al.  Systems of conservation laws , 1960 .

[2]  K. Lilly.  On the application of the eddy viscosity concept in the Inertial sub-range of turbulence , 1966 .

[3]  Douglas K. Lilly,et al.  ON THE COMPUTATIONAL STABILITY OF NUMERICAL SOLUTIONS OF TIME-DEPENDENT NON-LINEAR GEOPHYSICAL FLUID DYNAMICS PROBLEMS , 1965 .

[4]  Gareth P. Williams.  Numerical integration of the three-dimensional Navier-Stokes equations for incompressible flow , 1969, Journal of Fluid Mechanics.

[5]  Donald H. Lenschow,et al.  Concurrent Airplane and Balloon Measurements of Atmospheric Boundary-Layer Structure over a Forest , 1968 .

[6]  C. W. Hirt.  Heuristic stability theory for finite-difference equations☆ , 1968 .

[7]  J. Laufer,et al.  Investigation of turbulent flow in a two-dimensional channel , 1951 .

[8]  J. Deardorff,et al.  A three‐dimensional numerical investigation of the idealized planetary boundary layer , 1970 .

[9]  J. Deardorff,et al.  Lagrangian Statistics from Numerically Integrated Turbulent Shear Flow , 1970 .

[10]  Robert H. Kraichnan,et al.  Dispersion of Particle Pairs in Homogeneous Turbulence , 1966 .

[11]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[12]  K. Lilly.  The representation of small-scale turbulence in numerical simulation experiments , 1966 .

[13]  A. Arakawa.  Computational design for long-term numerical integration of the equations of fluid motion: two-dimen , 1997 .

[14]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[15]  G. Fischer.  A SURVEY OF FINITE-DIFFERENCE APPROXIMATIONS TO THE PRIMITIVE EQUATIONS , 1965 .

[16]  John L. Lumley,et al.  The structure of atmospheric turbulence , 1964 .

[17]  R. W. Stewart,et al.  Turbulence Spectra in the Wind Over Waves , 1963 .

[18]  Joseph Smagorinsky,et al.  Numerical weather analysis and prediction , 1962 .

[19]  J. Deardorff.  A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers , 1970, Journal of Fluid Mechanics.

[20]  Donald H. Lenschow,et al.  Airplane Measurements of Planetary Boundary Layer Structure , 1970 .