Abstract
Simulation of geophysical turbulent flows requires a robust and accurate subgrid-scale turbulence modeling. We propose an implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method. To validate this turbulence model, we performed direct numerical simulations of the transition of the three-dimensional Taylor–Green vortex and homogeneous stratified turbulence. Our analysis proves that the implicit turbulence model correctly predicts the turbulence energy budget and the spectral structure of stratified turbulence.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Bouruet-Aubertot, J. Sommeria, and C. Staquet. Stratified turbulence produced by internal wave breaking: Two-dimensional numerical experiments. Dyn. Atmos. Oceans, 23(1–4):357–369, 1996. Stratified flows.
M. E. Brachet, D. Meiron, S. Orszag, B. Nickel, R. Morf, and U. Frisch. Small-scale structure of the Taylor–Green vortex. J. Fluid Mech., 130:411–452, 1983.
M. E. Brachet. Direct simulation of three-dimensional turbulence in the Taylor–Green vortex. Fluid Dynam. Res., 8(1–4):1–8, 1991.
G. Brethouwer, P. Billant, E. Lindborg, and J.-M. Chomaz. Scaling analysis and simulation of strongly stratified turbulent flows. J. Fluid Mech., 585:343–368, 2007.
J.-P. Chollet and M. Lesieur. Parameterization of small scales of three-dimensional isotropic turbulence utilizing spectral closures. Journal of the Atmospheric Sciences, 38(12):2747–2757, 1981.
C. Cot. Equatorial mesoscale wind and temperature fluctuations in the lower atmosphere. J. Geophys. Res., 106(D2):1523–1532, 2001.
E. M. Dewan. Stratospheric wave spectra resembling turbulence. Science, 204(4395):832–835, 1979.
A. Dörnbrack. Turbulent mixing by breaking gravity waves. J. Fluid Mech., 375:113–141, 1998.
D. C. Fritts, L. Wang, J. Werne, T. Lund, and K. Wan. Gravity wave instability dynamics at high Reynolds numbers. Part I: Wave field evolution at large amplitudes and high frequencies. J. Atmos. Sci., 66(5):1126–1148, 2009.
K. S. Gage. Evidence for a k −5/3 law inertial range in mesoscale two-dimensional turbulence. J. Atmos. Sci., 36:1950–1954, October 1979.
J. R. Herring and O. Métais. Numerical experiments in forced stably stratified turbulence. J. Fluid Mech., 202(1):97–115, 1989.
S. Hickel, N. A. Adams, and J. A. Domaradzki. An adaptive local deconvolution method for implicit LES. J. Comput. Phys., 213:413–436, 2006.
S. Hickel, N. A. Adams, and N. N. Mansour. Implicit subgrid-scale modeling for large-eddy simulation of passive scalar mixing. Phys. Fluids, 19:095102, 2007.
S. Hickel, T. Kempe, and N. A. Adams. Implicit large-eddy simulation applied to turbulent channel flow with periodic constrictions. Theor. Comput. Fluid Dyn., 22:227–242, 2008.
H.-J. Kaltenbach, T. Gerz, and U. Schumann. Large-eddy simulation of homogeneous turbulence and diffusion in stably stratified shear flow. J. Fluid Mech., 280(1):1–40, 1994.
R. H. Kraichnan. Inertial ranges in two-dimensional turbulence. Phys. Fluids, 10(7):1417–1423, 1967.
J.-P. Laval, J. C. McWilliams, and B. Dubrulle. Forced stratified turbulence: Successive transitions with Reynolds number. Phys. Rev. E, 68(3):036308, September 2003.
D. K. Lilly. Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci., 40(3):749–761, 1983.
D. K. Lilly, G. Bassett, K. Droegemeier, and P. Bartello. Stratified turbulence in the atmospheric mesoscales. Theor. Comput. Fluid Dyn., 11:139–153, 1998.
E. Lindborg and G. Brethouwer. Stratified turbulence forced in rotational and divergent modes. J. Fluid Mech., 586:83–108, 2007.
E. Lindborg. The energy cascade in a strongly stratified fluid. J. Fluid Mech., 550(1):207–242, 2006.
O. Métais and J. R. Herring. Numerical simulations of freely evolving turbulence in stably stratified fluids. J. Fluid Mech., 202(1):117–148, 1989.
O. Métais and M. Lesieur. Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech., 239:157–194, 1992.
G. D. Nastrom and K. S. Gage. A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci., 42(9):950–960, 1985.
J. J. Riley and S. M. de Bruyn Kops. Dynamics of turbulence strongly influenced by buoyancy. Phys. Fluids, 15(7):2047–2059, 2003.
C.-W. Shu. Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput., 9(6):1073–1084, 1988.
L. M. Smith and F. Waleffe. Generation of slow large scales in forced rotating stratified turbulence. J. Fluid Mech., 451(1):145–168, 2002.
C. Staquet and F. S. Godeferd. Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 1. Flow energetics. J. Fluid Mech., 360:295–340, 1998.
H. A. van der Vorst. Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 13(2):631–644, 1992.
T. E. van Zandt. A universal spectrum of buoyancy waves in the atmosphere. Geophys. Res. Lett., 9(5):575–578, 1982.
M. L. Waite and P. Bartello. Stratified turbulence dominated by vortical motion. J. Fluid Mech., 517:281–308, 2004.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Remmler, S., Hickel, S. (2012). Direct Numerical Simulation and Implicit Large Eddy Simulation of Stratified Turbulence. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering '11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23869-7_38
Download citation
DOI: https://doi.org/10.1007/978-3-642-23869-7_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23868-0
Online ISBN: 978-3-642-23869-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)