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Stochastic parameterization for large eddy simulation of geophysical flows
Author(s):
Jinqiao
Duan;
Balasubramanya
T.
Nadiga
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1187-1196.
MSC (2000):
Primary 65C20, 60H15, 86A10
Posted:
October 27, 2006
MathSciNet review:
2262925
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Abstract:
Recently, stochastic, as opposed to deterministic, parameterizations are being investigated to model the effects of unresolved subgrid scales (SGS) in large eddy simulations (LES) of geophysical flows. We analyse such a stochastic approach in the barotropic vorticity equation to show that (i) if the stochastic parameterization approximates the actual SGS stresses, then the solution of the stochastic LES approximates the ``true" solution at appropriate scale sizes; and that (ii) when the filter scale size approaches zero, the solution of the stochastic LES approaches the true solution.
References:
-
- 1.
- L. Arnold.
Hasselmann's program visited: The analysis of stochasticity in deterministic climate models.
In J.-S. von Storch and P. Imkeller, editors, Stochastic climate models, pages 141-158, Boston, 2001. Birkhäuser. MR 1948294 (2003j:86007) - 2.
- Intergovernmental Panel on Climate Change (IPCC) Report on Climate Change 2001: The Scientific Basis, Section F.6., 2001.
- 3.
- P. S. Berloff. Random-forcing model of the mesoscale oceanic eddies, J. Fluid Mech. 529, 71-95, 2005.
- 4.
- P. S. Berloff, W. Dewar, S. Kravtsov, J. McWilliams and M. Ghil. Ocean eddy dynamics in a coupled ocean-atmosphere model: Diagnostics and parameterization. Preprint, 2005.
- 5.
- S. B. Pope. Turbulent Flows, Chapter 13, Cambridge University Press, 2000. MR 1881598 (2003f:76002)
- 6.
- G. D. Nastrom and K. S. Gage. A Climatology of Atmospheric Wavenumber Spectra of Wind and Temperature Observed by Commercial Aircraft, Journal of the Atmospheric Sciences: Vol. 42, No. 9, pp. 950-960, 1985.
- 7.
- C. Meneveau and J. Katz. Scale-invariance and turbulence models for Large-Eddy Simulation, Ann. Rev. Fluid Mech. 32, 1-32, 2000. MR 1744302 (2000k:76079)
- 8.
- J. Smagorinsky. General circulation experiments with the primitive equations: I. The basic experiment. Mon. Wea. Rev., 91,1963, 99-164.
- 9.
- J. Smagorinsky. Some historical remarks on the use of nonlinear viscosities. In Large Eddy Simulation of Complex Engineering and Geophysical Flows, B. Galperin and S. A. Orszag, Eds., Cambridge University Press, 1993, 3-36. MR 1248380
- 10.
- C. E. Leith. Diffusion approximation for two-dimensional turbulence. Phys. Fluids, 10, 1968, 1409-1416.
- 11.
- C. E. Leith. Stochastic models of chaotic systems. Physica D, 98, 1996, 481-491.
- 12.
- W. R. Holland. The role of mesoscale eddies in the general circulation of the ocean: Numerical experiments using a wind-driven quasi-geostrophic model. J. Phys. Oceanogr., 8, 1978, 363-392.
- 13.
- R. Bleck and D. B. Boudra. Initial testing of a numerical ocean circulation model using a hybrid- (quasi-isopycnic) vertical coordinate. J. Phys. Oceanogr., 11, 1981, 755-770.
- 14.
- A. J. Majda, I. Timofeyev and E. Vanden-Eijnden. Models for stochastic climate prediction, Proc. National Acad. Sci. 96, 1999, 14687-14691. MR 1731439 (2000h:86007)
- 15.
- A. J. Majda, I. Timofeyev and E. Vanden-Eijnden. Systematic Strategies for Stochastic Mode Reduction in Climate, Journal of the Atmospheric Sciences: Vol. 60, No. 14, pp. 1705-1722. MR 2030132 (2004j:86011)
- 16.
- J. R. Herring. Stochastic Modeling of Turbulent Flows. In Stochastic Modeling in Physical Oceanography, A. Adler, B.M. Culler, Eds., Birkhäuser, 1996. MR 1383874 (96k:76061)
- 17.
- R. H. Kraichnan. The structure of isotropic turbulence at very high Reynolds number. J. Fluid Mech. 5, 497-543, 1959. MR 0105963 (21:4697)
- 18.
- A. S. Monin and A. M. Yaglom. Statistical Fluid Mechanics, Vol. 1, The MIT Press, 769 pp., 1975.
- 19.
- L. C. Berselli, G. P. Galdi, T. Iliescu and W. Layton. Mathematical analysis for the rational large eddy simulation model. Math. Models Methods Appl. Sci. 12 (2002), no. 8, 1131-1152. MR 1924604 (2003k:76077)
- 20.
- J. Duan and P. E. Kloeden. Dissipative Quasigeostrophic Motion under Temporally Almost Periodic Forcing, J. Math. Anal. Appl. 236 (1999), 74-85. MR 1702691 (2001j:76115)
- 21.
- D. Blomker, J. Duan and T. Wanner. Enstrophy Dynamics of Stochastically Forced Large-Scale Geophysical Flows. J. Math. Phys., 43 (2002), 2616-2626. MR 1893690 (2003a:76017)
- 22.
- P. Constantin and C. Foias. Navier-Stokes Equations, Univ. of Chicago Press, Chicago, 1988. MR 0972259 (90b:35190)
- 23.
- J. Duan, P. E. Kloeden and B. Schmalfuss. Exponential Stability of the Quasigeostrophic Equation under Random Perturbations. Progress in Probability 49(2000), 241-256. MR 1948299 (2004b:76066)
- 24.
- J. Duan and B. Goldys. Ergodicity of Stochastically Forced Large Scale Geophysical Flows. Inter. J. Math. Math. Sci., 28 (2001), 313-320. MR 1887567 (2002k:37163)
- 25.
- V. P. Dymnikov and A. N. Filatov. Mathematics of Climate Modeling, Birkhäuser, Boston, 1997. MR 1426827 (99k:76058)
- 26.
- T. DelSole and B. F. Farrell. A stochastically excited linear system as a model for quasigeostrophic turbulence: Analytic results for one- and two-layer fluids, J. Atmos. Sci. 52 (1995) 2531-2547.
- 27.
- A. E. Gill. Atmosphere-Ocean Dynamics. Academic Press, New York, 1982.
- 28.
- K. Hasselmann. Stochastic climate models: Part I. Theory, Tellus 28 (1976), 473-485.
- 29.
- M. Kaya and W. Layton. On verification of models of the motion of large eddies in turbulent flows. Differential and Integral Equations 15 (2002), 1395-1407. MR 1920694 (2003f:76059)
- 30.
- B. T. Nadiga, D. Livescu and C.Q. McKay. Stochastic Large Eddy Simulation of Geostrophic Turbulence, Eos. Trans. AGU, 86(18), Jt. Assem. Suppl., Abstract NG23A-09, 2005.
- 31.
- B. T. Nadiga, D. Livescu, and C.Q. McKay. Geophysical Research Abstracts, Vol. 7, 05488, 2005.
- 32.
- R. J. Greatbatch and B. T. Nadiga. Four gyre circulation in a barotropic model with double gyre wind forcing, J. Phys. Ocean., 30 (2000), 1461-1471.
- 33.
- B. Oksendal.
Stochastic Differential Equations. Sixth Ed.,
Springer-Verlag, New York, 2003. MR 2001996 (2004e:60102) - 34.
- J. Pedlosky. Geophysical Fluid Dynamics, Springer-Verlag, 2nd edition, 1987.
- 35.
- B. L. Rozovskii. Stochastic Evolution Equations. Kluwer Academic Publishers, Boston, 1990. MR 1135324 (92k:60136)
- 36.
- R. Temam. Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1988. MR 0953967 (89m:58056)
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Additional Information:
Jinqiao
Duan
Affiliation:
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616
Email:
duan@iit.edu
Balasubramanya
T.
Nadiga
Affiliation:
Los Alamos National Laboratory, MS-B296, Los Alamos, New Mexico 87545
Email:
balu@lanl.gov
DOI:
10.1090/S0002-9939-06-08631-X
PII:
S 0002-9939(06)08631-X
Received by editor(s):
October 30, 2005
Received by editor(s) in revised form:
November 23, 2005
Posted:
October 27, 2006
Additional Notes:
The first author was partly supported by NSF Grants DMS-0209326 & DMS-0542450.
The second author was partly supported by the LDRD program at Los Alamos National Laboratory
Communicated by:
Edward C. Waymire
Copyright of article:
Copyright
2006,
American Mathematical Society
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