Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-06-26T15:09:57.974Z Has data issue: false hasContentIssue false

Information decay and the predictability of turbulent flows

Published online by Cambridge University Press:  20 April 2006

George F. Carnevale
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307
Greg Holloway
Affiliation:
Department of Oceanography, University of Washington, Seattle, Washington 98195

Abstract

A measure of predictability that has many superior features compared to currently used measures is introduced. Through statistical theory it is demonstrated that in inviscid truncated flow this new predictability measure increases monotonically in time while all initial information about the system decays. Under the influence of forcing and viscosity the behaviour of this measure is shown always to satisfy intuitive expectations.

Type
Research Article
Copyright
© 1982 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Basdevant, C., Legras, B., Sadourny, R. & Béland, M. 1981 A study of barotropic model flows: intermittency, waves and predictability. Preprint, Laboratoire de Meteorologie Dynamique, Paris.
Carnevale, G. F. 1979 Statistical dynamics of nonequilibrium fluid systems. Ph.D. thesis, Harvard University.
Carnevale, G. F. 1981 Entropy evolution in macroscopic two-dimensional fluids. J. Fluid Mech. (submitted).
Carnevale, G. F., Frisch, U. & Salmon, R. 1981 J. Phys. A: Math. & Gen. 14, 17011718.
Charney, J. G., Fleagle, R. G., Lally, V. E., Riehl, H. & Wark, D. Q. 1966 Bull. Am. Met. Soc. 47, 200220.
Cook, I. 1974 J. Plasma Phys. 12, 501507.
Edwards, S. F. 1964 J. Fluid Mech. 18, 239273.
Edwards, S. F. & McComb, W. D. 1969 J. Phys. A: Gen. Phys. 2, 157171.
Fournier, J. D. & Frisch, U. 1978 Phys. Rev. A17, 747762.
Frederiksen, J. S. & Sawford, B. L. 1980 J. Atmos. Sci. 37, 717732.
Hasselmann, K. 1966 Rev. Geophys. 4, 132.
Herring, J. R. 1965 Phys. Fluids 8, 22192225.
Holloway, G. & Hendershott, M. C. 1977 J. Fluid Mech. 69, 673688.
Holloway, G. 1981 Effects of Rossby wave propagation on the predictability of equivalent barotropic motion. Preprint, University of Washington, Seattle.
Kraichnan, R. H. 1959 J. Fluid Mech. 5, 497543.
Kraichnan, R. H. 1970 Phys. Fluids 13, 569575.
Leith, C. E. 1971 J. Atmos. Sci. 28, 145161.
Leith, C. E. & Kraichnan, R. H. 1972 J. Atmos. Sci. 29, 10411058.
Lilly, D. K. 1972 Geophys. Fluid Dyn. 4, 128.
Lorenz, E. 1963 Trans. N.Y. Acad. Sci., Ser. II, 25, 409432.
Lorenz, E. 1969 Tellus 21, 289307.
Montgomery, D. 1976 Phys. Fluids 19, 802810.
Orszag, S. A. 1970 J. Fluid Mech. 41, 363386.
Prigogine, I. 1962 Nonequilibrium Statistical Mechanics. Wiley-Interscience.
Rhines, P. B. 1975 J. Fluid Mech. 69, 417443.
Rose, H. A. & Sulem, P. L. 1978 J. de Physique 39, 441484.
Salmon, R., Holloway, G. & Hendershott, M. C. 1976 J. Fluid Mech. 75, 691703.
Smagorinsky, J. 1969 Bull. Am. Met. Soc. 50, 286311.
Thompson, P. D. 1957 Tellus 9, 275295.
Thompson, P. D. 1972 J. Fluid Mech. 55, 711771.