Skip to main content Accessibility help
×
Home

Entropy maximization tendency in topographic turbulence

  • Jieping Zou (a1) and Greg Holloway (a1)

Abstract

Numerical simulations of geostrophic turbulence above topography are used to compare (a) nonlinear generation of system entropy, S, (b) selective damping of enstrophy and (c) development of vorticity–topography correlation. In the damped cases, S initially increases, approaching a quasi-equilibrium (maximum S subject to the instantaneous, though decaying, energy and enstrophy). When strongly scale-selective damping is applied, onset of the vorticity–topography correlation follows the timescales for enstrophy decay. During the period of decay, it is shown that nonlinear interaction continues to generate S, offsetting in part the loss of S to explicit damping.

Copyright

References

Hide All
Basdevant, C. & Sadourny, R. 1975 Ergodic properties of inviscid truncated models of two-dimensional incompressible flows. J. Fluid Mech. 69, 673688.
Bretherton, F. P. & Haidvogel, D. B. 1976 Two-dimensional turbulence above topography. J. Fluid Mech. 78, 129154.
Carnevale, G. F. 1982 Statistical features of the evolution of two-dimensional turbulence. J. Fluid Mech. 122, 143153.
Carnevale, G. F. & Frederiksen, J. S. 1987 Nonlinear stability and statistical mechanics of flow over topography. J. Fluid Mech. 175, 157181.
Carnevale, G. F., Frisch, U. & Salmon, R. 1981 H theorems in statistical fluid dynamics. J. Phys. A: Math. Gen. 14, 17011718.
Carnevale, G. F. & Holloway, G. 1982 Information decay and predictability of turbulent flows. J. Fluid Mech. 116, 115121.
Carnevale, G. F. & Vallis, G. K. 1984 Applications of entropy to predictability theory. In Predictability of Fluid Motions, ed. G. Holloway & B. J. West, pp 577592. New York: Am. Inst. Phys.
Cummins, P. F. 1992 Inertial gyres in decaying and forced geostrophic turbulence. J. Mar. Res. 50, 545566.
Cummins, P. F. & Holloway, G. 1994 On eddy-topographic stress representation. J. Phys. Oceangr. (in press).
Fox, D. G. & Orszag, S. A. 1973 Inviscid dynamics of two-dimensional turbulence. Phys. Fluids 16, 169171.
Griffa, A. & Salmon, R. 1989 Wind-driven ocean circulation and equilibrium statistical mechanics. J. Mar. Res. 47, 457492.
Frederiksen, J. S. & Bell, R. C. 1983 Statistical dynamics of internal gravity waves-turbulence. Geophys. Astrophys. Fluid Dyn. 26, 257301.
Frederiksen, J. S. & Bell, R. C. 1984 Energy and entropy evolution of interacting internal gravity waves and turbulence. Geophys. Astrophys. Fluid Dyn. 28, 171203.
Frederiksen, J. S. & Sawford, B. L. 1980 Statistical dynamics of two-dimensional inviscid flow on a sphere. J. Atmos. Sci. 37, 717732.
Hart, J. E. 1979 Barotropic quasi-geostrophic flow over anisotropic mountains. J. Atmos. Sci. 36, 17361746.
Herring, J. R. 1977 On the statistical theory of two-dimensional topographic turbulence. J. Atmos. Sci. 34, 17311750.
Holloway, G. 1978 A spectral theory of nonlinear barotropic motion above irregular topography. J. Phys. Oceangr. 8, 414427.
Holloway, G. 1986 Comment on Fofonoff's mode. Geophys. Astrophys. Fluid Dyn. 37, 165169.
Holloway, G. 1992 Representing topographic stress in large scale ocean models. J. Phys. Oceangr. 22, 10331046.
Kaneda, Y., Gotoh, T. & Bekki, N. 1989 Dynamics of inviscid truncated model of two-dimensional turbulence shear flow. Phys. Fluid 1 (7), 12251234.
Kells, L. C. & Orszag, S. A. 1978 Randomness of low-order models of two-dimensional inviscid dynamics. Phys. Fluids 21, 162168.
Kraichnan, R. H. 1975 Statistical dynamics of two-dimensional flow. J. Fluid Mech. 67, 155175.
Leith, C. E. 1984 Minimum enstrophy vortices. Phys. Fluids 27, 13881395.
Miller, J. 1990 Statistical mechanics of Euler equation in two-dimensions. Phys. Rev. Lett. 65, 21372140.
Miller, J., Weichman, P. B. & Cross, M. C. 1992 Statistical mechanics, Euler's equation and Jupiter's red spot. Phys. Rev. A 45, 23282359.
Orszag, S. A. 1971 Numerical simulation of incompressible flows with simple boundaries. I. Galerkin (spectral) representation. Stud. in Appl. Maths 4, 293327.
Robert, R. & Sommeria, J. 1991 Statistical equilibrium states for two-dimensional flows. J. Fluid Mech. 229, 291310.
Salmon, R., Holloway, G. & Hendershott, M. C. 1976 The equilibrium statistical mechanics of simple quasi-geostrophic models. J. Fluid Mech. 75, 691703.
Shepherd, T. G. 1987 Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere. J. Fluid Mech. 184, 289302.
Wang, J. & Vallis, G. 1993 Emergence of Fofonoff states in inviscid and viscous ocean circulation models. J. Mar. Res. (in press).
Zou, J. & Holloway, G. 1993 Forced-dissipated statistical equilibrium of large scale quasigeostrophic flows over random topography. Geophys. Astrophys. Fluid Dyn. 69, 5575.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Related content

Powered by UNSILO

Entropy maximization tendency in topographic turbulence

  • Jieping Zou (a1) and Greg Holloway (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.