Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-07-05T17:54:05.307Z Has data issue: false hasContentIssue false
  • English
  • Français

Entropy maximization tendency in topographic turbulence

Published online by Cambridge University Press:  26 April 2006

Jieping Zou  and
Greg Holloway
Jieping Zou
Affiliation:
Institute of Ocean Sciences, PO Box 6000, Sidney, BC V8L 4B2, Canada
Greg Holloway
Affiliation:
Institute of Ocean Sciences, PO Box 6000, Sidney, BC V8L 4B2, Canada
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 263 , 25 March 1994 , pp. 361 - 374
Copyright
© 1994 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. & Sadourny, R. 1975 Ergodic properties of inviscid truncated models of two-dimensional incompressible flows. J. Fluid Mech. 69, 673–688.Google Scholar
Bretherton, F. P. & Haidvogel, D. B. 1976 Two-dimensional turbulence above topography. J. Fluid Mech. 78, 129–154.Google Scholar
Carnevale, G. F. 1982 Statistical features of the evolution of two-dimensional turbulence. J. Fluid Mech. 122, 143–153.Google Scholar
Carnevale, G. F. & Frederiksen, J. S. 1987 Nonlinear stability and statistical mechanics of flow over topography. J. Fluid Mech. 175, 157–181.Google Scholar
Carnevale, G. F., Frisch, U. & Salmon, R. 1981 H theorems in statistical fluid dynamics. J. Phys. A: Math. Gen. 14, 1701–1718.Google Scholar
Carnevale, G. F. & Holloway, G. 1982 Information decay and predictability of turbulent flows. J. Fluid Mech. 116, 115–121.Google Scholar
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 577–592. New York: Am. Inst. Phys.
Cummins, P. F. 1992 Inertial gyres in decaying and forced geostrophic turbulence. J. Mar. Res. 50, 545–566.Google Scholar
Cummins, P. F. & Holloway, G. 1994 On eddy-topographic stress representation. J. Phys. Oceangr. (in press).Google Scholar
Fox, D. G. & Orszag, S. A. 1973 Inviscid dynamics of two-dimensional turbulence. Phys. Fluids 16, 169–171.Google Scholar
Griffa, A. & Salmon, R. 1989 Wind-driven ocean circulation and equilibrium statistical mechanics. J. Mar. Res. 47, 457–492.Google Scholar
Frederiksen, J. S. & Bell, R. C. 1983 Statistical dynamics of internal gravity waves-turbulence. Geophys. Astrophys. Fluid Dyn. 26, 257–301.Google Scholar
Frederiksen, J. S. & Bell, R. C. 1984 Energy and entropy evolution of interacting internal gravity waves and turbulence. Geophys. Astrophys. Fluid Dyn. 28, 171–203.Google Scholar
Frederiksen, J. S. & Sawford, B. L. 1980 Statistical dynamics of two-dimensional inviscid flow on a sphere. J. Atmos. Sci. 37, 717–732.Google Scholar
Hart, J. E. 1979 Barotropic quasi-geostrophic flow over anisotropic mountains. J. Atmos. Sci. 36, 1736–1746.Google Scholar
Herring, J. R. 1977 On the statistical theory of two-dimensional topographic turbulence. J. Atmos. Sci. 34, 1731–1750.Google Scholar
Holloway, G. 1978 A spectral theory of nonlinear barotropic motion above irregular topography. J. Phys. Oceangr. 8, 414–427.Google Scholar
Holloway, G. 1986 Comment on Fofonoff's mode. Geophys. Astrophys. Fluid Dyn. 37, 165–169.Google Scholar
Holloway, G. 1992 Representing topographic stress in large scale ocean models. J. Phys. Oceangr. 22, 1033–1046.Google Scholar
Kaneda, Y., Gotoh, T. & Bekki, N. 1989 Dynamics of inviscid truncated model of two-dimensional turbulence shear flow. Phys. Fluid 1 (7), 1225–1234.Google Scholar
Kells, L. C. & Orszag, S. A. 1978 Randomness of low-order models of two-dimensional inviscid dynamics. Phys. Fluids 21, 162–168.Google Scholar
Kraichnan, R. H. 1975 Statistical dynamics of two-dimensional flow. J. Fluid Mech. 67, 155–175.Google Scholar
Leith, C. E. 1984 Minimum enstrophy vortices. Phys. Fluids 27, 1388–1395.Google Scholar
Miller, J. 1990 Statistical mechanics of Euler equation in two-dimensions. Phys. Rev. Lett. 65, 2137–2140.Google Scholar
Miller, J., Weichman, P. B. & Cross, M. C. 1992 Statistical mechanics, Euler's equation and Jupiter's red spot. Phys. Rev. A 45, 2328–2359.Google Scholar
Orszag, S. A. 1971 Numerical simulation of incompressible flows with simple boundaries. I. Galerkin (spectral) representation. Stud. in Appl. Maths 4, 293–327.Google Scholar
Robert, R. & Sommeria, J. 1991 Statistical equilibrium states for two-dimensional flows. J. Fluid Mech. 229, 291–310.Google Scholar
Salmon, R., Holloway, G. & Hendershott, M. C. 1976 The equilibrium statistical mechanics of simple quasi-geostrophic models. J. Fluid Mech. 75, 691–703.Google Scholar
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, 289–302.Google Scholar
Wang, J. & Vallis, G. 1993 Emergence of Fofonoff states in inviscid and viscous ocean circulation models. J. Mar. Res. (in press).Google Scholar
Zou, J. & Holloway, G. 1993 Forced-dissipated statistical equilibrium of large scale quasigeostrophic flows over random topography. Geophys. Astrophys. Fluid Dyn. 69, 55–75.Google Scholar