Advances in Geosciences www.adv-geosci.net 1680-7340 1680-7359 15 Topics in modern geophysical fluid dynamics 2008 10.5194/adgeo-15-17-2008 http://www.adv-geosci.net/15/17/2008/ http://www.adv-geosci.net/15/17/2008/adgeo-15-17-2008.html http://www.adv-geosci.net/15/17/2008/adgeo-15-17-2008.pdf 17 22 2008-03-12 The energy spectrum in a barotropic atmosphere M. V. Kurgansky kurgansk@udec.cl Department of Geophysics, Faculty of Physical and Mathematical Sciences, University of Concepción, Chile on leave from: A. M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia In a forced-dissipative barotropic model of the atmosphere on a spherical planet, by following mathematical techniques in (Thompson, P. D.: The equilibrium energy spectrum of randomly forced two-dimensional turbulence, Journal of the Atmospheric Sciences, 30, 1593–1598, 1973) but applying them in a novel context of the discrete spectrum on a rotating sphere, the "minus 2" energy spectrum for wavenumbers much greater than a characteristic wavenumber of the baroclinic forcing has been obtained if the forcing is taken in the simplest and most fundamental form. Some observation-based atmospheric kinetic energy spectra, with their slopes lying between "minus 2" and "minus 3" laws, are discussed from the perspective of the deduced "minus 2" energy spectrum. Batchelor, G. K.: Computation of the energy spectrum in homogeneous two-dimensional turbulence, Phys. Fluids, 12, Suppl II, 233–239, 1969. Baroud, C. N., Plapp, B. B., She, Z.-S., and Swinney, H. L.: Anomalous self-similarity in a turbulent rapidly rotating fluid, Phys. Rev. Lett., 88, 11, 114501, doi:10.1103/PhysRevLett.88.114501, 2002. Boer, G. J. and Shepherd, T. G.: Large-scale two-dimensional turbulence in the atmosphere, J. Atmos. Sci., 40, 164–184, 1983. Burgers, J. M.: Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion, Hon. Ned. Acad. Wet. Vern. Eerste Sectie, D1, XVII(2), 1–53, 1939. Charney, J. G.: Geostrophic turbulence, J. Atmos. Sci., 28, 1087–1095, 1971. Dymnikov, V. P. and Filatov, A. N.: Mathematics of Climate Modeling, Birkhäuser, Boston, 1997. Frederiksen, J. S. and Sawford, B. L.: Statistical dynamics of two-dimensional inviscid flow on a sphere, J. Atmos. Sci., 37, 717–732, 1980. Frederiksen, J. S., Dix, M. R., and Kepert, S. M.: Systematic energy errors and the tendency toward canonical distribution in atmospheric circulation models, J. Atmos. Sci., 53, 887–904, 1996. Frederiksen, J. S., Dix, M. R., and Davies, A. G.: On effects of closure-based eddy diffusion on the climate and spectra of a GCM, Tellus, 55A, 31–44, 2003. Gavrilin, B. L., Mirabel, A. P., and Monin, A. S.: On the energy spectrum of synoptic processes, Izv. Akad. Nauk. SSSR, Fiz. Atmos. Oceana, 8, 483–493, 1972. Kraichnan, R. H.: Inertial ranges in two-dimensional turbulence, Phys. Fluids, 10, 1417–1423, 1967. Lambert, S. J.: A diagnostic study of global energy and enstrophy fluxes and spectra, Tellus, 33, 411–414, 1981. Leith, C. H.: Diffusion approximation for two-dimensional turbulence, Phys. Fluids, 11, 671–673, 1968. Lorenz, E. N.: The predictability of a flow which contains many scales of motion, Tellus, 21, 289–307, 1969. Lorenz, E. N.: The Essence of Chaos, University of Washington Press, Seattle, 1994. Lynch, P. and Verkley, W.: Energy spectra from entropy principle, Proc. IUGG XXIV General Assembly – IAMAS, Abstract 5209, Perugia, Italy, 2–13 July 2007, available at: http://www.iugg2007perugia.it/webbook/, 2007. Monin, A. S.: Theoretical Geophysical Fluid Dynamics, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1990. Thompson, P. D.: The equilibrium energy spectrum of randomly forced two-dimensional turbulence, J. Atmos. Sci., 30, 1593–1598, 1973. Tran, C. V. and Shepherd, T. G: Constraints on the spectral distribution of energy and enstrophy dissipation in forced two-dimensional turbulence, Physica D, 165, 199–212, 2002. Trenberth, K. E. and Solomon, A.: Implications of global atmospheric spatial spectra for processing and displaying data, J. Climate, 6, 531–545, 1993. Zhou, Y.: A phenomenological treatment of rotating turbulence, Phys. Fluids, 7, 8, 2092–2094, 1995.