Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 13 1 2006 10.5194/npg-13-83-2006 http://www.nonlin-processes-geophys.net/13/83/2006/ http://www.nonlin-processes-geophys.net/13/83/2006/npg-13-83-2006.html http://www.nonlin-processes-geophys.net/13/83/2006/npg-13-83-2006.pdf 83 98 2006-04-04 Anisotropic turbulence and zonal jets in rotating flows with a β-effect B. Galperin bgalperin@marine.usf.edu S. Sukoriansky N. Dikovskaya P. L. Read Y. H. Yamazaki R. Wordsworth College of Marine Science, University of South Florida, St. Petersburg, FL 33701, USA Department of Mechanical Engineering/Perlstone Center for Aeronautical Engineering Studies, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel Atmospheric, Oceanic & Planetary Physics, Department of Physics, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK Numerical studies of small-scale forced, two-dimensional turbulent flows on the surface of a rotating sphere have revealed strong large-scale anisotropization that culminates in the emergence of quasi-steady sets of alternating zonal jets, or zonation. The kinetic energy spectrum of such flows also becomes strongly anisotropic. For the zonal modes, a steep spectral distribution, E(n)=CZ (Ω/R)2 n-5, is established, where CZ=O(1) is a non-dimensional coefficient, Ω is the angular velocity, and R is the radius of the sphere, respectively. For other, non-zonal modes, the classical, Kolmogorov-Batchelor-Kraichnan, <IMG WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0" src="http://www.nonlin-processes-geophys.net/13/83/2006/npg-13-83-2006-5.gif" ALT="$-\frac{5}{3}$"> spectral law is preserved. This flow regime, referred to as a zonostrophic regime, appears to have wide applicability to large-scale planetary and terrestrial circulations as long as those are characterized by strong rotation, vertically stable stratification and small Burger numbers. The well-known manifestations of this regime are the banded disks of the outer planets of our Solar System. Relatively less known examples are systems of narrow, subsurface, alternating zonal jets throughout all major oceans discovered in state-of-the-art, eddy-permitting simulations of the general oceanic circulation. Furthermore, laboratory experiments recently conducted using the Coriolis turntable have basically confirmed that the lateral gradient of ''planetary vorticity'' (emulated via the topographic β-effect) is the primary cause of the zonation and that the latter is entwined with the development of the strongly anisotropic kinetic energy spectrum that tends to attain the same zonal and non-zonal distributions, −5 and <IMG WIDTH="27" HEIGHT="35" ALIGN="MIDDLE" BORDER="0" src="http://www.nonlin-processes-geophys.net/13/83/2006/npg-13-83-2006-5.gif" ALT="$-\frac{5}{3}$">, respectively, in both the slope and the magnitude, as the corresponding spectra in other environmental conditions. The non-dimensional coefficient CZ in the −5 spectral law appears to be invariant,  <IMG WIDTH="59" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" src="http://www.nonlin-processes-geophys.net/13/83/2006/npg-13-83-2006-9.gif" ALT="$C_Z{\simeq}0.5$">, in a variety of simulated and natural flows. 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