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We report an analog laboratory study of planetary-scale turbulence and jet formation. A rotating annulus was cooled and heated at its inner and outer walls, respectively, causing baroclinic instability to develop in the fluid inside. At high rotation rates and low temperature differences, the flow became chaotic and ultimately fully turbulent. The inclusion of sloping top and bottom boundaries caused turbulenteddies to behave like planetary waves at large scales, and eddy interaction with the zonal flow then led to the formation of several alternating jets at mid-depth. The jets did not scale with the Rhines length, and spectral analysis of the flow indicated a distinct separation between jets and eddies in wavenumber space, with direct energy transfer occurring nonlocally between them. Our results suggest that the traditional “turbulent cascade” picture of zonal jet formation may be an inappropriate one in the geophysically important case of large-scale flows forced by differential solar heating., Engineering and Applied Sciences

The banded organization of clouds and zonal winds in the atmospheres of the outer planets has long fascinated observers. Several recent studies in the theory and idealized modeling of geostrophic turbulence have suggested possible explanations for the emergence of such organized patterns, typically involving highly anisotropic exchanges of kinetic energy and vorticity within the dissipationless inertial ranges of turbulent flows dominated (at least at large scales) by ensembles of propagating Rossby waves. The results from an attempt to reproduce such conditions in the laboratory are presented here. Achievement of a distinct inertial range turns out to require an experiment on the largest feasible scale. Deep, rotating convection on small horizontal scales was induced by gently and continuously spraying dense, salty water onto the free surface of the 13-m-diameter cylindrical tank on the Coriolis platform in Grenoble, France. A “planetary vorticity gradient” or “β effect” was obtained by use of a conically sloping bottom and the whole tank rotated at angular speeds up to 0.15 rad s−1. Over a period of several hours, a highly barotropic, zonally banded large-scale flow pattern was seen to emerge with up to 5–6 narrow, alternating, zonally aligned jets across the tank, indicating the development of an anisotropic field of geostrophic turbulence. Using particle image velocimetry (PIV) techniques, zonal jets are shown to have arisen from nonlinear interactions between barotropic eddies on a scale comparable to either a Rhines or “frictional” wavelength, which scales roughly as (β/Urms)−1/2. This resulted in an anisotropic kinetic energy spectrum with a significantly steeper slope with wavenumber k for the zonal flow than for the nonzonal eddies, which largely follows the classical Kolmogorov k−5/3 inertial range. Potential vorticity fields show evidence of Rossby wave breaking and the presence of a “hyperstaircase” with radius, indicating instantaneous flows that are supercritical with respect to the Rayleigh–Kuo instability criterion and in a state of “barotropic adjustment.” The implications of these results are discussed in light of zonal jets observed in planetary atmospheres and, most recently, in the terrestrial oceans., Engineering and Applied Sciences

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, \(-\frac{5}{3}\) 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 \(-\frac{5}{3}\), 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, \(C_Z{\simeq}0.5\), in a variety of simulated and natural flows. This paper provides a brief review of the zonostrophic regime. The review includes the discussion of the physical nature, basic mechanisms, scaling laws and universality of this regime. A parameter range conducive to its establishment is identified, and collation of laboratory and naturally occurring flows is presented through which the zonostrophic regime manifests itself in the real world., Engineering and Applied Sciences