Anisotropic turbulence and zonal jets in rotating flows with a β-effect

Abstract

Abstract. Numerical studies of small-scale forced, twodimensional 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)=C Z ( /R) 2 n −5 , is established, where C Z =O(1) is a non-dimensional coefficient, is the angular velocity, and R is the radius of the sphere, respectively. For other, non-zonal modes, the classical, Kolmogorov-Batchelor-Kraichnan, − 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 − 5 3 , respectively, in both the slope and the magnitude, as the corresponding spectra in other environmental conditions. The non-dimensional coCorrespondence to: B. Galperin (bgalperin@marine.usf.edu) efficient C Z in the −5 spectral law appears to be invariant, C Z 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.

Saturn Atmospheric Structure and Dynamics

“…Such a correlation is broadly consistent with the notion of an anisotropic upscale turbulent cascade in a geostrophically turbulent flow (e.g. Vasavada and Showman 2005;Galperin et al 2006; section 7.5). However, this phenomenon needs more detailed analysis, particularly with regard to the roles of different scales.…”

“…However, the above interpretation of L R does not carry over to studies with small-scale forcing. Indeed, recent work has clarified that the β effect cannot provide a source of energy dissipation and thus does not act to ``arrest'' the inverse cascade in any meaningful sense (Galperin et al 2006;Sukoriansky et al 2007). Furthermore, in some contexts (known as the "zonostrophic regime"; Galperin et al 2006Galperin et al , 2008, the wave-turbulence transition actually occurs at a wavelength L β ~ (ε/β 3 ) 1/5 (where ε is the small-scale isotropic energy injection rate) which may be significantly smaller than L R (Huang et al 2001;Sukoriansky et al 2007).…”

Turbulence, waves, and jets in a differentially heated rotating annulus experiment

“…Galperin et al 10 discussed the difference between stable and unstable flow regimes within the context of purely 2D barotropic theory. In the stable case, which they called frictionally dominated flow, they argued that Ekman and viscous damping act to damp the jets before they can intensify enough to break the Rayleigh-Kuo criterion.…”

“…Galperin et al 10 noted further properties of these idealized systems, including the importance of the large-scale damping mechanism in determining the steady-state jet structure. Finally, a recent experiment at the large-scale Coriolis facility 11 also reproduced ␤-plane multiple jet formation in a convectively driven laboratory flow.…”

Zonal Flow Regime Changes in a GCM and in a Simple Quasigeostrophic Model: The Role of Stratospheric Dynamics

“…1 of Hartmann and Lo 1998) shows a clear tropospheric double-jet structure in these two months (see also Gallego et al 2005); the origin of this structure is the subject of our investigation. Multiple-jet patterns have been also observed on the major planets, as well as in the rotating, differentially heated annulus (see the review paper by Galperin et al 2006, and references therein). These additional findings reinforce our interest in how this monthly mean feature is sustained in Earth's SH.…”