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

B. Galperin, S. Sukoriansky, N. Dikovskaya, P. L. Read, Y. H. Yamazaki, R. Wordsworth

Research output: Contribution to journalReview articlepeer-review

94 Scopus citations


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)=CZ(ω/R)2n-5, is established, where CZ=O(1) is a non-dimensional coef-ficient, 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 planet 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 -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 co-efficient CZ in the-5 spectral law appears to be invariant, CZ'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.

Original languageEnglish
Pages (from-to)83-98
Number of pages16
JournalNonlinear Processes in Geophysics
Issue number1
StatePublished - 1 Dec 2006

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Geophysics
  • Geochemistry and Petrology


Dive into the research topics of 'Anisotropic turbulence and zonal jets in rotating flows with a β-effect'. Together they form a unique fingerprint.

Cite this