Zonal jets and anisotropic turbulence in natural and laboratory flows

Systematic studies of barotropic two-dimensional (2D) turbulence on β-plane and on the surface of a rotating sphere have consistently revealed the zonation, or generation of zonal jets, and the emergence of a strongly anisotropic kinetic energy spectrum. For the zonal modes, a steep spectral distribution, E(k) = C_Z (Ω/R)² k^-5, has been established, where C_Z is a non-dimensional coefficient, Ω is the angular velocity, and R is the radius of the sphere, respectively. For all other, non-zonal modes, the classical, Kolmogorov-Batchelor-Kraichnan, -5/3 spectral law is preserved. A parameter range in which the flow regime with the anisotropic (-5, -5/3) spectrum can develop has been identified.

Natural rotating flows with β-effect, strong spatial anisotropy (caused by the geometrical constraints, stable stratification, rotation, etc.), and small Burger number are good candidates for realization of this flow regime on large scales. Recent experiments (Read et al., GRL, 2004) using the Coriolis turntable in Grenoble with the topographic β-effect have confirmed the mechanism of zonation and both spectral laws, -5/3 and -5. Spectral analysis of zonal flows on the outer planets also confirms the development of a strongly anisotropic spectrum with the -5 law for the zonal component. The available data is not sufficient to estimate the non-zonal spectrum.

Recent eddy-permitting simulations of general oceanic circulation have revealed the presence of systems of narrow zonal jets throughout all major oceans. Analysis of the circulation patterns points to strong spectral anisotropization and the establishment of the -5/3 and -5 spectral laws for non-zonal and zonal components thus confirming the existence of the new flow regime in the terrestrial oceans. The evidence of the presence of narrow alternating zonal jets in the ocean has also emerged from several long-term monitoring studies conducted throughout various cross-sections of the global ocean.

The non-dimensional coefficient C_Z in the -5 spectral law was found to be invariant, C_Z ≈ 0.5, in a variety of simulated and natural flows.