Inhomogeneity and anisotropy in planetary turbulence: zonostrophy and beyond?

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• Peter Leonard Read (University of Oxford)
• Thursday 06 January 2022, 15:30-16:30
• Seminar Room 1, Newton Institute.

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TURW01 - Turbulence: where do we stand and where are we heading?

Theoretical approaches to understanding and quantifying the properties of turbulence have traditionally started with assumptions of homogeneity and isotropy of flow structure and/or forcing and dissipation. But realistic flows seldom satisfy such assumptions. In a planetary atmosphere, flows are forced primarily by buoyancy contrasts on both large and small scales, leading to both large scale overturning and localised patches of convective turbulence that are far from homogeneous. Flow structure is also strongly influenced by stratification and background rotation, leading to highly anisotropic behaviours in the form of layered structures and strong zonal jets. In an attempt to understand the influence of rotation on large-scale planetary turbulence, the concept of the zonostrophic regime was proposed some 15 years ago by Galperin and Sukoriansky. This concept takes direct account of the non-local upscale transfers of kinetic energy by large-scale waves, leading to a pattern of zonally symmetric jets with a characteristic universal spatial spectrum. The zonal flows coexist with a non-axisymmetric turbulent flow that participates in a more conventional Kolmogorov-Kraichnan local inverse energy cascade on scales larger than the principal forcing of barotropic modes. Observations and models of atmospheres, oceans and planetary interiors, and also some laboratory experiments, are partly consistent with the zonostrophic regime, but with some marked discrepancies. However, the zonostrophic concept only applies to the barotropic component of the flow, leaving unaddressed the role of stratification in both the forcing of large-scale turbulence and the structure and characteristics of scales smaller than the forcing scale. Observations indicate the presence of a direct energy cascade at small scales, even at scales expected to be anisotropic due to either rotation or stratification. Elucidating the nature of this transition from inverse to direct cascade at decreasing scales is one of the key challenges to our understanding of planetary turbulence in atmospheres, oceans and planetary interiors. 

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