The structure of zonal jets in shallow water turbulence on the sphere

The large-scale motions of planetary atmospheres and oceans, constrained by strong stable stratification and rapid rotation, are characterized in part by quasi-two dimensional turbulent motion and in part by coherent structures, such as vortices, zonal jets, and low-frequency waves. These motions are intimately linked and understanding their complex and multiscale interactions presents a complex and formidable challenge. Broadly speaking, turbulent motions can be thought of as occurring primarily at small scales and zonal jets and wave motions at large scales. However, turbulence is organized into latitudinal bands by these zonal jets, while the jets themselves are maintained against dissipation by turbulent and wave motions, via eddy momentum fluxes (e.g., McIntyre, 1982; Baldwin et al., 2007, and references therein). Examples of zonal jets include the winter polar night jet in the Earth’s stratosphere and the sub-tropical jet stream (both driven diabatically but intensified by wave/turbulent processes), and, perhaps most famously, the jets responsible for the characteristic banded structure observed on the giant planets. These zonal jets are instrumental in determining the transport of heat, chemical tracers, kinetic energy and angular momentum. Transport is rapid along the jet axis, but is strongly inhibited across the jet axis due to enhanced “Rossby wave elasticity”, the dynamic resiliance of jets to latitudinal displacements, and strong latitudinal shear on the jet flanks. Transport of water vapor within the troposphere, for example, a major influence on climate, is sensitive to the latitudinal position of the atmospheric jet stream. In the stratosphere, details of wave breaking in the vicinity of the polar night jet determine the meridional transport of chemical species involved in ozone chemistry and ultimately determines the rate of ozone recovery (World Meteorological Organization, 2007). On the giant planets, jets separate regions of different trace chemical composition, giving rise to the coloured bands.