A Theory for the Formation and Equilibration of Equatorial Deep Jets from Stratified Turbulence

Abstract:

Equatorial deep jets (EDJs) are persistent, equatorially-trapped zonal jets found between ~500-2000m depth within one degree of the equator in all ocean basins. EDJs have a baroclinic vertical structure characterized by ‘stacked’ eastward and westward jets oscillating in the vertical with a wavelength of ~500m and amplitudes on the order of 10 cm/s. The spatial structure of the EDJs is strikingly different from that of other geophysical zonal jets such as ocean striations and Jupiter’s banded winds, which are not equatorially trapped and are often considered to be essentially barotropic. It is now well-understood that barotropic zonal jets emerge spontaneously from an instability of differentially-rotating turbulence (Constantinou et al. 2014). In contrast, existing theories for EDJs have been based on quite different dynamics, such as interference of equatorially-trapped waves (Wunsch 1977, McCreary 1984) and instability of mixed Rossby-gravity waves (Hua et al. 2008, Eden et al. 2008). In this work, we propose a new theory for the formation and maintenance of EDJs in which EDJs develop spontaneously from stratified turbulence. Using the stochastically-forced Boussinesq model (Smith 2001, Smith & Waleffe 2002), we show that stacked jets form spontaneously from turbulence due to spectrally-nonlocal interactions between internal gravity waves and the zonal mean flow, and that jet formation can be captured using the mean-field (or ‘quasilinear’) approximation to the dynamics. Using mean field dynamics and an associated second-order statistical closure theory (stochastic structural stability theory, Farrell & Ioannou 2003), we explain how the vertical scale of the EDJs is selected, as well as the role of differential rotation in determining their meridional structure.