The Statistical State Dynamics of Stacked Jet Formation from Stratified Turbulence

Equatorial deep jets (EDJs) are slowly-varying, equatorially-trapped zonal jets found between ~500-2000 m depth within one degree of the equator in all ocean basins. The spatial structure of the EDJs is that of ‘stacked’ eastward and westward jets, reversing sign with depth with a wavelength of ~500 m and amplitudes of ~10 cm/s. EDJs have been persistently identified in observations for nearly 40 years, yet understanding how EDJs are formed and maintained against dissipation remains a theoretical puzzle. Early theoretical work identified EDJs with interference patterns of wind-driven equatorially-trapped waves (Wunsch 1977, McCreary 1984). More recently, numerical studies (e.g., Ascani et al. 2015) have suggested that EDJs are maintained by their interactions with the faster-timescale ocean variability. This second physical mechanism, sometimes called rectification of the wave field, resembles the mechanism responsible for the formation of large-scale banded zonal jets on Jupiter (Constantinou et al. 2014). The methods of statistical state dynamics (SSD) have previously been used to show that Jupiter’s zonal jets form as an instability of the underlying statistical state of homogeneous turbulence produced by internal convection. In this work, we apply the tools of SSD to a simplified model of the EDJ system at the equator: two-dimensional, non-rotating, stratified Boussinesq turbulence driven by stochastic forcing. Stochastic forcing is included to produce a background spectrum of variability (i.e., gravity waves) while remaining agnostic regarding the physical mechanisms producing this spectrum. We show that stacked jets form spontaneously from the background turbulence due to an instability resulting from spectrally-nonlocal wave-mean flow interaction. At finite amplitude, the jets are maintained against dissipation by harvesting the energy of the internal wave spectrum. For strong forcing, the jets grow and equilibrate near the Ri=1/4 stability boundary. Near the bifurcation point at which the jets first emerge, the vertical scale of the jets is influenced by both the wavenumber spectrum of the background turbulence and the buoyancy frequency of the fluid. These results are confirmed by an analytical stability analysis of the SSD system linearized about the homogeneous turbulent state.