Equatorial Zonal Jet Formation through the Barotropic Instability of Low-Frequency Mixed Rossby–Gravity Waves, Equilibration by Inertial Instability, and Transition to Superrotation

Abstract

Abstract Depth-dependent barotropic instability of short mixed Rossby–gravity (MRG) waves is proposed as a mechanism for the formation of equatorial zonal jets. High-resolution primitive equation simulations show that a single MRG wave of very short zonal wavelength and small to moderate amplitude is unstable and leads to the development of a largely barotropic, zonally symmetric flow, featuring a westward jet at the equator and extra-equatorial jets alternating in direction with latitude. At higher but still moderate amplitude, westward flow still prevails at the equator at depths of maximum horizontal velocity amplitude in the initial wave, but the long-term equilibrated state can also feature eastward “superrotating” jets at the equator near the depths of zero horizontal velocity in the initial wave. The formation of the superrotating jets in the simulations is found to be sensitive to the inclusion of the nontraditional Coriolis force in the equations of motion. A linear theory is used to demonstrate the existence of exponentially growing horizontally nondivergent perturbations with a dominant zonally symmetric zonal velocity component. An argument for the sense and positioning of the jets relative to the equator is given in terms of inertial instability and the meridional mixing of planetary vorticity by the small zonal-scale components of the linearly unstable modes. In the long time evolution of the flow, if the amplitude of the westward equatorial jet becomes too great, zonally symmetric inertial instability limits the growth of the jets, and inertial adjustment leads to the homogenization of potential vorticity in latitude and depth around the equator.