Inertial nonlinear equilibration of equatorial flows

Abstract

We explore the nature of inertial equilibration of equatorial flows in the presence of mean meridional and vertical shears of the basic state, with oceanic applications in mind. The study is motivated by the observational evidence that the subthermocline equatorial mean circulation displays nearly zero Ertel potential vorticity away from the equator, when taking into account the non-traditional horizontal component of the Earth rotation. This observed state precisely verifies the marginal condition for inertial instability: a linear analysis for the equatorial β-plane confirms that the usual condition of instability, namely that Ertel potential vorticity should be of opposite sign to the vertical Coriolis parameter, remains valid even when the traditional approximation is relaxed. Analytical linear normal modes reveal that a meridional shear of the basic state leads to a vertical stacking of equatorially-trapped zonal flows of alternate signs, with a new centre of symmetry located at the dynamical equator. A vertical shear of the basic state causes a meridional stacking of extra-equatorial zonal flows.In an inviscid framework, a two-dimensional formulation is ill-posed and we resort to non-hydrostatic viscous simulations to determine the nonlinear normal forms of the system. The influence of a small-scale eddy diffusivity and a large-scale Rayleigh damping on the equilibrated vertical scale is determined numerically. The nonlinear equilibration occurs through a steady-state bifurcation from a basic state without jets to another steady state with secondary jets of alternate signs. The final state corresponds to eastward jets located on the geographic equator, while westward jets are located near the dynamical equator. These results are consistent with in situ observations of equatorial deep jets.The analogy between the equatorial meridional shear flow and the cylindrical Couette–Taylor flow with an axial density stratification is detailed. There is a strong similarity in the general symmetries and nonlinear normal forms of the two problems. Similarly to the homogeneous Couette–Taylor flow, the gap width between the two cylinders is important for determining the axial scale of the secondary flow through the Reynolds number. For the equatorial problem, an upper bound for the height scale of inertial jets is such that the corresponding equatorial radius of deformation times √2 fits between the geographic and dynamic equators.One of our main conclusions is that the raisond’être of the observed region of zero Ertel potential vorticity is to facilitate angular momentum exchanges between the two hemispheres and inertial deep jets are the byproducts of this angular momentum mixing.

Influence of the Barotropic Mean Flow on the Width and the Structure of the Atlantic Equatorial Deep Jets

“…This discrepancy may have different reasons: (i) Hua et al (1997) proposed nonlinear effects to broaden the jets; (ii) Greatbatch et al (2012) argued that turbulent isopycnal mixing of momentum reduces the meridional pressure gradient that is necessary to balance the jets and this requires, in the absence of diapycnal mixing, a broader cross-equatorial width; and (iii) the presence of a barotropic mean flow might affect the width and structure of the EDJs, the subject of this paper. Horizontal shear of the mean flow might reduce the meridional gradient of ambient absolute vorticity at the equator that would result in a larger effective equatorial radius of deformation.…”

Seasonal fluctuations in the deep central equatorial Atlantic Ocean: a data–model comparison

“…They are intensified above 2,000 m depth, equatorially trapped between 1.5°N and 1.5°S, seemingly zonally coherent over 10-20°, and they have a vertical scale of about 400-600 m in the Atlantic Ocean (they are associated with baroclinic modes with a mode number greater than 15). The two mechanisms proposed to explain their existence involve Kelvin and Rossby waves of a period greater than 2 years (Leetma and Spain 1981;Johnson and Zhang 2003) or inertial instability (Hua et al 1997;Send et al 2002). Although Boening and Schott (1993) and Gouriou et al (1999) observe a reversal of the jets at opposite seasons (but few years apart), recent analyses suggest that the variability occurs at a longer time scale (Send et al 2002;Johnson and Zhang 2003).…”

Nonlinear double-diffusive intrusions at the equator

“…The y and z-components ν y and ν z of viscosity and the y-component of diffusvity κ y are also assumed to be constant. We allow for a Rayleigh drag term with constant coefficient r following Hua et al (1997) (our numerical code is a slightly modified version of the code used by these authors). Since r does not act preferentially on small scales it is best viewed as representing unresolved large-scale forces maintaining the initial, unstable state.…”

“…Conditions are often favourable for microscale double-diffusive fingering, and mesoscale double-diffusive interleaving instabilities, of the type first described by Stern (1967), as well as inertial (or symmetric) instability, the theory of which goes back to Rayleigh (1916). Both of these mechanisms have been proposed as possible explanations of observed equatorial processes, in particular Richards (1991) extended linear double-diffusive interleaving theory to the equatorial β-plane and Hua et al (1997) proposed inertial instability as an explanation for deep equatorial jets, while Edwards and Richards (1999) developed a combined linear theory of double diffusive-inertial instability for the equatorial β-plane. Richards and Banks (2002), who consider an extensive set of measurements, find that the observed interleaving is consistent with both double-diffusive interleaving and inertial instability.…”

“…The numerical code was based on code written and kindly made available by S. le Gentil, as used by Hua et al (1997). We are indebted to Ray Schmitt and David Walsh for constructive criticism and many important suggestions during the review process.…”