Multiple Jets as PV Staircases: The Phillips Effect and the Resilience of Eddy-Transport Barriers

Abstract

A review is given that focuses on why the sideways mixing of potential vorticity (PV) across its background gradient tends to be inhomogeneous, arguably a reason why persistent jets are commonplace in planetary atmospheres and oceans, and why such jets tend to sharpen themselves when disturbed. PV mixing often produces a sideways layering or banding of the PV distribution and therefore a corresponding number of jets, as dictated by PV inversion. There is a positive feedback in which mixing weakens the "Rossby wave elasticity" associated with the sideways PV gradients, facilitating further mixing. A partial analogy is drawn with the Phillips effect, the spontaneous layering of a stably stratified fluid, in which vertically homogeneous stirring produces vertically inhomogeneous mixing of the background buoyancy gradient. The Phillips effect has been extensively studied and has been clearly demonstrated in laboratory experiments. However, the "eddy-transport barriers" and sharp jets characteristic of extreme PV inhomogeneity, associated with strong PV mixing and strong sideways layering into Jupiter-like "PV staircases," with sharp PV contrasts ⌬q barrier , say, involve two additional factors besides the Rossby wave elasticity concentrated at the barriers. The first is shear straining by the colocated eastward jets. PV inversion implies that the jets are an essential, not an incidental, part of the barrier structure. The shear straining increases the barriers' resilience and amplifies the positive feedback. The second is the role of the accompanying radiation-stress field, which mediates the angular-momentum changes associated with PV mixing and points to a new paradigm for Jupiter, in which the radiation stress is excited not by baroclinic instability but by internal convective eddies nudging the Taylor-Proudman roots of the jets.Some examples of the shear-straining effects for strongly nonlinear disturbances are presented, helping to explain the observed resilience of eddy-transport barriers in the Jovian and terrestrial atmospheres. The main focus is on the important case where the nonlinear disturbances are vortices with core sizes ϳL D , the Rossby (deformation) length. Then a nonlinear shear-straining mechanism that seems significant for barrier resilience is the shear-induced disruption of vortex pairs. A sufficiently strong vortex pair, with PV anomalies Ϯ⌬q vortex , such that ⌬q vortex k ⌬q barrier , can of course punch through the barrier. There is a threshold for substantial penetration through the barrier, related to thresholds for vortex merging. Substantial penetration requires ⌬q vortex տ ⌬q barrier , with an accuracy or fuzziness of order 10% when core size ϳL D , in a shallow-water quasigeostrophic model. It is speculated that, radiation stress permitting, the barrierpenetration threshold regulates jet spacing in a staircase situation. For instance, if a staircase is already established by stirring and if the stirring is increased to produce ⌬q vortex values well above threshold, then the s...

The structure of zonal jets in geostrophic turbulence

“…The aim of this paper was to examine the circumstances under which the equilibrium state of forced geostrophic turbulence might approach the staircase limit of perfectly homogenized zones of potential vorticity separated by sharp fronts, as studied recently by Dritschel & McIntyre (2008) and Dunkerton & Scott (2008). The question is of interest in part because of the existence of the simple analytic result relating jet separation to jet strength in the staircase limit, as reviewed in § 2.…”

“…Owing to the constraints of strong stable stratification and rapid rotation, the largescale motions of planetary atmospheres and oceans may, to a first approximation, be characterized by their quasi-two-dimensional motion. Zonal jets arise inevitably when potential vorticity is mixed horizontally over limited latitudinal regions, regardless of the form of the mixing (McIntyre 1982;Dritschel & McIntyre 2008;Dunkerton & Scott 2008;McIntyre 2008;Scott 2010). Potential vorticity mixing by planetary-scale Rossby waves in the polar winter stratosphere has already been discussed by McIntyre (1982), who noted the tendency for mixing to weaken potential vorticity gradients in a 'surf zone', while intensifying them on either side, resulting in an intensification of the polar night jet.…”

“…(Note that the prefactors of √ 2 and √ 6 used in Dritschel &McIntyre 2008 andDunkerton &Scott 2008, respectively, result from slight variations in the definition of L Rh .) In the equivalent barotropic case studied by Dritschel & McIntyre (2008), the result is exact in the limit of infinite Rossby deformation length, L D (defined in the parent shallow water system as the ratio of gravity wave speed to rotation). In the barotropic case R. K. Scott and D. G. Dritschel studied by Dunkerton & Scott (2008), the result is asymptotic in latitude, being exact for a staircase profile localized near the equator, but holding to a good approximation in midlatitudes.…”

“…Dritschel & McIntyre 2008, figure 7). It is worth noting that the above description explains quite naturally the asymmetry between eastward and westward jets sometimes discussed in the literature.…”

“…Two separate cases were considered recently: single-layer quasi-geostrophic barotropic flow on the sphere (Dunkerton & Scott 2008); and single-layer quasi-geostrophic equivalent barotropic flow on the β-plane (Dritschel & McIntyre 2008). In both cases the half-separation of the jets, L j , or the distance between adjacent peak eastward and westward velocity, is given by…”