An empirical three-layer fluid dynamical model for a combined JunoCam and MWR snapshot of Jupiter's north polar region

JunoCam images show a stable and approximately irrotational north polar cyclone, surrounded by eight circumpolar cyclones (CPCs) (Figure 1). The CPCs have been essentially stable over almost a decade since their discovery in 2016. They show only a minor zonal drift. Some of the CPCs develop and maintain a counter-rotating core that remains sustained over several months or longer. Those CPCs show a much stronger signature in MWR data than CPCs without a large embedded counter-rotating vortex. Between the north polar cyclone and the surrounding CPCs, up to about two additional large anti-cyclones occur that are not as stable or as long-lasting as the CPCs.

Figure 1: North polar CPC cluster seen by MWR and JunoCam. The north polar cyclone is nearly invisible in MWR data. CPCs with counter-rotating core tend to be brighter in MWR.

We have used a two-layer fluid dynamical model. In its first 2D layer we have assumed a steady flow with a north polar cyclone surrounded by CPCs with an optional counter-rotating core. A coupled second 2D layer behaves like an incompressible Euler flow, except for its coupling defined by a vorticity flux proportional to the vorticity difference between the two layers. This model develops almost no vertical vorticity flux for the north polar cyclone, but more vorticity flux for CPCs with a counter-rotating core than for those without such a feature, see Figure 2.

Figure 2

First row: Two-layer fluid model with an assumed steady 2D flow in layer 1 in the left panel, the simulated fluid layer 2 in the right panel, and the required vorticity flux at the center. Yellow means north anticylonic, blue means cyclonic vorticity.

Second row: Simulated vorticity flux blurred with color scheme adjusted to that of MWR.

 

The model vorticity flux resembles MWR data while the simulated fluid layer resembles JunoCam data. It is important to note that JunoCam is an optical imager and therefore sees the cloud tops, while MWR is a microwave radiometer whose 6 channels see thermal emission from about the 1-bar level to about the 100-bar level. Vertical vorticity flux between simulated layers might be interpreted as related to convection and induced heat transport between otherwise geostrophic fluid layers. This may then show up in temperature deviations in MWR data. Since the north polar cyclone and the CPCs without a counter-rotating core are closer to an equilibrium, and require less vorticity flux to remain stable, their geostrophic layer shows less temperature anomalies in MWR. However, this conceivable physical interpretation is beyond the limitations of the simplified empirical model.

 

Once an approximate underlying steady flow is inferred from MWR and JunoCam data, another deeper layer can be proposed to enable that inferred and assumed steady flow pattern. Such a deeper flow might host a rotationally symmetrical zonal flow that is suggested by observations of Jupiter's lower latitudes. The three-layer extension of the model starts with members of the family of rotationally symmetrical zonal flows, and attempts to infer a member that is suitable to induce an overlying fluid layer that resembles the CPC cluster that was previously assumed as an underlying steady flow to explain MWR and JunoCam data, see Figure 3.

 

Figure 3: A three-layer fluid-dynamical model with a rotationally symmetrical flow in layer 0 shown in the left panel. This layer induces a structure of CPCs (blue) with anticyclonic (orange) cores as shown in layer 2 in the right panel via an intermediate layer 1 as shown in the center panel.

 

For stable CPCs to form from a rotationally symmetrical zonal flow, a cylonic annulus with anticyclonic borders is required. The induced overlying layer will develop a cluster of CPCs if the coupling is adjusted to a suitable range. The number of CPCs is related to the width of the annulus, and depends to some degree on its structure in detail.

For a counter-rotating core to form and to be kept stable, the cyclonic annulus is best split into two with a suitable anticyclonic annulus inserted. Once the cyclones form in the overlying layer, they develop an anticyclonic core, if their centers happen to be located above the inserted anticylconic annulus. The modeled vorticity flux will accumulate anticyclonic vorticity in the core of the CPC from underneath.

Anticyclones can form between the north polar cyclone and the CPCs, if the shielding of the polar cyclone is modeled in the bottom-most layer as an anticyclonic annulus that is separated from the polar vortex.

The north polar cyclone needs to be shielded at some point within the polygon enclosed by the centers of the CPCs since otherwise the enclosed circulation would induce a net zonal CPC drift, see Figure 4a.

 

Figure 4

a: A cyclonic solid body vortex shielded by an anticyclonic annulus. Its radius can vary between that of the solid body vortex and that of the inner shielding of the cylconic annulus.

b: Model with two to three anticyclones forming from an underlying anticyclonic ring inside the CPC cluster.

 

The degree of freedom can be used to model an annulus that induces the formation of two or more large anticyclones, as shown in Figure 4b.

 

Distinct morphological structures within the CPCs tend to develop from an annular structure more naturally if the annuli of cyclonic and anticyclonic vorticity are separated more distinctly than based on a Gaussian-like cross section of their stream function, see Figure 5a.

 

Figure 5

a: An underlying steady flow with sharply defined annuli induces distinct structures.

b: An underlying steady flow that induces FFR-like flow.

 

Simulated structures resembling folded filamentary regions (FFRs) tend to form if the underlying concentric annuli structure does not show a sufficiently clear excess of cyclonic vorticity together with a border of shielding anticyclonic vorticity as a function of radius, as illustrated in Figure 5b. In that case, local chaotic turbulence tends to form easier than a distinct filament roll-up into large vortices. This scenario appears to be present outside the polar CPC cluster.