Jovian Dynamics. Part 1: Vortex Stability, Structure, and Genesis

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  • 1 Geophysical Fluid Dynamics Laboratory/NOAA, Princeton University, Princeton, New Jersey
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Abstract

The vertical of Jupiter's atmosphere is probed and isolated by evaluating the stability characteristics of planetary vortices over a wide parameter range. The resulting structures lead to simulating the genesis of single and multiple vortex states in Part I of this paper and the genesis of an equatorial superrotation and midlatitudinal multiple jets in Part II.

The stability and genesis of baroclinic Rossby vortices, the vortices associated with long solitary Rossby waves in a stratified fluid, are studied numerically using a primitive equation model with Jovian and oceanic parameters and hypo-thermal structures. Vortex stability, that is, coherence and persistence, depends primarily upon latitude location and vertical structure and is used to deduce possible stratifications for Jupiter's atmosphere. The solutions suggest that Jupiter's large-scale motions are confined to a layer of depth h and are bounded by an abyss with an impermeable interface at a depth H, such that h/H≤1/20. Consequently, they also extend earlier results derived with the reduced-gravity, shallow-water model, particularly the explanation for the origin, uniqueness, and longevity of the Great Red Spot (GRS).

Beginning at the equator, stable anticyclones are seen to exist only when they have the Hermitian latitudinal form, the Korteweg-deVries longitudinal form, the confined exponential vertical structure exp(Nz/H), and the amplitude range as prescribed by the analytical theory of Marshall and Boyd for N=8. Soliton interactions occur between equatorial vortices of similar horizontal and vertical form.

In middle and low latitudes, shallow anticyclones with an exponential structure of N=20 exist quasi-stably for a variety of sizes. Such vortices remain coherent but tend to migrate equatorward (where they disperse) at rates that depend upon their size, location, and vertical structure: large and medium anticyclones propagate primarily westward while migrating slowly, whereas small storms just migrate rapidly and then collapse. The migration of these large, shallow vortices can be reduced, but not stopped, in low latitudes by an easterly jet with the same vertical structure.

Anticyclones are stabler when they are thinner relative to the abyss. Thus, when N=60, their migration is sufficiently slow that it can be stopped by a weak easterly jet. Furthermore, absolute stability sets in when N=90 and migration ceases completely for the large, thin anticyclones that now just propagate westward. Such flows may also be usefully represented by a vertical structure that is linear in z for the velocity and static stability in the thin upper layer and vanishes in the abyss.

Large, thin (N≥90) anticyclones can exist indefinitely either freely or when embedded within an anticyclonic zone of alternating jet streams of similar vertical structure. This holds true for the confined linear-z representation also. The permanence of GRS-like, low-latitude vortices in Jovian flow configurations occurs in a variety of lengthy calculations with thin structures. Ocean vortices are less persistent because the thermocline is relatively thick.

The baroclinic instability of easterly jets is nonquasigeostrophic and takes on the form of solitary rather than periodic waves when the jets have a thin exponential (N≥90) or confined linear-z structure. Such nonlinear waves develop into vortices that exhibit a variety of configurations and evolutionary paths. In most cases multiple mergers tend toward an end state with a single large vortex. Two types of merging occur in which a stronger vortex either catches a weaker one ahead of it or reels in a weaker one from behind. This duality occurs because propagation rates depend as much on local as on global conditions. In a further complication, vortices generated by an unstable easterly tend to have an exponential structure for exponential jets but a first baroclinic eigenmodal structure for confined linear-z jets.

Single vortex states resembling the ORS, with sizes ranging from 15° to 50° in longitude and with temperature gradients, velocities, and propagation rates near the observed range, can be generated either directly through the growth of a local front in a marginally unstable easterly jet or indirectly through a series of mergers of the multiple vortices generated by a more unstable easterly jet. Sets of vortices can be produced simultaneously in the anticyclonic zones centered about latitudes −21°, −33°, and −41°, and have the same relative scales as Jupiter's GRS, Large Ovals, and Small Ovals. Thin anticyclones can also be generated at the equator by the action of vortices lying in low latitudes. Equally realistic long-lived vortices can also be generated by jets with structures matching the recent Galileo spacecraft observations by using other hyperbolic forms and greater depth scales.

Abstract

The vertical of Jupiter's atmosphere is probed and isolated by evaluating the stability characteristics of planetary vortices over a wide parameter range. The resulting structures lead to simulating the genesis of single and multiple vortex states in Part I of this paper and the genesis of an equatorial superrotation and midlatitudinal multiple jets in Part II.

The stability and genesis of baroclinic Rossby vortices, the vortices associated with long solitary Rossby waves in a stratified fluid, are studied numerically using a primitive equation model with Jovian and oceanic parameters and hypo-thermal structures. Vortex stability, that is, coherence and persistence, depends primarily upon latitude location and vertical structure and is used to deduce possible stratifications for Jupiter's atmosphere. The solutions suggest that Jupiter's large-scale motions are confined to a layer of depth h and are bounded by an abyss with an impermeable interface at a depth H, such that h/H≤1/20. Consequently, they also extend earlier results derived with the reduced-gravity, shallow-water model, particularly the explanation for the origin, uniqueness, and longevity of the Great Red Spot (GRS).

Beginning at the equator, stable anticyclones are seen to exist only when they have the Hermitian latitudinal form, the Korteweg-deVries longitudinal form, the confined exponential vertical structure exp(Nz/H), and the amplitude range as prescribed by the analytical theory of Marshall and Boyd for N=8. Soliton interactions occur between equatorial vortices of similar horizontal and vertical form.

In middle and low latitudes, shallow anticyclones with an exponential structure of N=20 exist quasi-stably for a variety of sizes. Such vortices remain coherent but tend to migrate equatorward (where they disperse) at rates that depend upon their size, location, and vertical structure: large and medium anticyclones propagate primarily westward while migrating slowly, whereas small storms just migrate rapidly and then collapse. The migration of these large, shallow vortices can be reduced, but not stopped, in low latitudes by an easterly jet with the same vertical structure.

Anticyclones are stabler when they are thinner relative to the abyss. Thus, when N=60, their migration is sufficiently slow that it can be stopped by a weak easterly jet. Furthermore, absolute stability sets in when N=90 and migration ceases completely for the large, thin anticyclones that now just propagate westward. Such flows may also be usefully represented by a vertical structure that is linear in z for the velocity and static stability in the thin upper layer and vanishes in the abyss.

Large, thin (N≥90) anticyclones can exist indefinitely either freely or when embedded within an anticyclonic zone of alternating jet streams of similar vertical structure. This holds true for the confined linear-z representation also. The permanence of GRS-like, low-latitude vortices in Jovian flow configurations occurs in a variety of lengthy calculations with thin structures. Ocean vortices are less persistent because the thermocline is relatively thick.

The baroclinic instability of easterly jets is nonquasigeostrophic and takes on the form of solitary rather than periodic waves when the jets have a thin exponential (N≥90) or confined linear-z structure. Such nonlinear waves develop into vortices that exhibit a variety of configurations and evolutionary paths. In most cases multiple mergers tend toward an end state with a single large vortex. Two types of merging occur in which a stronger vortex either catches a weaker one ahead of it or reels in a weaker one from behind. This duality occurs because propagation rates depend as much on local as on global conditions. In a further complication, vortices generated by an unstable easterly tend to have an exponential structure for exponential jets but a first baroclinic eigenmodal structure for confined linear-z jets.

Single vortex states resembling the ORS, with sizes ranging from 15° to 50° in longitude and with temperature gradients, velocities, and propagation rates near the observed range, can be generated either directly through the growth of a local front in a marginally unstable easterly jet or indirectly through a series of mergers of the multiple vortices generated by a more unstable easterly jet. Sets of vortices can be produced simultaneously in the anticyclonic zones centered about latitudes −21°, −33°, and −41°, and have the same relative scales as Jupiter's GRS, Large Ovals, and Small Ovals. Thin anticyclones can also be generated at the equator by the action of vortices lying in low latitudes. Equally realistic long-lived vortices can also be generated by jets with structures matching the recent Galileo spacecraft observations by using other hyperbolic forms and greater depth scales.

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