Timothy Edward Dowling

Jupiter's Great Red Spot as a Shallow Water System

Most current models of Jupiters Great Red Spot (GRS) are cast in terms of a two-layer model, where a thin upper weather layer, which contains the vortex, overlies a much deeper layer, which is meant to represent the neutrally stratified deep atmosphere. Any motions in the deep layer are assumed to be zonal and steady. This two-layer model is dynamically equivalent to a one-layer model with meridionally varying solid bottom topography, called the reduced-gravity model. Specifying the motions, or lack thereof, in the lower layer of the two-layer model is equivalent to specifying the bottom topography, and hence the far-field potential vorticity, in the reduced-gravity model. Current models of the GRS start by guessing the deep motions and then proceed to study vortices using the implied bottom topography. Here, using the GRS cloud-top velocity data, we derive the bottom topography, up to a constant that depends on the unknown radius of deformation (or equivalently, the product of the reduced gravity and the mean thickness of the upper layer). The bottom topography is inferred from three quantities derived from the velocity data—Bernoulli streamfunction, kinetic energy per unit mass, and absolute vorticity—all of which are functions only of horizontal position in the reference frame of the vortex. Far from the vortex, potential vorticity versus latitude is calculated from the observed cloud-top zonal velocity and the derived bottom topography. The results show that the deep atmosphere is in differential motion and that the far-field potential vorticity gradient changes sign at several latitudes. Numerical shallow water experiments are performed, using both the derived bottom topography and the bottom topographies prescribed by current models. The results of three published studies are reproduced in our numerical experiments. Each of these models is successful in maintaining a long-lived, isolated vortex, but only the present model yields absolute vorticity profiles along streamlines that agree with those observed for the GRS by Dowling and Ingersoll. In all the models, large vortices form by merging with smaller vortices. In the present, observationally based model, and in one other published model, the smaller vortices arise spontaneously because the observed cloud-top zonal velocity profile is unstable. These two models require an additional momentum source to maintain the upper-layer zonal velocity profile. In the other two models, the bottom topography stabilizes the zonal velocity profile. If dissipation is present, the latter two models require an additional source of smaller vortices to maintain the larger one. A crucial unanswered question for the present model, and for Jupiter itself, is how the cloud-top zonal velocity profile is maintained in its present unstable state.

Saturn’s rotation period from its atmospheric planetary-wave configuration

The rotation period of a gas giants magnetic field (called the System III reference frame) is commonly used to infer its bulk rotation. Saturns dipole magnetic field is not tilted relative to its rotation axis (unlike Jupiter, Uranus and Neptune), so the surrogate measure of its long-wavelength (kilometric) radiation is currently used to fix the System III rotation period. The period as measured now by the Cassini spacecraft is up to ∼7 min longer than the value of 10 h 39 min 24 s measured 28 years ago by Voyager. Here we report a determination of Saturns rotation period based on an analysis of potential vorticity. The resulting reference frame (which we call System IIIw) rotates with a period of 10 h 34 min 13 ± 20 s. This shifted reference frame is consistent with a pattern of alternating jets on Saturn that is more symmetrical between eastward and westward flow. This suggests that Saturns winds are much more like those of Jupiter than hitherto believed.

Potential Vorticity and Layer Thickness Variations in the Flow around Jupiter's Great Red Spot and White Oval BC

Layer thickness variations in Jupiters atmosphere are investigated by treating potential vorticity as a conserved tracer. Starting with the horizontal velocity field measured from Voyager images, fluid trajectories around the Great Red Spot (GRS) and White Oval BC are calculated. The flow is assumed to be frictionless, adiabatic, hydrostatic, and steady in the reference frame of the vortex. Absolute vorticity is followed along each trajectory; its magnitude is assumed to vary directly as the thickness, which is defined as the mass per unit area between potential temperature surfaces. To the accuracy of the observations. the inferred thickness is a separable function of trajectory and latitude. The latitude dependence has positive curvature near the GRS and BC. The relative variations of thickness with respect to latitude are generally larger than the relative variations of Coriolis parameter with respect to latitude—the beta effect. The data are a useful diagnostic which will help differentiate between models, of Jovian vortices. The present analysis employs a quasi-geostrophic model in which a thin upper weather layer, which contains the vortex, is supported hydrostatically by a much deeper lower layer. In this model, the upper free surface does not contribute to the observed variation of thickness along trajectories. Such variations are due exclusively to bottom topography—flow of the deep lower layer relative to the vortex. The observation are used to infer the form of the deep zonal velocity profile vs. latitude. The magnitude of the profile depends on the unknown static stability. The principal result is the existence of horizontal shear in the deep layer zonal velocity profile, i.e., the lower layer is not in solid body rotation and does not act like a flat solid surface. In this respect the data support the hypothesis of Ingersoll and Cuong concerning motions in the deep layer. However at some latitudes the data violate Ingersoll and Cuongs criterion governing the compactness of the vortices. At these latitudes the topography allows standing Rossby waves (wakes) extending far downstream to the west. Observed wavelike features, the filamentary regions, are possibly formed by this mechanism.

The Emergence of Multiple Robust Zonal Jets from Freely Evolving, Three-Dimensional Stratified Geostrophic Turbulence with Applications to Jupiter

Three-dimensional numerical simulations of freely evolving stratified geostrophic turbulence on the plane are presented as a simplified model of zonal jet formation on Jupiter. This study samples the parameter space that covers the low, middle, and high latitudes of Jupiter by varying the central latitude of the plane. The results show that robust zonal jets can emerge from initial small-scale random turbulence through the upscale redistribution of the kinetic energy in the spectral space. The resulting flow’s sensitivities to the flow’s deformation radius LD and the two-dimensional Rhines length L U/ (U is the characteristic turbulence velocity and is the meridional gradient of the planetary vorticity) are tested, revealing that whether the outcome of the upscale energy transfer becomes dominated by jets or vortices depends on the relative values of LD and L. The values of L and LD are varied by tuning the -plane parameters, and it is found that the flow transitions from a jet-dominated regime in L LD to a vortical flow in L LD. A height-to-width ratio equal to f /N, the Coriolis parameter divided by the Brunt–Vaisala frequency, has previously been established for stable vortices, and this paper shows that this aspect ratio also applies to the zonal jets that emerge in these simulations.

Earth as a Planet: Atmosphere and Oceans

Exhibiting striking similarities as well as differences with the fluid envelopes of other planets, the atmosphere and ocean of Earth provide the foundation for understanding planetary atmospheres generally. Here we survey the physical and chemical behavior of our home planets atmosphere, oceans, and climate. The Earths atmosphere is dominated by nitrogen and oxygen, with a vertical temperature profile consisting of alternating layers of decreasing and increasing temperature with height—the troposphere, stratosphere, mesosphere, and thermosphere. This structure is largely controlled by the height-dependence of solar energy absorption and infrared emission. At large scales, the atmospheric circulation is driven primarily by the latitudinal gradient in solar heating, and the circulation responds to this gradient by transporting heat from the equator to the poles. Near the equator, this heat transport is accomplished by the Hadley circulation, whereas in midlatitudes, large-scale, so-called baroclinic eddies accomplish this transport. In the troposphere, the equatorial flow is weakly westward, but the airflow is eastward in the midlatitudes where the jet streams reside. The Earth is unique in the solar system in having a surface ocean. We describe its vertical structure, large-scale circulation, salinity, and interaction with the atmosphere. We next turn to climate. The Earths climate is affected by numerous interacting positive and negative feedback mechanisms, including the greenhouse effect and feedbacks resulting from the distributions of ice and clouds. Over the past 50 years, the global mean surface temperature has been increasing, and numerous other climate changes are becoming evident. A widespread scientific consensus demonstrates that these changes have, to a large degree, occurred due to rapid increases in atmospheric greenhouse gases (primarily carbon dioxide) caused by burning of fossil fuels by humans. Over long timescales, Earth exhibits a wide range of climatic variations. In particular, we summarize the ice age cycles that have dominated climatic variation over the past 2 million years; understanding these cycles can provide insights into how the atmosphere/ocean system responds to perturbations generally. To close, we survey evidence for life on Earth as obtained from spacecraft flybys; this provides a reference point from which to assess humankinds ability to remotely detect surface life on other worlds.

Planetary science: Music of the stratospheres

Fifteen-year oscillations in Saturns equatorial stratosphere bear a striking resemblance to the shorter-term oscillations seen on Earth and Jupiter — akin to notes played on a cello, a violin and a viola. Both Earth and Jupiter have equatorial oscillations in their atmospheres, with two-year and four-year periodicity respectively. Two groups working independently now report a related phenomenon on Saturn. Orton et al. analysed wo decades of ground-based observations of Saturns stratospheric emissions to reveal an oscillation with a period of 14.8±1.2 terrestrial years. This is roughly half of Saturns year, suggesting seasonal forcing, as is the case with the Earths semiannual oscillation. Fouchet et al. used infrared spectrometry data from the Cassini probe to detect a similar equatorial oscillation.