Jupiter's Winds:
Vortex Pancakes versus Taylor Columns

FEATURED
Philip Marcus
UC Berkeley

ven with the improvements to the Hubble telescope, the Galileo probe of December 1995, and the impacts of comet Shoemaker-Levy in July 1994, astronomers still don't fully understand the dynamics of Jupiter's atmosphere, of which the Great Red Spot is only the most striking feature. For the most part, astronomers assume the swirling winds and vortices behave according to a generally accepted theory of rotating stars and planets that dates back to the 1970s.

The accepted theory, or "standard picture," makes some simplifying assumptions about how the turbulent gases behave in planetary atmospheres. Philip Marcus, a professor of mechanical engineering at UC Berkeley, and colleagues have been developing analytic models, novel interpretations of Jupiter observations, and 3-D computations to examine how well the accepted theory holds up under close scrutiny.

"In short, the goal of our research is to overthrow the standard picture," Marcus said. "We believe the theoretical underpinnings are at best weak and most likely incorrect."

2-D VERSUS 3-D TURBULENCE

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A DELICATE BALANCE

2-D VERSUS 3-D TURBULENCE

Turbulence has been a subject of computational science research since the days of the earliest supercomputers. Due to vertical stratification and rapid rotation, the large-scale components of geophysical and astrophysical flows are often nearly 2-D rather than 3-D. Therefore, there have been many 2-D turbulence studies in which a flow with an initially random distribution of vorticity is allowed to evolve. These calculations show that coherent structures form from the randomness; large, long-lived vortices self-organize out of a chaotic turbulent flow.

In 1986, Marcus and colleagues conducted some of these early 2-D simulations that suggested how Jupiter's Great Red Spot could form spontaneously in the atmosphere. Despite the simulation results, it wasn't until Harry Swinney and colleagues at the University of Texas at Austin were persuaded by Marcus's animated visualization to build an experimental apparatus and test the model in the lab. When the experiment succeeded, people took notice.

These original simulations, using 2-D approximations, replicated many important characteristics of the Great Red Spot, including the fact that it self-organized from a completely chaotic flow. "However, if you look at the details of Jupiter observations, they are inconsistent with the 2-D simulations," Marcus said. "So the questions become, how and why did the 2-D approximation work so well in describing so much of the flow, and what is happening in the third, vertical dimension that we cannot see directly? It turns out that the physics is subtle."

The standard picture, for example, would describe the Great Red Spot as the visible cap on a tall cylinder, with winds swirling around the cylindrical axis, that passes through the entire planet. Some astronomers, however, say that no such structure could exist in reality; according to this view, the spot is at most 10 or 20 kilometers deep--a vast pancake-shaped storm in the upper layers of the atmosphere.

In the terms of fluid dynamics, the Taylor-Proudman theorem says that for specific types of flows, turbulence can be approximated as a 2-D flow. Jupiter's atmosphere is one example of such a flow--at least in a high-level approximation. However, while the theorem holds true under idealized conditions, it falls apart when these conditions change.

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Figure 1: Voyager Photo of Jupiter

Jupiter's vortex street at approximately 41 degrees south longitude was photographed during one of the Voyager mission encounters with the giant planet.

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"If you don't look too closely, you can convince yourself that the 2-D explanation works well," Marcus said. "But some clues from Jupiter are staring us in the face. There are some real constraints on the 3-D structure based on the data from Jupiter." For example, the standard picture can't explain the odd wake or the calm center of the Great Red Spot. (In fact, some theoretical explanations based on the standard picture show an exponential peak for the speed of the center.)

Unlike 2-D turbulence, the behavior of which is well understood, the 3-D realm has substantial variation, and there is no consensus that in 3-D systems order can emerge out of chaos. That it can and does, as evidenced by Jupiter's striking examples, is the focus of Marcus's research group. The question becomes: How do pancake vortices like the Great Red Spot form and survive the turbulence? According to Marcus's interpretation, they thrive on it.

Marcus points to four categories of Jupiter observations that provide clues to the subtle physics involved: the cyclones and anticyclones, the shapes and colors of clouds, and the chains of vortices.

On Jupiter's surface, observations show that cyclones and anticyclones have very different structures. Most interpretations of the standard picture discount the existence of cyclones, saying that cyclones cannot really exist as long-term objects, even though observations over the past few decades have always shown cyclones on Jupiter.

In contrast, the simulations and experiments predict that cyclones and anticyclones should exist in equal numbers. In fact, they should exist, just as observations show they do, in long chains of vortices rotating in alternating directions--cyclone, anticyclone, cyclone, anticyclone.

By combining these clues with a mechanical engineer's perspective on fluid dynamics, Marcus is constructing a 3-D model of turbulence that could show how the vortices on Jupiter exist as flat pancakes on the surface layer rather than deep columns of winds. Marcus argues that the 3-D structure of the atmosphere permits pancakes to survive in turbulent flows. "We have to do the simulations first, then convince the experimentalists to build the apparatus," Marcus said.

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Figure 2: Simulating Jupiter's Atmosphere

A simulation by Philip Marcus and colleagues revealed differing cloud morphologies for Jupiter's cyclones and anticyclones caused by ageostrophic 3-D motions in the atmosphere. The simulation closely mirrored the photographed vortex street in Figure 1.

A DELICATE BALANCE

Marcus and colleagues are using NPACI's CRAY T90 at SDSC for their numerical simulations of turbulence, done with spectral methods rather than finite difference methods. The more efficient spectral methods are good for solving problems on regular geometries, such as the cylindrical geometries in the simulations. They are also investigating the possibility of porting their codes to UC Berkeley's Network of Workstations (NOW), one of NPACI's experimental architectures, to take advantage of parallel processing.

Their preliminary simulations suggest that there is a delicate balance between forcing and dissipation in Jupiter's atmosphere. The forcing of, or energy pumped into, the turbulent flow comes from the Sun's heat and the radiation from Jupiter's hot core; plumes and vortices are constantly mixing the atmosphere.

In addition, the Marcus group's simulations have shed light on the dissipative time scale for Jupiter. If the Sun's energy was blocked from reaching Jupiter, astronomers agree that the time it would take Jupiter's atmosphere to lose its heat--the radiative time scale--is on the order of 10 years. On the other hand, the dissipative time scale--the time it would take for the turbulence to die down--has been assumed to be a long time, based on the observation that the Great Red Spot has been visible for several hundred years.

However, Marcus's simulations suggest that the dissipative time scale is only about 10 years and is linked to the radiative time scale, to which dissipation had not been linked before. "The reason the atmosphere is highly dissipative is because it's 3-D," Marcus said. "This has to be backed up by calculations, which is what we're doing now." --DH

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