Hi there! Today we have a look at Jupiter, the largest planet of our Solar System. Several spacecrafts have visited it, from Pioneer 10 in 1972 to JUNO, which still operates. These missions have given us information on the behavior of its thick atmosphere, which raise the need for advanced modeling. This is why the authors of this study, An Equatorial Thermal Wind Equation: Applications to Jupiter, developed an equation modeling its behavior at low latitudes. This modeling appears to be successful for Jupiter when confronted to *Galileo* data, and for Neptune as well. The study, by Philip S. Marcus, Joshua Tollefson, Michael H. Wong, and Imke de Pater, has recently been accepted for publication in *Icarus*.

###### Outline

The atmosphere of Jupiter

The Galileo mission

The Thermal Wind Equation

The need for an equatorial extension

Successful modeling

It works for Neptune as well

The study and its authors

## The atmosphere of Jupiter

The planet Jupiter has a mean radius of 69,911 km, but is flattened at its poles. Its polar radius is 66,854 km, while the equatorial one is 71,492 km. This is a consequence of the rotation of the planet, which alters the shape of the atmosphere. Because, yes, Jupiter has a thick atmosphere. This is actually a gas giant planet.

It is pretty difficult to set an inner limit to the atmosphere of Jupiter, since when deep enough, the gaseous and liquid phases cohabit. This is not as if you would have encountered a solid surface. The thickness of the atmosphere is estimated to be some 5,000 km.

As you can imagine, the deeper you go, the higher the pressure. So, it may be convenient to measure the depth as a pressure and not as a distance, i.e. you express the depth in bars / pascals, instead of km / miles.

The atmosphere of Jupiter is mostly composed of hydrogen and helium, with some methane, hydrogen sulfide, and possibly water. It is composed as, from the bottom to the top:

- the troposphere,
- the stratosphere,
- the thermosphere,
- the exosphere.

Observing the atmosphere of Jupiter shows lateral bands, with different velocities. The winds are particularly strong at low latitudes, i.e. close to the equator.

The spacecraft Galileo delivered an atmospheric probe in December 1995, which transmitted measurements up to the depth of 23 bars, i.e. 150 km, before being destroyed.

## The Galileo mission

Galileo was a NASA mission, which operated around Jupiter between December 1995 and September 2003. It has been launched from Kennedy Space Center, in Florida, in October 1989, and made fly-bys of Venus, twice the Earth, and two asteroids, before orbital insertion around Jupiter in 1995. The two asteroids visited were Gaspra and Ida. Galileo gave us accurate images of these small bodies (some 15 and 40 km, respectively), and discovered the small moon of Ida, i.e. Dactyl.

Galileo journeyed around Jupiter during almost 8 years, studying the planet and its main satellites. It discovered in particular an internal ocean below the surface of Europa, and the magnetic field of Ganymede. It also gave us the variations of the temperature and pressure of the atmosphere over more than 1,000 km. And this is where you need a thermal wind equation.

## The Thermal Wind Equation

You can find in the literature a Thermal Wind Equation, which relates the horizontal variations of the temperature of an atmosphere to the variations of the velocity of the winds. This equation does not usually work at low latitudes, i.e. close to the equator, because at least one of its assumptions is invalid. The Rossby number, denoted Ro, and which represents the ratio between the inertial force and the Coriolis force in the fluid, should be small. In other words, the dynamics of the fluid (the atmosphere) should be dominated by the Coriolis force. But this does not work at low latitudes, when the centrifugal force dominates.

This Thermal Wind Equation is anyway often used, even at low latitudes, because the literature did not offer you any better option. This is why the authors of the present study developed its equatorial extension.

## The need for an equatorial extension

An obvious reason for developing such an equation holds even in the absence of data. You need to know the limitations of the Thermal Wind Equation, and a good way for that is to confront it with a more accurate one. In the presence of data, it is even better, because you can confront your two equations with the observations. And several phenomena remained to be explained:

- the wind variations (wind shear) measured by Galileo. The measurements were made at a latitude of 7°, which is pretty close to the equator,
- the velocity of a Jovian stratospheric jet,
- ammonia plumes, which had been detected in the deep atmosphere,
- on Saturn: an equatorial jet, at latitudes smaller than 3°,
- on Neptune: zonal vertical wind shear appears to be inconsistent with the temperature profile, which has been measured by another spacecraft, Voyager 2, in 1989. This is actually the only spacecraft which visited Neptune.

I do not want to detail the calculations, but the authors show that when the centrifugal force dominates (significant Rossby number), then the wind shear is related to the second derivative of the temperature with respect to the longitude, instead with the first derivative, as suggested by the classical Thermal Wind Equation. The authors show that their Equatorial Thermal Wind Equation is actually a generalization of the classical one.

## Successful modeling

Yes, this is a success. For instance, the authors show that the classical equation cannot be consistent with the detection of the ammonia plumes at the measured velocities, given the temperature required. However, it can be consistent with the equatorial equation, under an assumption on the longitudinal variation of the temperature. Either you consider that the equatorial equation is not accurate enough, or you see this result as a constraint on the temperature.

## It works for Neptune as well

Recently, the same authors, in another study measured the wind velocity on Neptune from the Earth, with the Keck Observatory, in Hawaii. The classical Thermal Wind Equation says that these measurements are inconsistent with the temperature profile given by Voyager 2. The Equatorial Thermal Wind Equation show that the two measurements are actually consistent. This is another success!

## The study and its authors

- You can find the study here. And now, the authors:
- The webpage of Philip S. Marcus,
- the one of Michael H. Wong,
- and the one of Imke de Pater.

And that’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter, Facebook, Instagram, and Pinterest.

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