As I continue to meditate, it seems to me the GRS must be more tornadoish in gross morphology than hurricanian. It's the adiabaticity thing. As the weather formation progresses toward the interior, pressure would shrink the diameter of the cloud so that it would take on a funnel shape, rather than a column shape.

One could estimate the diameter of the bottom, assuming the bottom is at the PPT (0.9 Jupiter radii) or around 10,000 km by dividing the hypothetical column into slices, each with equal mass. Using the ordinary equations of state, it wouldn't be hard to say how wide the bottom slice should be.

This informative website http://www.newmediastudio.org/DataDi...rr_Struct.html confirms that the air above a cyclone/hurricane circulates in the opposite (anticyclonic) direction, and includes an excellent diagram at Fig 12. It states “As air leaving the center of the hurricane reaches an elevation of about 12 km above sea level, it produces high pressure near the tropopause, and divergent flow away from the focus of the hurricane. This upper level outflow circulates in an anticyclonic direction, typically at a radius of 300 km, and is termed the anticyclonic jet." However, I still am struggling to picture this as a valid model for Jupiter, where the GRS looks more like an eddy in a river, and where it is hard to imagine, as Warren claims, that this near-invisible anticyclonic reverse jet circulation is sufficient to give us the false impression that the entire spot is spinning in the opposite direction from the hidden reality, and that this hidden reality is proven by teleology. I will also try to follow up on Warren’s claims that this is an example of teleology, as I still don't see how his ideas on this are helpful empirically.

No, the GRS is unusual: see figure 1 of Shetty et al.'s (2007, 4) new analysis of the GRS's velocity vectors as determined by the Voyager photos. There is a clear collar, whereas on the inside of the GRS, velocities aren't organized and they are small relative to the collar--a sign to me of turbulent upwelling. A regular eddy has organized velocity vectors through and through, down to the middle.

Huh?

The way you sling around the word 'teleology' shows you don't know where I'm coming from. I've said elsewhere that my metaphysical system is known as "scientific materialism": it's materialistic in that it only contemplates atoms and molecules as the building blocks of reality, and its epistemology is scientific in that science is the the best epistemological technique to understand all these atoms and molecules. I am not a Christian, nor a Bhuddist, nor anything else. I don't believe in God or gods, Mind or minds.

In other words, I don't make a distinction between the "real" purposes of self-conscious human scientists, and the "purely as if" teleology of lesser systems. Therefore I am free to posit teleological ascriptions wherever it is useful to do so. And when can such ascriptions be useful? Wherever a system has undergone a history of natural selection. This is ordinary in biology, but in the physical sciences not so much, but only because most people haven't considered the fact that physical systems do undergo natural selection, but without the genetic heredity and reproduction.

In my first post in that other ATM thread, what I proposed was a methodological panpsychism. "Panpsychism" was an unfortunate word choice, however. I should have said methodological "animism" or "shintoism". Rather, than one grand mind that rules over all, each individual system is more usefully considered as possessing its own Japanese "kami". The task of science is then to reverse engineer the apparent kami-driven behavior in order to come up with a materialistic explanation for the phenomenon based on atoms and molecules.

Again, let me remind you, I am a scientific materialist, and not an animist nor a devotee of Shintoism.

WRT the GRS, most people are accustomed to thinking of the Great Red Spot as a mere mechanical system subject to the whim of forces beyond its control; hence the reflex to the hypothesis that the GRS must be caused by some hidden object floating in the Jovian atmosphere. The teleological method suggests that since Jovian storms "compete" with each other by "eating" each other, the GRS might be usefully viewed as if it were alive. Thus, my question was not "How does fluid mechanics and turbulence theory generate a long lasting system like the GRS?" Rather, my question was, "If I were the GRS, what would I like to eat?" This led me to the seemingly-to-me-obvious hypothesis that the GRS is the tail end of a gas lift pipe that's tapping into the metallic envelope. Yet the gas lift hypothesis has apparently been overlooked in all the primary literature I've been able to uncover so far.

But of course (as grant hutchison pointed out with respect to my historical analysis of the discovery of buckyballs) anyone could have thought up the gas lift hypothesis for any of a number of reasons. My point is that I in fact thought of it while coming from an explicitly teleological or "design stance" a la Daniel Dennett. So that shows the teleological method can be useful at times. It is not, however, my position that the gas lift hypothesis is "proven by teleology" (whatever that means--and for anyone interested in knowing more about teleology, avoid taking seriously the wiki article on the subject because it's worse than useless). Whether the gas lift hypothesis will eventually become the mainstream view or not depends on how well it makes future predictions, and on how well it can illuminate models of Jupiter's interior.

Let's assume that the total system consisting the GRS is actually a funnel-shaped pipe. If you'll take a look at the graph on page four of Shetty et al. (October 4, 2007), you can clearly see a thick collar that encases a chaotic, turbulent zone where most of the hypothesized uplift takes place. The turbulent zone can be approximated as an ellipse whose semimajor axis is 5,000 km, and whose semiminor axis is 2,000 km. This works out to an area of about 30 million square kilometers.

Now, if the GRS is in a more-or-less steady-state, then the mass flux through any given horizontal section should be the same. That entails that any given, horizontal, thin slice with the same thickness will have the same number of molecules. Therefore, the area of any given slice will depend on the ambient temperature and pressure. The relevant gas law can be given as follows:

P₁V₁/T₁ = P₂V₂/T₂

Since our representative slices will have the same thickness, the equation reduces to:

P₁A₁/T₁ = P₂A₂/T₂

and where the '1' refers to conditions prevailing at the level of the cloud deck and '2' refers to conditions prevailing at the level of the plasma phase transition (PPT).

We can substitute the following reasonable values that I got from page 46 of Baganel, Dowling, and McKinnon's (2004) book entitled Jupiter: The Planet, Satelites and Magnetosphere that I got in the mail a couple of days ago.

• A₁ = 30,000,000 km^2
• T₁ = 160 K
• T₂ = 6,000 K
• P₁ = 1 bar
• P₂ = 1,000,000 bars

and thus solving for A₂, we can obtain a first-order order of estimate of the size of the area at the bottom of the GRS of about 1,000 km². This figure is much smaller than the visible GRS, but it is still a fairly beefy pipe capable of moving a lot of material.

Thus the next question would be the mass flux itself. I'm not sure how to go about estimating this. I would be open to any suggestions.

One way might be energetical considerations. How fast would metallic hydrogen have to be converted to molecular hydrogen in order to maintain the GRS in order to overcome the friction resulting from wind shear?

Naturally your calculation of pv/t = constant assumes that nothing changes when you move into Jupiter, e.g. chemical composition, magnetic field strength etc.

Here is a list on ADS of over 200 published papers on the GRS.

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

The thing about the ideal gas law is that it doesn't matter what kind of gases compose a given mixture--they all obey the same ideal gas law. As for magnetic fields, I'm proposing that the GRS is mainly composed of helium and molecular hydrogen--neutral molecules and atoms that aren't affected much by magnetic fields.

Thanks for the link, but your post would be more useful if it included a username and password for ScienceDirect. . . .

but you can only compare (1) and (2) if there have not been any phase transitions, which will change internal energy, entropy, enthalpy etc. I may be mistaken, but I do think that the perfect gas law only applies if those things are kept constant.

yeah, wouldn't we all wanna have a password for that.

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

You are correct sir, but I'm purposefully looking at the conditions just above the PPT, therefore, the model for the shape of the GRS assumes that the hydrogen will be existing in the molecular phase, and that there are no other important phase transitions as one proceeds from the cloud deck to the PPT.

Your larger point that such estimates are fraught with uncertainties is well taken, however. I'm just hoping for an order of magnitude ballpark approximation.

Pressure drops of ~10% are typical for both hurricanes and tornadoes on Earth. As long as such a system is self-sustaining, the pressure differential will also be sustained. (cf. Bernoulli's principle).

Bernoulli's principle guarantees there'll be low pressure at the bottom of the vortex. The problem is how to sustain the vortex. That takes energy. However, at the PPT metallic hydrogen has a density of about 1 gm/cm³, whereas molecular hydrodgen has a density of about 0.7 gm/cm³, assuming the phase transition is in fact first-order. The conversion also releases latent heat to the tune of ~0.5k_B per proton. However, until I can come up with a figure for the mass flux, I can't calculate how much latent heat could be expected to be released.

Sorry, but I have to disagree here (again). Bernouilli's principle can be see by blowing between two sheets of paper. Instead of the expected effect that the sheets move away from eachother, they move towards eachother.

A tornado is created by a low pressure system, to which air is flowing and diverted by the coriolis force. Now where does Bernouilli come into play? As long as the low pressure is maintained the tornado can be maintained, and as the wind rotates around the low pressure it is difficult to "fill it up". But this is all coriolis. Note that tornados need energy from the warm sea water. If there is no energy source they peter out, and no Bernouilli will help you maintain the tornado. It will, however, enhance the low pressure region. When you want Bernouilli, then you have to go to a house and have the wind blow along the window. The fast wind along the window has a lower pressure on the window then the standing air in the house. This is Bernouilli acting, and thus the windows "explode" outward, instead of inward.

The energy you need is to maintain the low pressure to get your vortex. Before you can get Mr. Bernouilli to work you have to have a low pressure to create your vortex.
You want to create heat from the phase transition? There is enough heat generated by Jupiter by its slow contraction. I am not sure how how get the value of 0.5 k_B per proton, at the same time this is no heat, it has the units J/K.

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

You sure you mean tornado and not hurricane? Tornados are pretty small to be affected by the coriolis and, since they most often occur in the central plains here in the US and only rarely in coastal areas, I'm not sure where they would get the warm sea water.

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"Think of the rivers of blood spilled by all those generals and emperors so that, in glory and triumph, they could become the momentary masters of a fraction of a dot." --Carl Sagan "Pale Blue Dot"

Tell me something I don't know.

The Bernoulli principle can be stated as follows: "The pressure in a fluid decreases as the speed of the fluid increases."

So, since tornados have high winds, the high winds cause low pressure. And yes of course maintaining a tornado requires inputs of energy.

I agree--I think. . . .

There is enough heat to drive ordinary convection from the gravitational contraction. I'm looking for a special source of energy to drive an extraordinary phenomenon.

My source is Guillot et al. (2004, 41, in Baganel et al.'s Jupiter: The Planet, Satellites and Magnetosphere, Cambridge University Press): "[A]s the planet cools, a fraction of the envelope is converted from one phase to the other with an associated latent heat release (or absorption). The effect on the evolution [of Jupiter as a whole] is not very pronounced for a latent heat of ~0.5k_B per proton."

Unfortunately, this is exact to such a degree that is it dangerous. Here, the pressure is considered a scalar, however, if you look more closely, you will find that the pressure in such a system is a vector with components along the flow and perpendicular to the flow. Indeed, the total (scalar) pressure may go down, but if you look at the vector properties you will find that it is the components perpedicular to the flow that decrease.

I will have to wait till monday to look up in my copy at work what exactly they mean and how you can use this.

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

Ah tornado, hurricane, what's in a name!
Guess I mixed them up, however, for a tornados to get a rotational funnel, would they not have to be created by some coriolis effect? Or do you have another mechanism how this comes about?

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

Tornadoes may get their initial rotation direction from the t-storm cell, which is obviously caused by the coriolis effect (although not in all cases...tornadoes can spin clockwise in the northern hemisphere..and sometime a storm cell will produce two tornadoes, each spinning a different direction), but the tornado itself is too small for the effect to apply. The high-speed rotation of a tornado is a product of high vertical wind shear.


From here
Regardless..this is OT. My apologies Warren.

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I was just sitting here contemplating the immortal words of Socrates who said, "I drank what?"

"Think of the rivers of blood spilled by all those generals and emperors so that, in glory and triumph, they could become the momentary masters of a fraction of a dot." --Carl Sagan "Pale Blue Dot"

Generally, it is accepted to be wind shear between two layers of air with differing properties, IIRC.

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Exactly. So you have a tornado with a whirling wall of air that's mostly going in a corkscrew pattern. Then the pressure components perpendicular to the corkscrew flow decrease. Outside the tornado, this entails that the ambient air pressure presses inward following the decrease in the pressure component perpendicular to the direction of the rotation due to the Bernoulli effect. But because of conservation of momentum, the more the tornado gets pressed inward, the faster it spins (in the manner of ice skaters) until a balance is reached between the ambient pressure and the centrifugal force of the whirling wall of air combined with the inner pressure.

Meanwhile, on the inside, the pressure component perpendicular to the corkscrew flow decreases--this time the decrease is towards the outside, however. The decrease in the pressure component near the wall will cause the air inside the whirling wall to move toward the wall, with the result that the air pressure in the very center of the vortex drops. Therefore, air will flow into the column from the opening of the vortex at the bottom of the column on the ground.

Thus, cut off the supply of fresh air at the bottom, and you kill the tornado. Cutting off the supply of fresh air causes the internal pressure to decline even more; then the ambient air presses on the side of the tornado, crushing the life out of it. Hence the phenomenon of "roping" right before a tornado dissipates--it gets real skinny and then does the "funky chicken" (American slang for convulsions associated with the onset of death).

I'm more than a little confused about this myself, and am trying to figure it out.

Wow, the silence is deafening! I must really be on to something here!

Mass Flux

The mainstream view of the GRS is that it is rather like a "pancake" (e.g., Marcus 1993, Simon-Miller et al. 2002), that is basically 2-dimensional and much less deep than it is wide. The view taken here, however, is that the GRS is more like a tornado: it is very much a 3-D creature, funnel shaped and penetrating to depths that rival the magnitude of its breadth.

On the theory presented here, the GRS is a plasmavore that feeds on metallic hydrogen at the plasma phase transition zone (PPT). Current models suggest the PPT--if it exists at all--lies between 0.9 and 0.78 R_J, or at about 7,000 to 16,000 km below the cloud deck. So, the GRS would have to reach that far down. But considering that the GRS is a 14,000 km X 24,000 km ellipse at the cloud deck, reaching the PPT is not so far-fetched.

The GRS has a peculiar morphology compared to other Jovian vortices in that it has an organized, rapidly moving "collar" that surrounds an inner turbulent zone. So the GRS can be envisioned as a sort of funnel shaped pipe that pumps material from deep within Jupiter up into the stratosphere. The inner dimensions of the pipe, as mentioned in a previous post, can be described by an ellipse whose semimajor axis is about 5,000 km and whose semiminor axis is about 2,000, with an area of about 3 X 10⁷ km². So it would be of interest to estimate the amount of upwelling through this pipe.

We can obtain an order-of-magnitude estimate of the mass flux through the center of the GRS if we assume an upwelling rate of 50 m s^-1. Since typical upwelling occurs at the rate of tens of meters per second, the 50 m s^-1 figure is not unreasonable. 500 m s^-1 would be the equivalent of over 1,000 mph, which greatly exceeds the maximum winds ever observed on Jupiter, and 5 m s^-1 is much too slow a figure, given the typical wind velocities found all over Jupiter.

Given an area of 3 X 10⁷ km² and a 50 m s^-1 average velocity, that works out to 1.5 X 10¹⁵ m³. Assuming a pressure of 1 bar and a temperature of 170^o K, from the ideal gas law (PV = nRT) we can estimate the molar flux:

10⁵ N 1.5 X 10¹⁵ m³ mole K
-------------------------- = 10¹⁷ moles s^-1
m² s 8.314 N m 170 K

Assuming a helium molar fraction of about 13.6%, a hydrogen molar fraction of 86%, with the rest made up by much heavier molecules, a density of 2.5 gm per mole of atmosphere is not unreasonable. So that yields a mass flux of 2.5 X 10¹⁴ kg s^-1.

Energy Flux

The formula for calculating kinetic energy is (½) mv². This works out to an energy flux of 3 X 10¹⁷ watts or 3 X 10²⁴ erg s^-1. That is a lot of watts. To put this figure in perspective, consider that about 8 X 10²⁴ erg s^-1 is the total radiation emitted by Jupiter of which 5 X 10²⁴ erg s^-1 consists of absorbed solar energy that is re-emitted. In other words, the kinetic energy flux flowing through the GRS is about the same as the total intrinsic power of the whole planet.

Conditions Prevailing at the Bottom of the GRS

Because pressure rapidly increases with depth within the interior of Jupiter, under the plasmavore model, the GRS will take on a pronounced funnel shape, as opposed to the mainstream pancake shape, but with a much more squashed appearance compared to the archetypical terran tornado. In an earlier post, I had estimated the area of the opening at the bottom of the vortex as about 1,000 km²--equivalent to a circle with a 35 km diameter. However, I had assumed that the ideal gas laws prevail in the interior of Jupiter--but the ideal gas laws do not prevail within gas giants. This fact makes the study of gas giants even more problematic and challenging than the study of stars, because at stellar densities, the ideal gas laws once again begin to work. The main problem is the equation of state of hydrogen. Determining the EOS is not an exact science, but the gas giants offer severe constraints that limit what the hydrogen EOS must be like. See Saumon, Chabrier, and Van Horn (1995) for an excellent discussion of EOS theory.

Current theory suggests that the density of the molecular envelope at the upper boundary of the PPT is maybe 0.7 gm cm^-3. Now, since energy and mass are conserved, and if the flow through the pipe that consists the GRS is approximately adiabatic and isobaric with respect to the surroundings, then the vertical velocity component at the mouth of the GRS must be the same as the vertical velocity at the top. We can calculate the volume flow from the given density (0.7 gm cm^-3) and given mass (2.5 * 10¹⁴ kg): that works out to 3.6 X 10¹¹ m³ s^-1. And from the volume flow and the known vertical velocity component, the area of the bottom must be: 3.6 X 10¹¹ m³ / 50 m s^-1 = 7.2 X 10⁹ m².

If the opening was round, that would work out to a 100 km pipe diameter! That's about 1% of the diameter of the opening at the visible top of the GRS. The shape would be rather like a one meter long straight trumpet-style bugle with a bell the size of a tuba.

Caloric Requirements of a Plasmavore

Clearly, there is much more kinetic energy wrapped up in the outer collar of the GRS than in the central upwelling zone. However, given the large sizes and low viscosities involved, there may not be very much friction for the rotating wall to overcome. And although there is a vast amount of kinetic energy stored within the whirling wall, since the material mostly goes in circles, little actual work gets done. So it's hard to calculate the ongoing energy requirements the whirling wall.

On the other hand, if the turbulent interior is in fact the interior of a pipe that's continously pumping fluid from the bottom of the molecular envelope up into the stratosphere, that represents real work requiring constant energy input, and the energy required to power that work must be accounted for. At a minimum, there must be enough power to accelerate 2.5 X 10¹⁴ kg s^-1 up to a velocity of 50 km s^-1 on the particular model being described here. In other words, the power source must be equivalent to the kinetic power going through the top of the GRS--3 X 10¹⁷ J s^-1.

On the theory that the GRS is a plasmavore, the required energy comes from the conversion of metallic hydrogen to molecular hydrogen. Saumon et al. (1995)'s Table 1. lists the ∆S across the PPT for various pressures and temperatures.

Let's assume that the temperature is 6,000 K (log[6000]=3.78), so that's the second line down, where it says the difference in entropy between the metallic and molecular states (∆S) is 0.590k_B. Multiplying by the gas constant R (which is equal to the product of Boltzmann's and Avogadro's constants) converts this figure into SI units, which equals 4.91 J mole^-1 K^-1. If we further assume that the Gibbs free energy of the phase change is zero (which is reasonable, since we aren't compressing any gasses), according to the standard formula for calculating the enthalpy (latent heat) of a phase change is:

∆H = T∆S

that yeilds:

6000^o K * 4.91 J mole^-1 K^-1 ~ 30 kJ mole^-1

Since 1 mole of protons is equivalent to 1 gm of hydrogen, the latent heat liberated by converting metallic hydrogen to molecular hydrogen is roughly 3 X 10⁷ J kg^-1 K^-1. Now we can calculate the mass flux of metallic hydrogen required for a power source:

3 X 10¹⁷ J kg
------------- = 10¹⁰ kg s^-1
s 3 X 10⁷ J

If we assume a helium mass fraction of ~0.25, then the total flow of material extracted from the metallic region is about 1.3 X 10¹⁰. This is only about 0.005% of the total mass flux through the interior of the GRS. Earlier I had suggested that perhaps all the material sucked out by the GRS comes from beyond the PPT. The above calculations show what a crazy idea that was. If all the hydrogen that was pumped started out as metallic hydrogen, that would generate ~ 5 X 10²¹ watts or about 10,000 times the Jupiter's intrinsic power.

How it Works

Very little material is being scooped up from the PPT. What happens is that like a waterspout, a small "cloud" of metallic hydrogen "droplets" will be kicked up a the base of the GRS. Ordinarily, within terran tornados, such debris tends to weaken the tornado, but with the GRS the effect is the opposite. As the metallic hydrogen droplets get sucked up into the GRS, they rise and the pressure decreases to the point where they will undergo the phase transition to molecular hydrogen, thus releasing their latent heat and reinforcing the convection.



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The silence is deafening, because you keep from defining your problem in detail, and overwhelm us with your calculations that we cannot check, because we have not the knowledge to follow your reasoning.

Like, you say that mainstream has found from data that the GRS is a pancake and you assume it is a very long tornado.

In the flow in the pipe you come up with an ad-hoc transport of XXX mole/sec through the pipe.

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

You know, I'm beginning to think that might not be a coincidence.

The amount of actual mass removed from the PPT almost seems trivially small. Earlier, I had written that a prediction of the plasmavore model is that the GRS should be enriched in helium. But even if the metallic zone were 90% helium (and that's totally outside the realm of sane possibility), it would increase the GRS He volume mixing ration from 0.136 to 0.1361--well below even the Gallileo atmospheric probe's precision.

However, on longer time scales, the amount of material removed from the PPT might possibly be significant if the Great Red Spot or ones like it have existed pretty much since Jupiter became a going concern. Jupiter is 314 Earth masses. If 14 of those are sequestered in the core, and the molecular envelope takes up 10% of the rest, that leaves a metallic envelope of about 270 Earth masses, or 1.6 * 10²⁷ kg. Thus the turnover time of the metallic zone would be on the order of 4-5 billion years--about the age of the solar system. On the other hand, the turnover time of the molecular envelope would be only 400 million years. This result entails that the molecular envelope will track variations in helium abundance within the metallic zone as long as it takes longer than 400 million years for the He abundance to change significantly. Since helium "rain" is a very slow process, it's quite likely that the metallic (at least within the upper, miscible region) and molecular zones should have similar helium mass fractions (Y).

Perhaps even more significant, however, is the energy flux. As noted in post #78, the energy flux through the GRS is basically equal to the intrinsic power of Jupiter. This represents a true consilence:

On the one hand, we have a set of facts, the observed luminosity of Jupiter less the solar flux intercepted by Jupiter, and on the other, an energy flux based on typical upwelling rates within Jupiter, the diameter of the inner, turbulent zone within the GRS, and the observed composition and density of the Jovian atmosphere--and both sets of facts agree quite well.

Assuming this agreement is not a coincidence could have important implications for models of the interior of Jupiter. A conundrum in current theory is the respective effective temperatures of Jupiter and Saturn. Early models of the thermal evolution Jupiter and Saturn assumed that the sole source of internal heat was gravitational contraction. This worked fine for Jupiter in that it predicted that Jupiter should be at the temperature that we observe at its present age of 4.5 billion years. Saturn, however, should have achieved its present temperature 2 billion years ago, according to the early "homogeneous" models (e.g., Grossman et al. 1980)--so-called because they assume no phase separation between hydrogen and helium

So in order to save the situation, it was realized that at high enough pressures and temperatures where hydrogen becomes fully ionized (at the PPT, the metallic hydrogen is a mixture of neutral H and H⁺), helium becomes immiscible, so that it forms "droplets" that outweigh the forces of convection, and this helium "rain" then settles around the ice/rock core. Such helium sedimentation would release gravitational potential energy that would be converted to heat, and thus slow down the cooling rate of gas giant planets like Jupiter and Saturn. This theory has worked great for Saturn in that Saturn's temperature can now be reconciled with its age; but now Jupiter suffers from the opposite problem.

Jupiter's observed helium mass fraction Y as observed by the Galileo probe is about 0.23 compared to a protosolar value of 0.27. The natural explanation for this discrepancy is helium sedimentation, but under the EOS's that make Saturn's temperature and age work out, Jupiter should be hotter than it is now, and so now researchers are wondering if "some other factor must be involved that without helium separation would allow the planet to cool more quickly than current homogeneous models predict" (Fortney and Hubbard 2003, 29).

One theory that's been hot lately is the erosion of core material. The theory is that core material is eroded by downwelling plumes and then is swept up against gravity into the metallic envelope, so that some of the internal heat is converted back to gravitational potential energy, thus leading to a lower overall luminosity. I haven't delved into this too much, but one problem that immediately leaps out to me is that if core erosion is intended to counterbalance the heating effects of helium sedimentation, then how is it that the core is supposed to be eroded without sucking up the precipitated helium as well?

The plasmavore model of the GRS, however, can perhaps offer a cooling mechanism.

According to the mainstream three-layer model, heat is generated in Jupiter's interior by gravitational contraction and helium sedimentation. This heat is transported convectively to the PPT, where there is an entropy jump, and which therefore forms an "impenetrable barrier" to convection. So heat is transported across the PPT via radiative conduction, and then convection once again takes over, and carries the heat into the upper atmosphere where it is radiated into space.

On the plasmavore model, the GRS removes enough metallic hydrogen from the PPT to cause it to lower in depth by about 1 cm year^-1. However, on short time scales at least, the pressure and temperature conditions don't change, so the metallic hydrogen removed by the GRS will have to be replaced with H₂ from the molecular envelope. The energy required for this phase change comes from the interior. So what happens is gravitational contraction and helium sedimentation generate heat, this heat is transported convectively to the PPT where it converts H₂ into metallic hydrogen. The GRS then sucks out an equivalent amount of metallic hydrogen, and pumps the resultant latent heat into the upper atmosphere where it radiates to space.

So the question naturally arises: What's to stop the GRS from taking more metallic hydrogen than can be regenerated by the interior heat flux? Well, what would happen is that the energy for the latent heat absorption required to replace the lost metallic hydrogen in excess of that which the interior is able to provide would have to come from the lower boundary layer of the molecular envelope--where else? But this shouldn't be a problem because the molecular envelope now has the extra energy pumped into it by the GRS, and convection will ensure that this excess heat energy will eventually be transported back down to the PPT where it can be used to regenerate metallic hydrogen. So it all goes round and round, and the luminosity matches the interior intrinsic power. The problem is that not only is there no net cooling effect were such to happen, but such an analysis would seemingly show that the size of the GRS is arbitrary, and so the apparent fact that its power equals the intrinsic power really is a coincidence after all.

However, consider that the GRS isn't ordinary convection: it's a fast track from the interior to the stratosphere that moves 50 to 500 times faster ordinary convection. So, if the GRS removed more metallic hydrogen than could be regenerated by the intrinsic power, then hot energetic material would be pumped into the upper atmosphere, while the lower boundary layer at the PPT would be supercooled because of the heat extracted in order to make up the metallic hydrogen deficit.

The result is a classic temperature inversion (where warm, low density material overlies cold, dense material), and that will stifle convection.

Because of the temperature inversion, heat will not flow back downwards to help recharge the PPT; hence, the observable luminosity less solar absorption will exceed the intrinsic power, resulting in extra cooling. Meanwhile, as the planet cools, the PPT will sink because as the temperature declines, it takes more pressure to make metallic hydrogen.

As the PPT sinks, the pressure at the mouth of the GRS will increase, thus constricting the opening, and reducing the mass flux. If this process were carried out to its logical conclusion, the mouth would eventually be pinched off, and the flow of matter and energy shut off. The GRS would then "rope out" like a dissipating tornado on Earth, as the plasmavore starved to death. But this doesn't happen because once the power of the GRS was reduced to that of the intrinsic power, further sinking of the PPT would cease, except for that resulting from the ordinary cooling of the planet, and the current dynamic equilibrium that we observe today would prevail.

And so, the GRS could explain the apparent differences in cooling rates between Saturn and Jupiter. Saturn probably never had red spots because of its weaker gravity; the PPT on Saturn was way too far down for an ordinary vortex to reach, and thus red spots could never gain a foothold there.

So, the plasmavore model suggests that the GRS is basically a permanent fixture on Jupiter. Moreover, it suggests that in earlier times when the PPT was closer to the surface, the GRS was probably much bigger than it is today. This suggests that extrasolar gas giants of Jupiter's mass and larger probably also have red spots, and that these planets cool faster than the standard models would suggest. If such a planet early in its evolution could be resolved by a superpowerful telescope, the extra-large red spot predicted by the plasmavore model should show up as a variation in luminosity timed to match the rotation of the planet.

I tried to rephrase the problem clearly in post #78, incorporating the results of several days of mathematical calculations and literature reviews. If there's something you don't understand, please feel free to ask about it.

It's a stretch to say that the pancake model was "found from data". It was arrived at because 2-dimensional numerical simulations are easier to do than 3D simulations.

I arrived at my figure of 50 m s^-1 from the following passage from page 46 of Guillot et al. (2004) in Jupiter: the Planet, Satellites, and Magnetosphere:

So, I figured that if the latent heat released from water condensation can drive updrafts of 10s of meters per second, then latent heat released by metallic hydrogen condensation should be able to achieve at least similar velocities. Like I said in post #78, I was mainly interested in an order-of-magnitude estimate, so don't quote me as saying that the updraft in the GRS is exactly 50 m s^-1. I stated my reasons for why I thought that 50 m s^-1 was a not unreasonable ballpark figure suitable for back-of-the-envelope calculations for exploring the implications of the plasmavore model. If you don't think that 50 m s^-1 is reasonable, then you should state your reasons why you think 5 m s^-1 or 500 m s^-1 or 0.0 m s^-1 would be more reasonable.

Thanks for commenting, tusenfem.

EDIT: If I seem to go into excruciating detail with my algebra, it's because I don't trust myself to get it right--I've triple-checked the math myself, but I don't doubt there are mistakes.

The metallic envelope, of course! I should have thought of that. . . .

While convection in the molecular envelope would be slowed by latent heat absorption at the PPT, thermal instability would actually be enhanced in the metallic envelope. So, because radiative transfer would dominate in the molecular envelope and convective transfer would prevail in the metallic envelope, the primary heat resource would still come from the metallic layer no matter how much metallic hydrogen in excess of the intrinsic power the GRS pumped out. As the metallic envelope cools, the PPT sinks, the pressure on the throat of the GRS increases, and the rate of cooling slows until an equilibrium is reached where the power pumped out equals the intrinsic power.

So, quite literally, the PPT and the GRS function as a cyclic, heat absorption, refrigeration unit. Metallic hydrogen "condenses" into molecular hydrogen, the stratosphere functions as a heat exchanger, space is the heat sink, and elsewhere along the PPT, the PPT is the evaporator that absorbs heat, causing local cooling. You could say the GRS is Jupiter's air conditioner.

Actually, the GRS/PPT/stratosphere systemisn't a heat absorption refrigerator at all--it's more of a strange sort of mechanical refrigerator. In an ordinary refrigerator, a compressor compresses the vaporized refrigerant (e.g, freon or ammonia). As the refrigerant condenses back to liquid, latent heat is released and radiates away. The liquid refrigerant then passes through an expansion valve that lowers the pressure of the refrigerant and sends it into the zone to be cooled. There, the refrigerant boils back into vapor, and boiling requires inputs of heat, so it sucks heat out of the zone to be cooled, thus lowering its temperature. The compressor then recompresses the vaporized refrigerant, and the process is repeated.

On Jupiter, gravity serves the function of the compressor, the GRS is the expansion valve that releases the pressure, and hydrogen is the refrigerant. Hydrogen on Jupiter is very weird, however, in that it behaves just the opposite of ordinary, Terran refrigerants. That is, on Jupiter, compression drives a phase change by causing molecular hydrogen vapor to "condense" into metallic hydrogen--but the condensation absorbs heat! Then the GRS releases the pressurized metallic hydrogen, where it "boils" back into molecular hydrogen vapor--but the boiling releases latent heat!

The attached figure would be a good schematic of what happens on Jupiter if the arrow in the drawing was reversed. "A" is the metallic envelope in the interior of Jupiter that is being cooled; "C" is the Great Red Spot; the purple and red coil is the stratosphere that radiates away the excess heat, and "B" is the gravitational "compressor".

Attached Thumbnails

 

Due to the extreme size of the GRS I looked at a reference to turbidity and was wondering if the flow rates might need a whole new system to describe them. It is just so big that if the walls of the storm had sufficient altitude there could also be a vacuum effect as a driver.

The upper level of the storm if it was high enough may be in a vacuum region of immense size by comparison to the base of the storm. This article on turbidity here

It goes into the charge particle effect in filters dust and sand but the point is the size of the GRS would be if an electrical component is present was there any variation to the measure of the GRS around the time the comet Holmes experienced the million fold increase in brightness?

As the gravity of Jupiter draws the weight of the storm down and the atmosphere provides the negative pressure to hold the sides of the storm out it may be a vacuum driven system and very different to pipe flow dynamics as we know them on earth.

That's basically what I'm saying, that the GRS functions as a vortex tube, but with a turbulent inner flow.

Turbidity is just a measure of how much crud is mixed in with a given fluid. I don't see how that would be very relevent, given that hydrogen and helium are the dominant species.

The GRS naturally varies through time; it would be difficult to point to any particular variation and say for sure that it was caused by comet Holmes.

I don't doubt that.

I'm having horrible deja vu that I came across this whole idea in the stacks at some university library several years ago and that there must be some reason the theory never caught on. . . .

Edit: it's the Av³ thing. It seems awful familiar.

The Great Red Spot as a plasmavore:

An alternate cooling mechanism for Jupiter?

Warren J. Platts

Dept. of Philosophy, Colorado State University, Fort Collins, CO 80523
Author E-mail address: warrenplatts@comcast.net


Pages: 10

1. Introduction

Traditional approaches to modeling the Great Red Spot of Jupiter typically assume a two-dimensional “pancake” shape, and attempt to reproduce the major features of the GRS from the first principles of fluid dynamics (e.g., Marcus 1993). An alternative approach might be to ask, “If I were the GRS, what would I like to eat?” (cf. Dennett 1971). The obvious answer is metallic hydrogen. If the GRS was a vortex tube extending to the plasma phase transition (PPT), small amounts of metallic hydrogen would be entrained in the updraft and converted to molecular hydrogen releasing latent heat; the latent heat would provide lift, and the process would become self-sustaining. Such a system is analogous to the degassing operations on Lake Nyos and Monoun, Cameroon (Kling et al. 2005); a pipe is extended from the surface to the CO₂ saturated bottom layer; once flow is mechanically initiated, bubbles of CO₂ form providing lift, and the flow becomes self-sustaining.

Reasonable assumptions yield a net energy flow through the GRS that is equivalent to Jupiter's intrinsic power. One is tempted to theorize that the power levels are in dynamic equilibrium.

The GRS could provide a cooling mechanism that would reconcile inhomogeneous models of the thermal evolution of Jupiter and Saturn. Early homogeneous models (no helium-hydrogen phase separation) accurately predicted the evolution of Jupiter, but found that Saturn should have achieved its present effective temperature over two billion years ago (Grossman et al. 1980). However, inhomogeneous models that invoke helium phase separation and sedimentation within the fully ionized regions of the metallic envelope can prolong Saturn's cooling long enough to reconcile its predicted effective temperature with the observed temperature (Fortney and Hubbard 2003).

Jupiter's helium mass fraction Y determined by the Galileo probe is 0.231 compared to a protosolar value of 0.27 (Guillot et al. 2004). The natural explanation for this discrepancy is helium phase separation, but under the EOS's that make Saturn's temperature and age work out, Jupiter should be hotter than it is now (Fortney and Hubbard 2003). Consequently, there may be some other mechanism for cooling. One suggestion is core erosion and redistribution (Guillot et al. 2004). An alternative explanation is that the flow of the GRS is controlled by the depth of the PPT. In the early stages of Jupiter's history, the PPT was perhaps closer to Jupiter's surface. At that time, the GRS or its equivalent may have been much larger than it is now, allowing transformation of metallic hydrogen into molecular hydrogen at a rate faster than could be recharged by the intrinsic power. The GRS-driven cooling would cause the PPT to sink, constricting the flow through the GRS until the power of the GRS matched the intrinsic power.

2. The plasmavore model

The GRS is a singular example of a persistent, annular vortex. It consists of an anticyclonic, high-velocity "collar" that surrounds a broad quiescent interior (Shetty et al. in press, Fig. 1). The interior can be described by an ellipse with an area of 3 x 10⁷ km².

The model presented here assumes the interior is a turbulent updraft within a vortex tube formed by the collar. Since condensation of water on Jupiter drives convective updrafts in the tens of m s^-1 (Guillot et al. 2004), it is reasonable to suppose that latent heat released by the conversion of metallic hydrogen to molecular hydrogen could lead to similar velocities. The mass flow rate through the vortex tube is derived from the ideal gas law (pV = nRT):

(1) Mass flow _GRS = M_JAvp / RT

where MJ is the average molar mass of the Jovian atmosphere, A is the area of the turbulent interior of the GRS at the cloud deck, and v is the average velocity of the updraft. The net power of the GRS is given by:

(2) P_GRS= M_J Av³p / 2RT

Given pressure of 1 bar, temperature of 170° K, average molar weight of 2.341 gm mole^-1 (Taylor et al. 2004, Tab. 4.2), and average velocity of 50 m s-1, the total mass flow through the vortex tube would be 2.5 x 10¹⁴ kg s^-1 having a power of 3.1 x 10²⁴ erg s-1, compared to Jupiter's intrinsic power of 3.350 x 10²⁴ erg s^-1 (Guillot et al. 2004, Tab. 3.3).

If the mass flow at the bottom of the vortex tube is the same as at the top, and the width of the vortex tube is barotropic, then the average velocity of the updraft is constant, and the area at the bottom opening of the vortex tube is given by

(3) A_bot ≈ mass flow_GRS / vρ

where ρ is the density of the molecular phase near the PPT. Assuming a density of 0.7 gm cm^-3 (Saumon et al. 1995), A_bot would be on the order of ~7 x 10³ km².

Equation 2 is highly sensitive to the chosen velocity, but we can see how Jupiter's intrinsic power constrains the plasmavore model if we considered what would happen if the GRS "ingested" more metallic hydrogen than could be recharged by the intrinsic power. The mass flow of metallic hydrogen required to power the GRS is:

(4) mass flow_met = P_GRSM_H / RT∆S

where M_H is the molar mass of metallic hydrogen, and ∆S is the positive entropy jump associated with the phase transition from metallic hydrogen to molecular hydrogen. If the entropy jump for the phase transition was 0.590 k_B per proton for a PPT temperature of 6000° K (Saumon et al. 1995, Tab. 1), the required flow of metallic hydrogen would be on the order of ~10¹⁰ kg s^-1. Such a flow would provide a significant mixing mechanism between the metallic and molecular envelopes: the turnover time for the metallic envelope would be on the order of ~10⁹ yr, but that for the molecular envelope would be on the order of ~10⁸ yr.

If the flow of metallic hydrogen was not replenished, the PPT could be expected to sink at a rate on the order of ~1 cm yr^-1; but on short time scales, the pressure and temperature surfaces would not be expected to sink as well. Thus, the flow of metallic hydrogen through the GRS would be balanced by an equal and opposite flow of molecular hydrogen into the metallic envelope elsewhere along the PPT; the phase transition from molecular hydrogen to metallic hydrogen will absorb heat energy equal to the energy liberated by the GRS. Extracting more latent heat than the intrinsic power, however, will cause the PPT to cool and sink. As the PPT sinks, the pressure on the throat of the GRS will increase, constricting the vortex tube, thus reducing the mass flow.

If the rate of latent heat extraction by the GRS was less than the intrinsic power, the temperature would increase, and the PPT would rise until the pressure on the throat of the GRS relaxed enough to allow a GRS net power equal to the intrinsic power (or the PPT reached the theoretical equilibrium depth it would have in the absence of the GRS). The net result of these opposing processes would be a dynamic equilibrium.

3. An alternate cooling mechanism

If the plasmavore hypothesis is true, the GRS functions quite literally as an expansion valve and gravity as a compressor in a natural refrigeration system. Hydrogen is the refrigerant, but it acts oppositely of ordinary refrigerants: the compression cycle converts molecular hydrogen to metallic hydrogen absorbing heat; the pressure drop induced by the expansion valve converts metallic hydrogen to molecular hydrogen releasing heat.

Early in Jupiter's evolutionary history, the depth of the PPT must have been less than it is now. Less pressure on the throat of the GRS would have allowed conversion of metallic hydrogen to molecular hydrogen at a rate higher than could be replenished by the intrinsic power. As the PPT cooled, the lower layers of the molecular envelope would cool, whereas the upper atmosphere would be receiving energy inputs from the GRS; the resulting temperature inversion would inhibit convection within in the molecular envelope while thermal instability in the metallic envelope would be enhanced. The natural refrigeration system that would result would speed up the thermal evolution of Jupiter.

The gravity of Saturn is much less than Jupiter; thus, the PPT on Saturn is at a much lower depth than on Jupiter. Presumably, the GRS is the evolutionary descendent of a large, ordinary vortex that formed from the fusion of other large vortexes; the plasmavore model suggests that there is a theoretical limit to the depth that large, self-sustaining, vortex tubes can reach, beyond which plasmavorous red spots are not sustainable. It is likely that the PPT depth on Saturn was always too low for a GRS analog to form; the above theoretical considerations would not affect inhomogeneous models of Saturn's evolution. In consequence, the plasmavore hypothesis can bring inhomogeneous evolutionary models of Jupiter and Saturn into closer agreement.

4. Future prospects

That the GRS is a tornado-like, gas-lift pump powered by latent heat released by the conversion of metallic hydrogen to molecular hydrogen, could explain some other puzzling aspects of Jupiter. Most obviously, the plasmavore hypothesis can explain why the Great Red Spot is red, while this aspect is difficult to explain if the GRS is a shallow, pancake-shaped vortex. In addition, the GRS can explain the overall south to north flow of the stratosphere as revealed by Comet S-L9 debris.

The plasmavore model of the GRS could have important implications for extrasolar gas giants. One prediction is that gas giants > M_JUP early in their evolution should have temperature inversions resulting from red spot activity; indeed, evidence has recently been found for the presence of such a temperature inversion on an extrasolar planet, HD 209458b (Knutson et al. 2007). Another prediction is that large red spots should form on planets early in their evolution that would induce a noticeable visual contrast. Consequently, one can expect variation in observable infrared radiation in larger gas giants with large orbital separations from their parent star (e.g., 2M1207b) or on so-called "rogue" planets (e.g., Cha110913-773444).

References

Dennett. D. 1971. Intentional systems. J. Philosophy 68, 87-106.

Fortney, J.J., Hubbard, W.B. 2003. Phase separation in giant planets: Inhomogeneous evolution of Saturn. Icarus 164, 228-243.

Grossman, A.S., Pollack, J.B., Reynolds, R.T., Summers, A.L., Groboske, H.C., Jr. 1980. The effect of dense cores on the structure and evolution of Jupiter and Saturn. Icarus 42, 358-379.

Guillot, T., Stevenson, D.J., Hubbard, W.B., Saumon, D. 2004. The interior of Jupiter. In: Bagenal, F., Dowling, T.E., McKinnon, W.B. (Eds.), Jupiter: The Planet, Satellites and Magnetosphere. Cambridge Univ. Press, New York, pp. 35-57.

Kling, G.W., Evans, W.C., Tanyileke, G., Kusakabe, M., Takeshi, O., Yoshida, Y. 2005. Degassing Lakes Nyos and Monoun: Defusing certain disaster. Proc. Nat. Acad. Sci. 102, 14185-14190.

Knutson, H.A., Charbonneau, D., Allen, L.E., Burrows, A., Megeath, S.T. 2007. The 3.6-8.0 micron broadband emission spectrum of HD 209458b: Evidence for an atmospheric temperature inversion. Astrophys. J., in press.

Marcus, P.S. 1993. Jupiter's Great Red Spot and other vortices. Annual Review of Astronomy and Astrophysics 31, 523-573.

Saumon, D., Chabrier, G., Van Horn, H.M. 1995. An equation of state for low-mass stars and giant planets. Astrophys. J. Suppl. 99, 713-741.

Shetty, S., Asay-Davis, X.S., Marcus, P.S. 2007. On the interaction of Jupiter's Great Red Spot and zonal jet streams. J. Atmos. Sci., in press.

Taylor, F.W., Atreya, S.K., Encrenaz, Th., Hunten, D.M., Irwin, P.G.J., Owen, T.C. 2004. The composition of the atmosphere of Jupiter. In: Bagenal, F., Dowling, T.E., McKinnon, W.B. (Eds.), Jupiter: The Planet, Satellites and Magnetosphere. Cambridge Univ. Press, New York, pp. 59-78.

An analog model of the GRS theory presented here might be an apparatus consisting of two cylindrical tanks, each wider than it is tall, stacked on top of each other. The would preferably be clear or at least equipped with a viewing window. The bottom tank would be sealed, except for two small drain holes in the top and bottom in the center. The top tank drains into the lower. The top tank would have colorant added to observe the flow.

First step is to get the lower water rotating, either by stirring or rotating the whole tank. The top tank is then set on top, and the lower drain plug removed, so that the as water drains out, it is replaced by water from the upper tank.

Thus, the upper tank is analogous to the plasma phase transition, the lower tank is analogous to the molecular envelope, and the lower drain represents the entrance to the stratosphere in the upper atmosphere (so everything's upside down--gravity simulates the latent heat energy released by the phase transition from metallic to molecular hydrogen. According to the plasmavore model, it's possible for material to flow from one layer through an intermediate, middle layer into a third layer with little mixing with the middle layer.

So, the question is, will the water from the top tank form a stable vortex and drain straight through, or will most of the water drain out from the lower tank, to be refilled slowly from the top down? The plasmavore model of the GRS predicts that a stable vortex will form, so that most of the water draining out of the lower tank will actually come from the upper tank, with little mixing with the lower tank water.