Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

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Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

Owen Densmore
Administrator
OK, so why hexagon?

Isn't this impossible as a weather artifact?  More likely a physical artifact on the surface?

   -- Owen

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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn's Hexagon Storm - News Watch

Nick Thompson

That’s exactly the way it looked in my sink two years ago.  So THERE you doubters and scorners.  Fie on you, all.  Vindicated at last. 

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

From: Wedtech [mailto:[hidden email]] On Behalf Of Bruce Sherwood
Sent: Saturday, December 14, 2013 8:41 PM
To: Wedtech@Redfish. Com
Subject: Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

 

Thanks for the link!

 

Remember that Saturn is a "gas giant", and it is thought that any solid surface is far below the top of the atmosphere. So no, I don't think it can be associated with a surface feature.

 

Note that Jupiter's Great Red Spot has stayed intact for hundreds of years (though it does show changes).

 

Bruce

 

On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:

OK, so why hexagon?

 

Isn't this impossible as a weather artifact?  More likely a physical artifact on the surface?

 

   -- Owen


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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn's Hexagon Storm - News Watch

Steve Smith



That’s exactly the way it looked in my sink two years ago.  So THERE you doubters and scorners.  Fie on you, all.  Vindicated at last. 

Looks like Jesus in the Tortilla to me! 

No... it doesn't look like a hexagon to me, it looks like a six-lobed 2D standing wave... with major (outward bulging lobes) at 60 degrees (X60) and of course, 30 degrees out of phase from these "minor" inward facing anti-lobes (and probably a whole series of harmonics on down to some much smaller scale).

My first thought was it was a "cam-gear".

I'm betting on Bruce and Ruth maybe giving us more insight?!

Cool!

- Steve
PS.  I had to check my calendar to make sure we weren't any where near April 1

 

Nick

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

From: Wedtech [[hidden email]] On Behalf Of Bruce Sherwood
Sent: Saturday, December 14, 2013 8:41 PM
To: Wedtech@Redfish. Com
Subject: Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

 

Thanks for the link!

 

Remember that Saturn is a "gas giant", and it is thought that any solid surface is far below the top of the atmosphere. So no, I don't think it can be associated with a surface feature.

 

Note that Jupiter's Great Red Spot has stayed intact for hundreds of years (though it does show changes).

 

Bruce

 

On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:

OK, so why hexagon?

 

Isn't this impossible as a weather artifact?  More likely a physical artifact on the surface?

 

   -- Owen


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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

Stephen Guerin
In reply to this post by Owen Densmore
On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:
OK, so why hexagon?

What about good old-fashioned Bénard hexagonal cells from convection?

eg: http://goo.gl/yQL2La 

Inline image 2

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On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:
OK, so why hexagon?

Isn't this impossible as a weather artifact?  More likely a physical artifact on the surface?

   -- Owen

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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

David Eric Smith
I would be surprised if this were it, Steve.

Benard cells are a packing phenomenon, so they rely on the cooperative effect through the lattice to form.  I assume this Saturn jet stream basically has a latitudinal instability, and the interference effect from having it recycle either adjusts the wavelength, or adjusts the position of the circumference, so that it finds a consistent re-entrant pattern.

A thing that would be very cool is if, as the northern-hemisphere summer goes on, enough more heat enters that part of the atmosphere that it drives the stream differently, the natural wavelength of the instability changes, and the belt goes into a new polygon like a pentagon, perhaps with a period of chaos or something else complicated in the transition.

But, I have never done a real fluid-dynamics calculation, so this is of course completely idle on my part.

Eric


On Dec 15, 2013, at 12:51 AM, Stephen Guerin wrote:

On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:
OK, so why hexagon?

What about good old-fashioned Bénard hexagonal cells from convection?

eg: http://goo.gl/yQL2La 


--- -. .   ..-. .. ... ....   - .-- ---   ..-. .. ... ....
1600 Lena St #D1, Santa Fe, NM 87505
office: (505) 995-0206 tollfree: (888) 414-3855
mobile: (505) 577-5828  fax: (505) 819-5952   
tw: @redfishgroup  skype: redfishgroup  gvoice: (505) 216-6226


On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:
OK, so why hexagon?

Isn't this impossible as a weather artifact?  More likely a physical artifact on the surface?

   -- Owen

_______________________________________________
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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

Gillian Densmore
I would like to say now: I thought I'd give understanding vortex's a whirl.
Boy did my head spin
:P
(thank you thank you! I'll be here all week! try the chicken!)



On Sun, Dec 15, 2013 at 3:48 AM, Eric Smith <[hidden email]> wrote:
I would be surprised if this were it, Steve.

Benard cells are a packing phenomenon, so they rely on the cooperative effect through the lattice to form.  I assume this Saturn jet stream basically has a latitudinal instability, and the interference effect from having it recycle either adjusts the wavelength, or adjusts the position of the circumference, so that it finds a consistent re-entrant pattern.

A thing that would be very cool is if, as the northern-hemisphere summer goes on, enough more heat enters that part of the atmosphere that it drives the stream differently, the natural wavelength of the instability changes, and the belt goes into a new polygon like a pentagon, perhaps with a period of chaos or something else complicated in the transition.

But, I have never done a real fluid-dynamics calculation, so this is of course completely idle on my part.

Eric


On Dec 15, 2013, at 12:51 AM, Stephen Guerin wrote:

On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:
OK, so why hexagon?

What about good old-fashioned Bénard hexagonal cells from convection?

eg: http://goo.gl/yQL2La 


--- -. .   ..-. .. ... ....   - .-- ---   ..-. .. ... ....
1600 Lena St #D1, Santa Fe, NM 87505
office: <a href="tel:%28505%29%20995-0206" value="+15059950206" target="_blank">(505) 995-0206 tollfree: <a href="tel:%28888%29%20414-3855" value="+18884143855" target="_blank">(888) 414-3855
mobile: <a href="tel:%28505%29%20577-5828" value="+15055775828" target="_blank">(505) 577-5828  fax: <a href="tel:%28505%29%20819-5952" value="+15058195952" target="_blank">(505) 819-5952   
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On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:
OK, so why hexagon?

Isn't this impossible as a weather artifact?  More likely a physical artifact on the surface?

   -- Owen

_______________________________________________
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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

Steve Smith
In reply to this post by David Eric Smith
Eric -

Nicely stated.

This is what I was fumbling around for... I am surprised not to be able
to find much if anything about this in the popular literature describing
the hexagon.

I'd not be surprised if an aspiring SF writer, following the footsteps
of Bob Forward wouldn't be able to integrate an event such as you
described into a good story.

I did find someone who did build an analog model that demonstrates
similar properties:

http://news.discovery.com/space/a-laboratory-model-of-saturns-eerie-hexagon.htm

This wouldn't be FRAIM without an element of idleness ;)

- Steve

> Benard cells are a packing phenomenon, so they rely on the cooperative
> effect through the lattice to form.  I assume this Saturn jet stream
> basically has a latitudinal instability, and the interference effect
> from having it recycle either adjusts the wavelength, or adjusts the
> position of the circumference, so that it finds a consistent
> re-entrant pattern.
>
> A thing that would be very cool is if, as the northern-hemisphere
> summer goes on, enough more heat enters that part of the atmosphere
> that it drives the stream differently, the natural wavelength of the
> instability changes, and the belt goes into a new polygon like a
> pentagon, perhaps with a period of chaos or something else complicated
> in the transition.
>
> But, I have never done a real fluid-dynamics calculation, so this is
> of course completely idle on my part.
>
>


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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

Steve Smith
In reply to this post by David Eric Smith
Eric sed:

But, I have never done a real fluid-dynamics calculation, so this is of course completely idle on my part.

http://news.discovery.com/space/a-laboratory-model-of-saturns-eerie-hexagon.htm

BTW, reading the text of their description, I realized why the structure looked like a "planetary cam gear" to me...   by their explanation, it may well be: 

Planetary in this case being the colloquial term for Epicyclic:
    http://en.wikipedia.org/wiki/Epicyclic_gearing

and Cam Gear  referring to the "teeth" of the gear devolving into lobes as if on a cam:


The "inner" vortex acts as the "sun gear" at the center and a set of eddies act as the "Planetary gears" and the "hexagon" we see acts as the outer "ring gear".

The article mentions that similar phenomena appear in hurricanes... I'm guessing (idly) that it is the alignment of this counter-rotating pattern with the (rotational?) pole of Saturn that allows it such long term stability not seen, for example, in hurricanes.

I suggested Bob Forward as a good figure to build a fiction about it, but it is Larry Niven (Ringworld and Integral Trees) that I think are a better inspiration.

- Steve


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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

Steve Smith
In reply to this post by Gillian Densmore
On 12/15/13 7:49 AM, Gillian Densmore wrote:
I would like to say now: I thought I'd give understanding vortex's a whirl.
Boy did my head spin
careful, you might cloud the issue more, as Doug suggested!


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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn's Hexagon Storm - News Watch

Nick Thompson
In reply to this post by David Eric Smith

Could somebody say a bit more about what we are looking at here.  Are we looking, as it appears, at a large proportion of the whole disc of Saturn, or are we looking at a round photograph of what could be a very small part of the whole disc of Saturn?  It must be the latter, right? 

 

N

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

 

From: Friam [mailto:[hidden email]] On Behalf Of Eric Smith
Sent: Sunday, December 15, 2013 3:48 AM
To: [hidden email]; The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

 

I would be surprised if this were it, Steve.

 

Benard cells are a packing phenomenon, so they rely on the cooperative effect through the lattice to form.  I assume this Saturn jet stream basically has a latitudinal instability, and the interference effect from having it recycle either adjusts the wavelength, or adjusts the position of the circumference, so that it finds a consistent re-entrant pattern.

 

A thing that would be very cool is if, as the northern-hemisphere summer goes on, enough more heat enters that part of the atmosphere that it drives the stream differently, the natural wavelength of the instability changes, and the belt goes into a new polygon like a pentagon, perhaps with a period of chaos or something else complicated in the transition.

 

But, I have never done a real fluid-dynamics calculation, so this is of course completely idle on my part.

 

Eric

 

 

On Dec 15, 2013, at 12:51 AM, Stephen Guerin wrote:



On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:

OK, so why hexagon?

 

What about good old-fashioned Bénard hexagonal cells from convection?

eg: http://goo.gl/yQL2La 

 

 

--- -. .   ..-. .. ... ....   - .-- ---   ..-. .. ... ....

1600 Lena St #D1, Santa Fe, NM 87505

office: (505) 995-0206 tollfree: (888) 414-3855

mobile: (505) 577-5828  fax: (505) 819-5952   

tw: @redfishgroup  skype: redfishgroup  gvoice: (505) 216-6226

 

On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:

OK, so why hexagon?

 

Isn't this impossible as a weather artifact?  More likely a physical artifact on the surface?

 

   -- Owen


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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

Stephen Guerin
In reply to this post by David Eric Smith
Here's the paper from the Oxford group Steve Smith mentioned:

As I watch this video, http://www.youtube.com/watch?v=60an32_Xses, it appears to me there is a cooperative effect arising from the six vortices on the outside of the hexagon. 

Inline image 2

I would take a layman's guess that the number of vortices change as a with the driving force of the ratio of the ring and tank velocities - though I haven't seen a video of this. 

Interesting to me, is the regime diagram in the paper, which describes the different polygon regimes and the chaotic regime as Eric mentioned:

Inline image 4

The authors describe the emergent hex as "wavemodes caused by the nonlinear equilibration of baro-tropically unstable zonal jets". 

And later: "In fluid-dynamical laboratory studies of various kinds of instability, patterns of waves or chains of vortices aligned in polygonal patterns are commonly found, regardless of the axisymmetric geometry used for the container. These can arise, for example, from a small differential rotation imposed on an already rotating fluid. Where the pattern extends completely around the experiment in a zonally periodic domain, this may form a regular, stable polygon and associated train of vortices. The zonal wavenumber or number of vortices observed depends on the wavelength that is most energetically favoured, which in turn depends on flow. parameters that take into account the strength of forcing as well as other geometric and dynamical factors of the system. Although the flow becomes non-axisymmetric during the instability, it typically remains vertically uniform so that both the polygon and vortices extend throughout the whole depth of the system, with coherence along a direction parallel to the axis of rotation and no phase tilt with height."

And in the summary "The trapping of fluid in vortices indicates the strongly nonlinear character of the equilibrated flow, whose stability and preferred lengthscale is ultimately determined more by vortex stability and transport optimisation arguments (Hollerbach et al., 2004; Polvani and Dritschel, 1993) than by linear perturbation theory. It is noteworthy that the vortices are more prominent in the dye visualisations than in the velocity field, which may explain why these features are not always easily identifiable in the observations of the hexagon."




--- -. .   ..-. .. ... ....   - .-- ---   ..-. .. ... ....
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office: (505) 995-0206 tollfree: (888) 414-3855
mobile: (505) 577-5828  fax: (505) 819-5952   
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On Sun, Dec 15, 2013 at 3:48 AM, Eric Smith <[hidden email]> wrote:
I would be surprised if this were it, Steve.

Benard cells are a packing phenomenon, so they rely on the cooperative effect through the lattice to form.  I assume this Saturn jet stream basically has a latitudinal instability, and the interference effect from having it recycle either adjusts the wavelength, or adjusts the position of the circumference, so that it finds a consistent re-entrant pattern.

A thing that would be very cool is if, as the northern-hemisphere summer goes on, enough more heat enters that part of the atmosphere that it drives the stream differently, the natural wavelength of the instability changes, and the belt goes into a new polygon like a pentagon, perhaps with a period of chaos or something else complicated in the transition.

But, I have never done a real fluid-dynamics calculation, so this is of course completely idle on my part.

Eric


On Dec 15, 2013, at 12:51 AM, Stephen Guerin wrote:

On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:
OK, so why hexagon?

What about good old-fashioned Bénard hexagonal cells from convection?

eg: http://goo.gl/yQL2La 


--- -. .   ..-. .. ... ....   - .-- ---   ..-. .. ... ....
1600 Lena St #D1, Santa Fe, NM 87505
office: <a href="tel:%28505%29%20995-0206" value="+15059950206" target="_blank">(505) 995-0206 tollfree: <a href="tel:%28888%29%20414-3855" value="+18884143855" target="_blank">(888) 414-3855
mobile: <a href="tel:%28505%29%20577-5828" value="+15055775828" target="_blank">(505) 577-5828  fax: <a href="tel:%28505%29%20819-5952" value="+15058195952" target="_blank">(505) 819-5952   
tw: @redfishgroup  skype: redfishgroup  gvoice: <a href="tel:%28505%29%20216-6226" value="+15052166226" target="_blank">(505) 216-6226


On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:
OK, so why hexagon?

Isn't this impossible as a weather artifact?  More likely a physical artifact on the surface?

   -- Owen

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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

Tom Johnson
If these systems move into a dynamic hexagonal mode, might it be possible that, if one could drill down into the thing, some fractal relationships would appear?

-tj


On Sun, Dec 15, 2013 at 9:54 AM, Stephen Guerin <[hidden email]> wrote:
Here's the paper from the Oxford group Steve Smith mentioned:

As I watch this video, http://www.youtube.com/watch?v=60an32_Xses, it appears to me there is a cooperative effect arising from the six vortices on the outside of the hexagon. 

Inline image 2

I would take a layman's guess that the number of vortices change as a with the driving force of the ratio of the ring and tank velocities - though I haven't seen a video of this. 

Interesting to me, is the regime diagram in the paper, which describes the different polygon regimes and the chaotic regime as Eric mentioned:

Inline image 4

The authors describe the emergent hex as "wavemodes caused by the nonlinear equilibration of baro-tropically unstable zonal jets". 

And later: "In fluid-dynamical laboratory studies of various kinds of instability, patterns of waves or chains of vortices aligned in polygonal patterns are commonly found, regardless of the axisymmetric geometry used for the container. These can arise, for example, from a small differential rotation imposed on an already rotating fluid. Where the pattern extends completely around the experiment in a zonally periodic domain, this may form a regular, stable polygon and associated train of vortices. The zonal wavenumber or number of vortices observed depends on the wavelength that is most energetically favoured, which in turn depends on flow. parameters that take into account the strength of forcing as well as other geometric and dynamical factors of the system. Although the flow becomes non-axisymmetric during the instability, it typically remains vertically uniform so that both the polygon and vortices extend throughout the whole depth of the system, with coherence along a direction parallel to the axis of rotation and no phase tilt with height."

And in the summary "The trapping of fluid in vortices indicates the strongly nonlinear character of the equilibrated flow, whose stability and preferred lengthscale is ultimately determined more by vortex stability and transport optimisation arguments (Hollerbach et al., 2004; Polvani and Dritschel, 1993) than by linear perturbation theory. It is noteworthy that the vortices are more prominent in the dye visualisations than in the velocity field, which may explain why these features are not always easily identifiable in the observations of the hexagon."




--- -. .   ..-. .. ... ....   - .-- ---   ..-. .. ... ....
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On Sun, Dec 15, 2013 at 3:48 AM, Eric Smith <[hidden email]> wrote:
I would be surprised if this were it, Steve.

Benard cells are a packing phenomenon, so they rely on the cooperative effect through the lattice to form.  I assume this Saturn jet stream basically has a latitudinal instability, and the interference effect from having it recycle either adjusts the wavelength, or adjusts the position of the circumference, so that it finds a consistent re-entrant pattern.

A thing that would be very cool is if, as the northern-hemisphere summer goes on, enough more heat enters that part of the atmosphere that it drives the stream differently, the natural wavelength of the instability changes, and the belt goes into a new polygon like a pentagon, perhaps with a period of chaos or something else complicated in the transition.

But, I have never done a real fluid-dynamics calculation, so this is of course completely idle on my part.

Eric


On Dec 15, 2013, at 12:51 AM, Stephen Guerin wrote:

On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:
OK, so why hexagon?

What about good old-fashioned Bénard hexagonal cells from convection?

eg: http://goo.gl/yQL2La 


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On Sat, Dec 14, 2013 at 8:31 PM, Owen Densmore <[hidden email]> wrote:
OK, so why hexagon?

Isn't this impossible as a weather artifact?  More likely a physical artifact on the surface?

   -- Owen

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J. T. Johnson
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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

Arlo Barnes
On Sun, Dec 15, 2013 at 1:27 PM, Tom Johnson <[hidden email]> wrote:
If these systems move into a dynamic hexagonal mode, might it be possible that, if one could drill down into the thing, some fractal relationships would appear?
Hm. What was your thinking behind that?

When I first heard (a few years ago) that Saturn had a hexagon, the source suggested it might have a cymatic cause, which it seems to me is basically saying the same thing as Eric's phrasing. I believe it also claimed there were similar less prominent patterns in the other gas giants, lemme try to find it:

Edit: Okay, so it seems as usual a few people have proposed this idea. I had forgotten how cymatics had been embraced by the fringe, so some sources are a little sketchier looking than others - or as one blogger said, "I discovered that Cymatics aka Tonoscope has a trail of New Age websites in Google. All claiming eternal life when listening to vibrations...?! But peculiar it is." (Another blog counters "When it comes to bizarre phenomena like this, all the explanations sound far-fetched because the universe is more bizarre than we imagine.")
Several of the sites look familiar; I leave you to do the search, but the page that was most likely the one to have introduced me to the phenomenon was this one. No mention of other gas giants, must have been my imagination.

Although the flow becomes non-axisymmetric during the instability, it typically remains vertically uniform so that both the polygon and vortices extend throughout the whole depth of the system, with coherence along a direction parallel to the axis of rotation and no phase tilt with height.
It seems this would change with differently-curved space (as induced by the gravity of Saturn) and indeed, we see <a href="http://Although the flow becomes non-axisymmetric during the instability, it typically remains vertically uniform so that both the polygon and vortices extend throughout the whole depth of the system, with coherence along a direction parallel to the axis of rotation and no phase tilt with height.&quot;">no south-polar hexagon.

What we really need is a probe more durable than anything we have produced so far that we can just drop into Saturn/Jupiter/what have you to see what is in there. There is (as always) an appropriate Clarke short story: A Meeting with Medusa.

-Arlo James Barnes

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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn's Hexagon Storm - News Watch

Arlo Barnes
In reply to this post by Nick Thompson
On Sun, Dec 15, 2013 at 9:40 AM, Nick Thompson <[hidden email]> wrote:

Could somebody say a bit more about what we are looking at here.  Are we looking, as it appears, at a large proportion of the whole disc of Saturn, or are we looking at a round photograph of what could be a very small part of the whole disc of Saturn?  It must be the latter, right?

So we now have a collection of old and new images from Voyager and Cassini (I remember when somebody told me about Cassini/Huygens circa 2003, I expected great things, especially from Huygens. Turns out that while pictures from the slushy surface of Titan are neat, the orbiter yielded better long-term rewards) and some are better than others.
Inline image 1
-Arlo James Barnes

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Re: [WedTech] Fwd: Cassini Photo: Stunning New Views of Saturn’s Hexagon Storm – News Watch

Stephen Guerin
In reply to this post by Tom Johnson
On Sun, Dec 15, 2013 at 1:27 PM, Tom Johnson <[hidden email]> wrote:
If these systems move into a dynamic hexagonal mode, might it be possible that, if one could drill down into the thing, some fractal relationships would appear?
 
"Big whirls have little whirls that feed on their velocity,
and little whirls have lesser whirls and so on to viscosity."    




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