Titan's dunes

[chris]

Cassini investigator Ralph Lorenz has an interesting presentation on dunes of Titan:

http://saturn.jpl.nasa.gov/multimedia/p ... Lorenz.pdf

--Chris

[t00fri]

I would be interested to know what parameters determine the typical distance between individual dunes.

What's the spread in dune distances (riple wavelengths) one encounters on Earth? Or are the dune distance patterns roughly universal in certain parameter regimes? Do they depend mainly on average wind speeds?

+++++++++++++++++
How do the dune distances on Earth compare with those on Titan? Can I compute average wind speeds from the observed distances on Titan?
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etc.

Bye Fridger

[selden]

Apparently wind driven sand dunes have a relatively complex wavelength function: dune height affects wavelength, for example.

See http://www.nps.gov/archive/whsa/Sand%20 ... eology.htm

[t00fri]

Apparently wind driven sand dunes have a relatively complex wavelength function: dune height affects wavelength, for example.

See http://www.nps.gov/archive/whsa/Sand%20 ... eology.htm

Selden,

thanks for the URL. It does not surprise me that little universality of the ripple patterns is found in various scale regimes. Despite the complexity of the mechanisms involved, there might still be limited parameter domains where certain scale universalities are observed, corresponding to the balancing of various effects against each other.

If correct, such scale regimes would be interesting to search for on Titan...

Finally, here is one of many fascinating dune views from within my high-quality 64k texture set,


Bye Fridger

[LordFerret]

Those (dune) patterns are also amazingly similar in appearance to certain pattern features found in fingerprints... the thought of which is what immediately struck me in viewing that image.

Amazing detail in that texture set by the way!

[t00fri]

Let me get back a bit to some fascinating speculations about ~ universal/constant ripple distances in case of dunes and the possible origin of these characteristic ripples.

This is NOT stuff that you will easily find by just clicking the right WEB sites ...Hi Selden!

Unfortunately it involves somewhat advanced concepts of theoretical physics, namely a phenomenon that we call "spontaneous symmetry breaking (SSB)" . It is what happens in particle physics to provide mass to the so-called W,Z gauge bosons, but also occurs in many areas of classical physics.

The best known example of SSB that we usually teach our students is this: consider a vertical stick on top of which acts some weight. What are the preferred states of equilibrium? First note the axial symmetry of the force that acts along the stick. One possible solution is that this axial symmetry is retained, despite the pressure onto the top end of the stick. In this case, the stick is just compressed, but remains straight as it would be without the weight on top. That "ground state" is however VERY unstable, provided the compression force on top of the stick is sufficiently strong. The slightest perturbation will suffice to make the system switch into another "ground state" of less symmetry and lower energy: the stick bends by a certain amount under the pressure, until equilibrium is reached due to the elasticity of the stick. The force is still axially symmetric, yet the new "ground state" is NOT. This ground state is actually the stable one!

This is what we call "spontaneous symmetry breaking"

Note that there exist infinitely many, physically equivalent stable ground states for the bent stick! They correspond to arbitrary rotational orientations of the bent stick around the original axis.

I have witnessed some spectacular manifestations of spontaneous symmetry breaking when flying long distances along huge glacier fields at low altitude in helicopters in Greenland, watching the striking flow patterns of melting water...

What does SSB possibly have to do with the pattern of flowing off water at the end of glaciers or the regular ripple patterns of dunes?

Consider first the striking water flow patterns in case of glaciers. The unstable configuration of unbroken symmetry would have been that the water flows downhill over the morainal sand as a thin undisrupted film. Some slightest grainyness of the soil, however, suffices to make this uniform flow pattern switch to one, where many narrow canals of water flow downhill parallel to each other. That looks spectacular if viewed from above!

A characteristic feature of SSB is that the original symmetry does not tend to be broken completely. There is always a lower, so-called "rest-symmetry" that survives. In case of the glacier flows the rest symmetry is that the average distance between neighboring flow canals is constant. This constant canal distance represents a characteristic, i.e. universal length scale of the SSB phenomenon under consideration! What is actually the rest symmetry in case of our stick example??

Now I leave it to you to contemplate about the possible relation of SSB and the striking parallel ripple patterns in case of the dunes (cf. my Celestia image above!).

Again the unstable configuration would be that the wind transports the sand masses as a whole on account of the pressure it exercises on the sand. Slight disturbances might then again cause the sand layer to break up into ripples, again of characteristic "wavelength", being a manifestation of the "rest symmetry" remaining after SSB!.

Think about it

Bye Fridger

PS: For some more general reading about the concept of symmetry and the possibilities of symmetry-breaking, see e.g.

http://plato.stanford.edu/entries/symmetry-breaking/

[Scytale]

quite offtopic: I love popularized quantum physics, except for the fact that it reminds me all the time that we only have some control over one of the four interactions that we are aware of. That oughta put us in our place, and dim out human accomplishments for the next few hundred years or so

T00fri, to the best of your knowledge, is there any chance that they will open some parts of the LHC to the public for visitation (I've no doubt that at best it would be a very restricted and controlled tour... but I'd like it nevertheless).

[t00fri]

quite offtopic: I love popularized quantum physics, except for the fact that it reminds me all the time that we only have some control over one of the four interactions that we are aware of. That oughta put us in our place, and dim out human accomplishments for the next few hundred years or so

T00fri, to the best of your knowledge, is there any chance that they will open some parts of the LHC to the public for visitation (I've no doubt that at best it would be a very restricted and controlled tour... but I'd like it nevertheless).

Certainly, once the LHC has entered regular operations and a stable working condition, (guided) visits will be possible and are also important to establish "live contact" to the population. At my lab in Hamburg (DESY)

http://www.desy.de

regular guided tours are available to the population (Saturday) whenever the HERA collider is not running, of course.

Bye Fridger

[t00fri]

I just remembered a more explicit illustration of the classical example of spontaneous symmetry breaking that I was discussing above:

http://www.celestiaproject.net/~t00fri/images/wb1.pdf

It is from a very nice lecture on Theoretical Particle Physics that my wife gave in summer of last year for the DESY summer students,

http://www.desy.de/f/students/lectures2006/schrempp.pdf
http://www.desy.de/f/students/summer_lectures.2006.html

Bye Fridger