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/
