Saturday, November 10, 2007

Gravity Waves in the Sky

This is what I've seen this Wednesday morning when I looked out of my window:

The sky way grey and overcast, but there was a distinct, wavy pattern in the cloud cover, like ripples on water, or on sand:

The similarity to waves on a water surface is not by chance - in fact, the physical phenomenon, called gravity waves [1] or buoyancy waves, is the same: If two layers of different fluids meet at an interface, disturbances of the interface can spread as waves. For waves on a water surface, the fluids are the water, and the air above it.

But the same can also happen at surfaces between layers of water with different density, for example with different salinity and temperature, or at the interface between distinct layers of air. If the upper layer of air is below the dew point and carries a close cover of cloud, disturbances of the interface layer can show up as a wavy pattern in the ceiling - it's just the same as waves on water. However, since the differences in density between the two fluids are much smaller in the atmosphere than at the interface water-air, the wavelength of gravity waves in the atmosphere is much longer, and the frequency is lower.

But they can look quite impressive, if they come as Giant Atmospheric Waves Over Iowa.

[1] Be careful not to mix up gravity waves - waves at the interface of fluids in a gravitational field - and gravitational waves - undulating disturbances of the space-time metric.


  1. Thanks for this nice post!

    It took me a while to recognize the building in the background! They've really added a lot of office buildings there. Coincidentally, in one of the last 'Physik Journal' issues there was an article on the almost periodic ripples that form on loose shoulder (recall them from South Africa?) I guess that's a similar effect? Will see if I find the reference (though I think I've unfortunately thrown away the issue yesterday). Best,


  2. Stefan,

    Nice pictures! One slight quibble: I don't think you need a definite interface to support gravity waves, just a density that varies with height - which could be considered just continuous set of density interfaces.

  3. "Waschbrettpisten im Labor" Dirk Kadau, Physik Journal Oct 2007, (unfortunately I realized I've forgotten not only my password but also my login name for the DPG and I'm afraid the email account I'm registered with doesn't exist anymore, so complete login failure).

    References to this article

    Washboard Road: The Dynamics of Granular Ripples Formed by Rolling Wheels

  4. Don't know if this actually happens, but when black holes merge would the gravity waves in the horizon be radiated away as gravitational waves?

  5. Hi CIP,

    I'm not sure what you mean with 'gravity waves in the horizon'. In case that's what you mean: because of the no-hair theorem a (classical) black hole needs to settle down in a state with a 'ripple-free' horizon, and the ripples are emitted in gravitational waves. Related: in case you haven't seen it, there is a stunningly beautiful movie (~7.5 MB Quicktime) for gravitational wave emission in the merging of two black hole. More info here. Best,


  6. Hi Bee,

    I wonder of gravity waves are visible?

    They may be detectable?

    The gravity wave of the Earth relative to the Sun may have a period of 365.25 Earth days as a helical function?

  7. Hi Bee,

    Nice cloud images! Had never seen anything like the "gravity waves" in the video you linked to. The finer ripple patterns in your photos are probably due to the Kelvin-Helmholtz effect. That may be involved in the larger waves also. (For sure it's present in sand ripples.)

    The self-organization in those waves is interesting. It's popular to think of particles as little irreducible building blocks out of which the universe is constructed. (Bottom up approach.) I like the idea particles are self-organizing things that also depend on large-scale properties of the environment they arise in. (Top down.) A little like these oscillons.



  8. Oops,

    Sorry Stefan! I should have addressed that to you.

  9. Did you take this pictures in Frankfurt??

  10. Hi Maurizio,

    yes, the photo was taken Wednesday morning in Frankfurt - the building you can see in the centre is the Torhaus tower at the S-Bahn Station "Messe".

    I have to say I was a bit appointed by the quality of the photo - the real "waves and ripples" impression was much better than what can be conveyed by the photo. I had to increase "by hand" the contrast and that "gamma" factor so that one can see something at all.

    Dear Bee,

    playing around a bit with brightness and contrast to bring a better visibility to the patterns in the cloud cover made the foreground completely dark - otherwise you would have recognized the buildings more easily...

    Thank you for the reference to the Physik-Journal - I somehow had missed that article when browsing the October issue..

    Best, Stefan

  11. This a opportunity to get "two birds" with one stone?

    I was thinking of Garrett's E8 article and Stefan's here.

    On March 31, 2006 the high-resolution gravity field model EIGEN-GL04C has been released. This model is a combination of GRACE and LAGEOS mission plus 0.5 x 0.5 degrees gravimetry and altimetry surface data and is complete to degree and order 360 in terms of spherical harmonic coefficients.

    High-resolution combination gravity models are essential for all applications where a precise knowledge of the static gravity potential and its gradients is needed in the medium and short wavelength spectrum. Typical examples are precise orbit determination of geodetic and altimeter satellites or the study of the Earth's crust and mantle mass distribution.

    But, various geodetic and altimeter applications request also a pure satellite-only gravity model. As an example, the ocean dynamic topography and the derived geostrophic surface currents, both derived from altimeter measurements and an oceanic geoid, would be strongly correlated with the mean sea surface height model used to derive terrestrial gravity data for the combination model.

    Therefore, the satellite-only part of EIGEN-GL04C is provided here as EIGEN-GL04S1. The contributing GRACE and Lageos data are already described in the EIGEN-GL04C description. The satellite-only model has been derived from EIGEN-GL04C by reduction of the terrestrial normal equation system and is complete up to degree and order 150.

    How many really understand/see the production of gravitational waves in regards to Taylor and Hulse?

    To see Stefan's correlation in terms of "wave production" is a dynamical quality to what is still be experimentally looked for by LIGO?

    As scientists, do you know this?

  12. Thus the binary pulsar PSR1913+16 provides a powerful test of the predictions of the behavior of time perceived by a distant observer according to Einstein's Theory of Relativity.

    Since we know the theory of Relativity is about Gravity, then how is it the applications can be extended to the way we see "anew" in our world?

    A sphere, our earth, not so round anymore.

    Uncle has tried to correct me on "isostatic adjustment."

    Planets are round because their gravitational field acts as though it originates from the center of the body and pulls everything toward it. With its large body and internal heating from radioactive elements, a planet behaves like a fluid, and over long periods of time succumbs to the gravitational pull from its center of gravity. The only way to get all the mass as close to planet's center of gravity as possible is to form a sphere. The technical name for this process is "isostatic adjustment."

    With much smaller bodies, such as the 20-kilometer asteroids we have seen in recent spacecraft images, the gravitational pull is too weak to overcome the asteroid's mechanical strength. As a result, these bodies do not form spheres. Rather they maintain irregular, fragmentary shapes.
    K. Shumacker. Scientific America

    Do not have time to follow up at this moment.

  13. Dear CIP,

    thanks for pointing out that a sharp interface is not necessary for the occurance of gravity waves - yes, that's probably true!

    Dear Amara,

    thanks for the link to the Jupiter photos... The Shoemaker-Levy impact is somehow like throwing a big stone in a big lake ;-)

    Dear Bee,

    ah, in the meantime I've found the article on the washboard road...funny, especially when I try to imagine the real lab experiment these guys have made.... How could I forget about the Kalahari sand dunes - especially since there is quite a lot of Kalahari sands in the kitchen ;-). By chance, when looking for some info about the washboard road, I came across this Physics News Update about dunes on Mars - they seem to need 1000 years to travel a few meters, because the atmosphere is much thinner than on Earth, and wind speeds high enough to move the dune occur only a few times a decade.

    Best, Stefan

  14. Hi Kris,

    I should have addressed that to you.

    never mind, and thanks a lot for your reference at the Kelvin-Helmholtz instability, "when velocity shear is present within a continuous fluid or when there is sufficient velocity difference across the interface between two fluids." (Wikipedia). Hm, when I look again at the pictures, I guess you're right that the smaller ripples are not gravity waves, but examples of these Kelvin-Helmholtz instabilities - after all there is also a lot of shear flow going on in the atmosphere...

    Best, Stefan

  15. How could I forget about the Kalahari sand dunes

    Err, what I had in mind where the ripples on the shoulder roads...

  16. Err, what I had in mind where the ripples on the shoulder roads...

    oops, sorry, right, you didn't even mention the dunes... You see, I was already daydreaming ahead ;-), about the landscape I could look at while you as the driver were focussing your attention on the gravel road :-)...

  17. Hi Stephan,

    there is also a lot of shear flow going on in the atmosphere...

    Yes. You get it between atmospheric layers and also at the ground, where there is always a static boundary layer. The Kelvin-Helmholtz effect produces a series of horizontal vortices or "rollers" between shearing layers.

    When ripples are forming in sand, there is a vortex attached to each ripple. Waves in a field of wheat are actually rollers moving across. I'm wondering whether those large atmospheric gravity waves might have rollers embedded in them also.

    Best, Kris

  18. You might as well as call this post of yours Stefan "a adventure into the mathematical abstract?:)

    This is not real?:)Bee it's not real?:)


    Plato said,"Wherever there are no gravitational waves the spacetime is flat. One would have to define these two variances. One from understanding the relation to "radiation" and the other, "to the perfectly spherically symmetric."

    To think hydro-dynamically you had to know when the universe ever receded to such a point, and then you have all this energy(but within it) it had to be transferable from the universe "before" to the way it is "now."

    There had to be a "relativistic condition" even within the quark Gluon state, that would have allowed such a transfer?

  19. Hi Chris..., it's really Stefan, not Stephan... :-)


  20. Lagrangian's L5?

    You look at the Sun Earth relation and you see the way the universe is in terms of the gravitational inclinations? You may point to the very beginning?

    The "relativistic conditions" had to exist at all stages. Thus you must look at the universe as all "gravitationally pervasive."

    Graviton condensation?

    It's a bulk perspective now. And E8 is dimensional related. That is why Garrett Lisi's model is put in context as proceeding from the beginning of this universe.

    Not "nothing." Not just a "mathematical construct."

  21. Ouch! I had that one coming. A bee sting!

  22. Hi Kris,

    never mind :-)... I highly appreciate your comments, anyway...

    Hi Plato,

    again, your comments are way beyond my intellectual capability ;-) Maybe I have a better chance to understand them when their relation to the original post is more than just the word "gravity" in both of them?

    Best, Stefan

  23. There are, I think, two plausible explanations (or the combination of both) for the top picture. It could be due to gravity waves that arise from perturbations to a stably stratified atmosphere. Or it could be unstable waves that arise from Kelvin-Helmholtz type instability.

    The two are not mutually exclusive. The criterion for K-H instability involves Richardson number, which is a combination of vertical density stratification and vertical wind shear. A flow can be statically stable and yet K-H'ly unstable. Thus, it is possible for the gravity waves and K-H waves to coexist. (If a flow is statically unstable one would not see shallow gravity waves but deep convective clouds. That's another flow regime.)

    Just my guess.

    The organized pattern in the sand in bottom picture is probably unrelated to gravity waves but I don't remember the correct explanation.

  24. Kris, Stefan, et al,

    In principle, it is possible to determine whether the observed feature are normal gravity waves or waves produced by K-H instability.

    The gravity waves are produced by external perturbations to a stably stratified atmosphere. They don't grow spontaneously. Thus, their scale are determined by the scale of the external perturbations. The K-H waves, on the other hand, are the most unstable eigen modes of the flow due to the combined shear-stratification instability. If we have the observation of the vertical profiles of the velocity and density of the atmosphere at the time the picture was taken, the instability problem can be solved to determine the scale of the most unstable mode. One can then compare this scale to the scale of the observed waves to determine if K-H instability is relevant.

  25. Stefan, thanks for your forgiveness!

    In the wiki page on gravity waves, I was struck by the image of those in the wake of an island. I could imagine there are also horizontal vortices there, as chickenbreeder suggests, mixed in with the gravity waves. Apparently that does happen in lee waves.

    Reminds me of vortex shedding, which is discussed in the Feynman Lectures. It's ubiquitous but often overlooked.

    The collapse of the Takoma Narrows suspension bridge is still cited in textbooks as an example of resonance. For decades, it was written that the cause was wind gusting at precisely the bridge's resonant frequency, an unusual condition not foreseen by the bridge designers. Actually it was due to a steady wind, with vortex shedding at a rate determined by the bridge structure. Basically the same everyday phenomenon that makes a flag flap -- or a singer's vocal cords.

    Probably all musical wind instruments involve this phenomenon, but I've never seen it discussed in a textbook on sound. A flute is described as a tube of a certain length which only allows standing waves at certain harmonic frequencies. (Just calculate those, never mind how the waves got there.) It's been learned vortex shedding is also crucial for insect flight. (So much for the rumor that bumblebees can't fly.)

    Last time I looked, UCSB was still using a textbook citing waves in wind-blown wheat to make the point that waves don't transport their medium. (No vortex rolls mentioned.) Of course the actual medium there is primarily air, which does go places. (Kick a wheat field on a calm day, and see how far the wave goes.) And waves often do transport their media.

    All the best,


  26. "With the discovery of sound waves in the CMB, we have entered a new era of precision cosmology in which we can begin to talk with certainty about the origin of structure and the content of matter and energy in the universe-Wayne Hu


    Maybe I have a better chance to understand them when their relation to the original post is more than just the word "gravity" in both of them?

    Your "toying with the way we see gravitational and gravity waves?" Dealing with the objective world with ancient ideas?

    I pointed to the differences.

    Plato:Wherever there are no gravitational waves the spacetime is flat. One would have to define these two variances. One from understanding the relation to "radiation" and the other, "to the perfectly spherically symmetric."

    But still to see such dynamics in terms of the "mathematical abstract" I see see no reason why you would "lesson my points" on helping one to see these differences in the space around us.

    This recording was produced by converting into audible sounds some of the radar echoes received by Huygens during the last few kilometres of its descent onto Titan. As the probe approaches the ground, both the pitch and intensity increase. Scientists will use intensity of the echoes to speculate about the nature of the surface.

    So I may point to the ways in which one may synthesized the views of the world in relation to not only "sound" as Kris just talks about, but also about how one may transform that sound "to colour."

    3.1 As Cytowic notes, Plato and Socrates viewed emotion and reason as in a kind of struggle, one in which it was vitally important for reason to win out. Aristotle took a more moderate view, that both emotion and reason are integral parts of a complex human soul--a theory proposed by Aristotle in explicit opposition to Platonism (De Anima 414a 19ff). Cytowic appears to endorse the Platonic line, with the notable difference that he would apparently rather have emotion win out.

    Cosmic variance may talk about "synesthesia" yet you cannot stop the changes such understanding brings to the emotive forces that surround earth and us. A psychological exercise with regards to the weather?

    Such a shift to bulk perspective is not without it's lessons on progressing the views of gravity in "all situations."

    I am not so smart, just that I may see differently then you Stefan. :)

    We can't actually hear gravitational waves, even with the most sophisticated equipment, because the sounds they make are the wrong frequency for our ears to hear. This is similar in principle to the frequency of dog whistles that canines can hear, but are too high for humans. The sounds of gravitational waves are probably too low for us to actually hear. However, the signals that scientists hope to measure with LISA and other gravitational wave detectors are best described as "sounds." If we could hear them, here are some of the possible sounds of a gravitational wave generated by the movement of a small body in spiralling into a black hole.

  27. This comment has been removed by the author.

  28. There was an astonishing example of gravity waves in "Secrets of the Deep" that aired this morning on the Discovery Channel. The operators of a manned submersible near the floor of the Caribbean saw a large ring of mussels and other marine life on the seafloor surrounding an empty circle of water. When they tried to descend into the circle, the submarine BOUNCED OFF because the water in the circle was a "lake" of superdense brine. Their impact with the "lake" surface caused waves that propagated across the ocean/brine interface and lapped up against the marine growth at the "shore." The effect was so striking that the submersible crew had to remind themselves that they were already under water.

  29. Hi Jim,

    that sounds fascinating! I had a similar example in mind when writing the post, but couldn't find a good link or even a video clip... I once have seen a movie showing waves at the interface of two differnet layers of water with different salinity, in laboratory conditions, and with one layer coloured - that looked quite impressive. On a smaller scale, you somtimes can such pattern is layered drinks, say latte macchiato...

    Best, Stefan


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