Scientists discover new water waves

Jul 19, 2011 by Lisa Zyga feature
The even (left) and odd (right) standing solitary waves, whose motions can be seen in the video below. Image copyright: Jean Rajchenbach, et al. ©2011 American Physical Society

(PhysOrg.com) -- By precisely shaking a container of shallow water, researchers have observed wave behavior that has never been seen before. In a new study, Jean Rajchenbach, Alphonse Leroux, and Didier Clamond of the University of Nice-Sophia Antipolis in Nice, France, have reported the observation of two new types of standing waves in water, one of which has never been observed before in any media.

In their study, which is published in a recent issue of , the scientists explain how they discovered the new waves. They confined inside a Hele-Shaw cell, which is a container made of two parallel glass plates separated by a small gap. In this case, the plates were positioned vertically, like the two sides of an ant farm. The plates were 30 cm wide, and the gap between them was just 1.5 mm. The water inside was about 5 cm deep.

The researchers mounted the Hele-Shaw cell on a shaker, which vertically vibrated the cell and the water inside. While carefully controlling the and , they recorded the water with a .

When the researchers slowly increased the amplitude, two-dimensional standing waves with large amplitudes began to form on the water’s surface. As the researchers explained, these waves are called Faraday waves, which form on the surface of a vibrating fluid when the vibration frequency exceeds a certain value, and the surface becomes unstable.

The researchers observed two different shapes of Faraday waves, one having even symmetry and the other having odd symmetry. The even symmetry can be seen as a vertical “mirror” symmetry between the wave’s left and right sides. The odd symmetry of the second wave is only approximate, since the wave’s lower half is not exactly the same shape as the upper half. Because the researchers used an external probe to briefly perturb the surface, they think that the different wave patterns are likely attributed to the probe motion.

Scientists discover new water waves
The even standing solitary wave. Video copyright: Jean Rajchenbach, et al. ©2011 American Physical Society

Scientists discover new water waves
The odd standing solitary wave. Video copyright: Jean Rajchenbach, et al. ©2011 American Physical Society

When analyzing the standing waves, the researchers found that the two-dimensional even wave resembles the profile of a three-dimensional “axisymmetric oscillon,” a type of wave that has previously been observed at the surface of a layer of vibrating bronze beads. To the researchers’ knowledge, the odd standing wave has never been observed in any fluid media.

“These waves are both strongly localized, and stationary,” Rajchenbach told PhysOrg.com. “Until now, two main classes of water solitary waves had been described: propagative solitons (the famous 'Korteweg de Vries’) and envelope solitons (described by the nonlinear Schrodinger Equation), consisting of a large wave packet enveloping a large number of arches of 'carrier' waves. The observed waves belong to a different category of solitary waves.”

When trying to understand how surface instabilities could have caused these waves to form, the researchers encountered some problems due to the waves’ large amplitudes, since general amplitude equations describe waves with significantly smaller amplitudes. But in general, the researchers think that the novel wave patterns likely arise from the overlap of flat and wavy regions, both of which result from shaking-induced instabilities. The instabilities may involve mechanisms that also play a role in other fields, such as nonlinear optics, chemistry, and biology, as well as in sea waves.

“The main interest of our work obviously applies to sea nonlinear waves, and strengthens our knowledge concerning the formation of ocean waves of large amplitudes (giant 'rogue' or 'tsunamis'),” Rajchenbach said.

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More information: Jean Rajchenbach, et al. “New Standing Solitary Waves in Water.” Physical Review Letters 107, 024502 (2011). DOI: 10.1103/PhysRevLett.107.024502

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antialias_physorg
5 / 5 (10) Jul 19, 2011
This screams for finite element modeling. Would be very interesting to see whether we can reproduce this kind of asymmetric standing wave in a simulation.

Only goes to show that you can find extraordinary stuff in the most ordinary circumstances.
WirelessPhil
1 / 5 (12) Jul 19, 2011
Yes, just like ocean or lake waves just before they break.
So what did this cost and of what use is it?
ArkavianX
5 / 5 (1) Jul 19, 2011
Simple phase variance here, look at the symmetrical wave, its closer to the center, whereas the odd wave, is asymmetric and further from center of vibration. The rebound wave is what finishes the phase variance, by getting to the center at the same time you get the symmetrical response; whereas away from the center, a new wave already arrives collapsing the rebound before it can get close enough.

We have symmetrical and/or pairs of sensory organs for same reason, one ear closer to source whereas other is not, takes in more sound, thus we know to turn our heads if needing to pay attention.

Same effect here.
hush1
1 / 5 (2) Jul 19, 2011
Interesting comment. Normally hearing is phase insensitive.
Phase is not use for orientating the direction of sound in human hearing.

Reflection from boundaries create the standing wave.
The boundary conditions are absolutely critical.

The setup presents extreme boundary conditions. I have no idea how to incorporate surface tension into the Fourier Analysis of the nonlinear wave equation.

Absolute critical to all of this is where and how the impulse from the MOTION of the PLEUEL (German) is generated and imparted to the Hele-Shaw cell.

There is zero different to computer modeling a piano string and this fluid counterexample.

As said, there are other parameters that enter the differential wave equation as well as the number of degrees of freedom.
ArkavianX
1.5 / 5 (2) Jul 19, 2011
Degree of freedom applied to the piano string is what does in the counter example, granted the string has at least some elasticity, but it cannot show it to the naked eye without moving the entire string; water, however, easily can because its a liquid, only constrained by the to transparent plates and standard atmos-pressure.

As well, surface tension, of any barrier substance, when air meets water, in this case, has nearly absolute freedom provided an energy source gives it motive to do something.

Kedas
not rated yet Jul 19, 2011
What is the difference between the first one and dropping something in the water?
Isaacsname
5 / 5 (1) Jul 19, 2011
They should try viewing it through an Iphone.

http://www.youtub...=related
LKD
4 / 5 (1) Jul 19, 2011
This reminds me of soundwaves and how they interact with a reflection. Is it possible this is a response to frequency and the longitudinal reverberations distorting the water, much like the way you can amplify or nullify a sound wave depending on the period?
danman5000
5 / 5 (2) Jul 19, 2011
What is the difference between the first one and dropping something in the water?

I believe in this case, the wave is a standing wave and does not spread out like ripples in a pond.
Callippo
2.5 / 5 (2) Jul 19, 2011
What the wave surface actually does, it demonstrates the formation of stable particle in undulating environment. These two modes of vibrations correspond two dual modes of quantum waves, which we can observe often (so called the "doppelganger state" - see example of context there http://arxiv.org/...24v1.pdf ).

The standing wave illustrates the fundamental point of each particle environment, every wave expands the surface a bit, so it behaves like the gravitating lens and it slows down its own propagation. The soliton is a mixture of waves, which are bouncing back and forth along the resulting lens and which are reflecting from 1D boundaries of that lens with total reflection mechanism.
jim_deane
5 / 5 (3) Jul 19, 2011
It would be interesting to try this with several layers of slightly different density and color, so that we could see the interior flow/structure of the fluid.
Callippo
2.3 / 5 (3) Jul 19, 2011
It seems for me, the first wave corresponds the s-orbital and the second one p-orbital, i.e. the second excited state of quantum wave. Note that at the second case the apparatus vibrates faster and the watter layer is deeper, so that the surface ripples can spread faster along it (it corresponds the vibrating string of higher tension).

http://media-2.we...AA41.jpg
Caliban
not rated yet Jul 19, 2011
Would be nice to see a 3D demonstration of this. The Even form seems to mimic an impact structure. The Odd wave form seems to almost be propagated torsionally- although these appearances may just be some perceptual artifact.
210
5 / 5 (1) Jul 20, 2011
Yes, just like ocean or lake waves just before they break.
So what did this cost and of what use is it?

Wireless? You are called WirelessPhil..?!
Check this: "When the researchers slowly increased the oscillation amplitude, two-dimensional standing waves with large amplitudes began to form on the waters surface. As the researchers explained, these waves are called Faraday waves, which form on the surface of a vibrating fluid when the vibration frequency exceeds a certain value, and the surface becomes unstable."
Wireless...raw scientific research often leads to inventions and cures, tomorrow, a week from now, a century from now. BUT, if nobody does these experiments we may never have an iPhone-whose-frame-is-the antenna. Nor would we have Smart-Antennas. Faster ships @ sea use their propellers WORST enemy: Supercavitating hulls. If we did not study those small bubbles caused during cavitation, after all they're just bubbles, we'd nevr know!knowledge...
word-to-ya-muthas
eigenbasis
not rated yet Jul 20, 2011
Eigenmodes
jsa09
5 / 5 (2) Jul 20, 2011
I remember doing this experiment when I was in my teens using various apparatus I had around the house. At the time I thought it was fun and so did my brothers. For the life of us though we all assumed it was common knowledge because it did not seem that hard to reproduce. Standing wave type effect in a closed system does not seem all that unexpected but I guess being ignorant can mean you don't have a clue what you just did.
antialias_physorg
not rated yet Jul 20, 2011
The standing waves aren't the surprising finding here (the standing wave depicted in the first video is just to show that the apparatus can produce standard standing wave patterns).

It's the asymmetric standing wave in the second video that hasn't been observed before. Though I'd like to know if the air bubbles depicted contribute substantially to it or where they come from (possibly from interaction with the external probe?)
210
not rated yet Jul 20, 2011
They should try viewing it through an Iphone.

http://www.youtub...=related

WOW!!!!
210
not rated yet Jul 20, 2011
What is the difference between the first one and dropping something in the water?

The difference is 'Dropped Stone = Displacement by kinetic mass; The second method is agitation (Like a washing machine) of the ENTIRE mass; an earthquake is the most common natural form that we have to the second method.
word-to-ya-muthas
Astricus
not rated yet Jul 20, 2011
The second motion is primarily caused by the attachment of the bubbles, these can be imagined as being weights with elastic attachment to the surface and viscous drag associated with the movement of the bubble membrane. Some one of you here will b able to describe this in more technical terms. Also if memory serves me correctly there are some Bernoulli equations relating to the movement of the surface of a drum. Which just may be useful to define the observed "unusual" motion. Other things to consider are the heating effect of the vibrations and hence the difference in elasticity of the meniscus caused. Water molecules join with other molecules to form drops which are in effect like balloons. These stretch and expand when heated...
kade
not rated yet Jul 23, 2011
The thing that interested me about these two video,s is that the first wave repeated at half the frequency of the drive vibration, and the second or so called odd standing wave was at the same frequency as the drive vibration but alternated in which peak was at the high pressure and which was at the low pressure. It would seem that there is a lateral flow oscillation in the second case which is abscent in the first.
Isaacsname
not rated yet Jul 23, 2011
The thing that interested me about these two video,s is that the first wave repeated at half the frequency of the drive vibration, and the second or so called odd standing wave was at the same frequency as the drive vibration but alternated in which peak was at the high pressure and which was at the low pressure. It would seem that there is a lateral flow oscillation in the second case which is abscent in the first.


I'm probably just seeing things here, but it looks like the bubbles trapped between the two wavefronts start moving downward just before the oscillation, 2nd vid. They stretch out and back again, when the crest of the wave is on the left ( More noticable ), they start moving downward first.
Caliban
not rated yet Jul 23, 2011
What is the difference between the first one and dropping something in the water?

The difference is 'Dropped Stone = Displacement by kinetic mass; The second method is agitation (Like a washing machine) of the ENTIRE mass; an earthquake is the most common natural form that we have to the second method.
word-to-ya-muthas


True, but the two phenomena can be equivalent, locally -just a question of what agency supplies the energy. These waves don't just spontaneously arise from Brownian motion or some such. At least, not as far as we know.

macsglen
not rated yet Jul 23, 2011
They should try viewing it through an Iphone.

http://www.youtub...=related

The oscilloscope reinvented!
Very cool!
A_Paradox
not rated yet Jul 24, 2011
Well, all the sage comments above notwithstanding, this kind of article should carry a user warning that prolonged staring at minute detail in wave motion videos is dangerous; you could go blind!

Astricus, to me it looks like the little bubbles in the single wave example are being formed by a minute and brief 'breaking wave' process as each anti-node at its deepest trough starts returning upwards. My guess is that there is a potential higher frequency component which gets damped each time.

Kade, as I see it the upper, faster, wave motion is just like two, side by side, of the lower example but in which the two closest anti nodes have combined. In each case I can count "one.two.one.two" where each beat is a cycle of the container, and see that the anti-node is back to its original state on each count of one.
A_Paradox
not rated yet Jul 24, 2011
Kade, ...cont You are right I think that there is a lateral motion - in fact there has to be lateral motion associated with any surface wave in a liquid. I think several effects are combining here: surface waves are impeded by the bottom when their wave length >= depth, the edge of the container must be either a node or anti-node for a standing wave to form, and the system will maximise its entropy.

I think the entropy issue implies trade offs between momentum of the water and friction/viscosity imposed by contact with the walls of the container. The wave length & nod vs anti-node aspect constrains the vibrational frequency[ies] and location of anti-nodes.

AND I just noticed something else! In each case the container's movement is NOT straight up and down. In the upper video the top moves a bit to the right as it goes up; the opposite occurs in the lower video. That explains why the greatest wave motion is offset from centre in each case: towards the side with greatest acceleration