Fuck Yeah Fluid Dynamics

Celebrating the physics of all that flows. Ask a question, submit a post idea or send an email. You can also follow FYFD on Twitter and Google+. FYFD is written by Nicole Sharp, PhD.

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Posts tagged "standing wave"

captainandry asks:

What would happen to a fish or swimmer in a standing wave?

First of all, check out the video that inspired this question, which shows a standing water wave created in a wave tank. Before we tackle the standing wave, it’s helpful to know what motion exists in a typical water wave. For deep water waves, the motion of a particle as the waves pass is circular, with a decreasing radius with increasing depth. Below a certain depth the energy of the surface wave doesn’t penetrate. Here’s an animation, where the red dots represent massless particles and the blue circles show their paths:

In shallower waters, the circular paths get compressed into ellipses. The image below shows pathlines for particles at different depths as a water wave passes. Notice how the paths are circular near the surface, where the depth is much greater than the wavelength, while close to the bottom, the pathlines are elliptical.

So what about motion for a standing water wave? Such a wave has no apparent horizontal motion, as seen in the animation below:

Similar to the way that decreasing the depth compresses the circular particle motion into an ellipsoid, creating a standing wave compresses the horizontal motion of any particle near the surface. What this means is that anything floating near the surface of the standing wave will simply bob up and down. Unless it’s located at one of the nodes (marked by red dots), in which case it won’t move at all! As with the other types of water waves, the amount of displacement will decrease with depth. People and fish, of course, are not massless particles, so their motion will be damped by inertia, but the same principles apply. 

(Photo credits: P. Videtich; R. L. Wiegel and J.W. Johnson; Wikipedia)

Researchers at Argonne National Laboratory are using acoustic levitation of droplets to further pharmaceuticals. By placing two precisely aligned speakers opposite one another, a standing wave can be created. At nodes along the standing wave, there is no net transfer of energy, but the acoustic pressure is sufficient to cancel the effect of gravity, allowing light objects like droplets to levitate. This is why, in the video, you see the droplets are placed at equally spaced distances and if one is slightly off the node, it vibrates noticeably. The benefit of this levitation to pharmaceutical research comes at the molecular level; drugs formed from solutions kept in a solid container are likely to be crystalline in structure and thus less efficiently absorbed by the body. If the drug can instead be kept in an amorphous state by evaporating the solution without a container, then the resulting drug may be effective at a lower dosage than its crystalline counterpart. (Video credit: Argonne National Laboratory, via Laughing Squid, submitted by @__pj)

A standing wave is created in a wave tank by fixing a wall at one end and moving the other wall—the wave generator—at a frequency such that the outgoing waves are superposed on those reflecting back from the wall. This doubles the amplitude of the wave. In the standing wave (also called clapotis), the surface rises and falls in a mirrored pattern: troughs become crests become troughs and so on. When the wave generator is turned off, the standing wave’s energy dissipates and eventually the tank stills. The sloshing motion that persists in the meantime is known as a seiche, which commonly occurs in nature in lakes, seas, bays, and any partially enclosed body of water. Some definitions include tides as a form of seiche due to the periodic nature of the moon’s force on Earth’s waters. See this animation of a seiche for more. (submitted by Daniel)

The vibration caused by rubbing a Tibetan singing bowl excites standing waves in a Faraday instability on the surface of water in the bowl. As the amplitude of excitation increases, jets roil across the surface, creating a spray of droplets, some of which actually bounce on the surface as it vibrates. For more see the BBC and SciAm articles.

Some sand dunes can “sing”, but not because of the wind! When loose sand slides down over harder, packed sand, a standing wave is formed, causing the entire surface of the dune to vibrate on a single frequency. We hear this as a musical note - typically an E, F, or G. (via io9)

When vibrated, fluid surfaces can exhibit standing waves known as Faraday waves. In this experiment, increased forcing of these standing waves causes the formation of a jet. Under the right conditions, as the standing wave collapses, a singularity forms on the fluid surface when velocity and surface curvature diverge. The narrow jet column forms as a result of the fluid’s kinetic energy getting focused by the collapse. For more, see this letter to Nature. #

A thin layer of the non-Newtonian fluid oobleck on a vibrating surface (in this case, a speaker) is a great way to show off nonlinear standing waves known as Faraday waves. The waves form because, under these circumstances, the flat surface of the air/oobleck interface has actually become unstable.

This video explores some of the non-Newtonian behaviors of oobleck when shaken. The pattern across the surface once the vibrations start is called Faraday waves, a type of nonlinear standing wave that forms once a critical vibrational frequency is passed and the flat surface of the fluid becomes unstable. Toward the end of the video, the frequency of the vibrations is increased until “finger-like protrusions” form. This is a behavior exhibited by shear-thickening non-Newtonian fluids.