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Vortex rings are a special soliton wave that are known to carry matter over a distance as well as energy. This can easily be demonstrated using a cardboard 'vortex canon' filled with smoke. The smoke makes the vortex rings visible as they are fired out of the canon.

But to my question - are there any other types of waves that are also known to carry matter?

Most traveling waves that travel through media leave the media and any matter behind as the energy propagates forward.

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  • $\begingroup$ Oceanic internal waves come to mind, though I'm no expert on these. $\endgroup$ – paisanco Jan 25 '15 at 1:20
  • $\begingroup$ Internal waves don't transfer water, but ocean currents do $\endgroup$ – docscience Jan 25 '15 at 3:10
  • $\begingroup$ Some electromagnetic waves in plasmas can trap particles and carry them away from their original locations. There are also forms of solitons in plasmas that carry bulk flows of plasma in addition to propagating. Now that I think about it, would rogue waves in the ocean count (they are soliton-like but I do not recall whether they produce a net transfer of fluid)? $\endgroup$ – honeste_vivere Jan 30 '15 at 0:17
  • $\begingroup$ @honeste_vivere Rogue waves, just like wind driven waves don't lead to any transport of water over a distance. But regarding the plasma waves - what is the specific structure of these waves that lead to mass transport? Vortex rings are unique in that they create a traveling region (torus) of low pressure. As a result the torus grows over distance as it entrains the surrounding fluid. But what was originally trapped within the torus is carried along. $\endgroup$ – docscience Jan 30 '15 at 15:55
  • $\begingroup$ @docscience - It depends on the mode. In some cases, the electric fields form, effectively, potential wells. If the wave has a finite group velocity (hmmm, maybe phase is enough...), then it can carry particles trapped in these wells away from the region they were originally located. Because the plasma is magnetized, it often creates a lot of difficulty for particles to move between regions. Thus, a magnetosonic soliton (e.g., SLAMS) could potentially create an isolated region of compressed/heated plasma that it carries along. Though I will have to think about this some more. $\endgroup$ – honeste_vivere Jan 30 '15 at 20:30
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In an electric circuit with alternative current, this current is a wave that carries matter, the electrons, through media - e.g. resistors.

In a DC circuit the electrons also form a wave that flows, but I chose the AC because its oscillations remind a wave that displays minima and maxima as it flows.

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Deep water surface gravity waves transport mass. This is known as $\textit{Stokes drift}$ and is very important for upper ocean processes (eg Langmuir circulation).

The Stokes drift arises due to the elliptical particle trajectories induced by deep-water waves (that is, the orbits are not closed circles). This leads to a second order mass transport in the small parameter (taken to be $ak$, for $a$ the wave amplitude and $k$ the wavenumber).

I can quantify this if you'd like.

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