# Are water waves (i.e. on the surface of the ocean) longitudinal or transverse?

I'm convinced that water waves for example:

are a combination of longitudinal and transverse. Any references or proofs of this or otherwise?

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Fluids can't sustain transverse oscillations, as far as I know, but I can't think of a reference off the top of my head. –  David Z Mar 8 '11 at 1:13
The waves in your picture are exhibiting highly nonlinear behavior. It'll be a lot easier to answer the question for linear waves, depending on what you want. –  Mark Eichenlaub Mar 8 '11 at 4:56
This question (deliberately?) mixes ambiguous terminology with nontrivial physics. The ocean surface is just 2-dimensional so both transverse and longitudinal waves on the surface have 1 polarization only, and they can't really be distinguished mathematically. It's just about the formalism. What you would have to ask is the direction of the possible gradient of pressure inside the water. It is mostly vertical (outside the plane where the wave propagates, so it's mostly longitudinal, despite the orthogonality) and then in the direction of motion (longitudinal) but none in the 3rd L/R direction. –  Luboš Motl Mar 8 '11 at 5:34
@Lubos I don't understand your comment. The surface is two-dimensional, but it exists in three-dimensional space. The question is, if you have a leaf floating on the surface of the water, how does the leaf move as a wave passes? Back-and-forth in the direction of propagation of the wave or up-and-down perpendicular to the wave's propagation? –  Mark Eichenlaub Mar 8 '11 at 5:56
Dear Mark, I wrote the very same thing. What Carl really wants to ask is how a leaf moves in the 3D space. But that's not the same thing as the question whether the waves are transverse or longitudinal. Technically, both front-rear motion and the vertical ones should be counted as longitudinal waves. The waves are waves in 2 dimensions of the surface only, so the only truly transverse direction is the horizontal left-right direction perpendicular to the direction of the wave, and non-turbulent waves don't have any such component. So both modes you mentioned are longitudinal (or scalar) waves. –  Luboš Motl Mar 8 '11 at 8:24

Each point is moving according to:
$x(t) = x_0 + a e^{-y_0/l} \cos(k x_0+\omega t)$
$y(t) = y_0 + a e^{-y_0/l} \sin(k x_0+\omega t)$

With $x_0,y_0$ -- "motion centre" for each particle, $a$ -- the amplitude, $l$ -- decay length with depth.

So you have exact "circular" superposition of longitudinal and transverse waves.

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In your animation the medium is rather compressible. –  Vladimir Kalitvianski Mar 8 '11 at 16:50

In deep waters, the fluid particles describe circles when a wave passes by. So, in a sense, these waves are neither transverse nor longitidinal. For a demonstration, see for example Howard Georgi's book (chapter 11).

In very shallow waters the particles go essentially back and forth. In the intermediate cases they follow eliptical trajectories.

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Thanks for the link to the book. –  Helder Velez Mar 8 '11 at 2:48
Thanks for the link! –  Jaime Mar 8 '11 at 9:11

The ocean waves are usually called "surface" waves. Whatever a particle trajectory is, the deeper in water, the smaller its amplitude. Several lengths below surface the water is still.

However deep inside there may be volume waves - from submarines, for example. They are detectable.

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Interesting comment on volume waves. Perhaps we should have some sort of question on that. –  Carl Brannen Mar 8 '11 at 23:17

I think the wave nature of water is both transverse and longitudinal. When we drop a stone in water that we can see there the transverse waves but then we can heard sound also, so, water waves are transverse as well as longitudinal waves!

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I will just say what I think I know:
In the open ocean or great lakes the waves are transverse: the water goes up and down. They are originated by the winds in the surface.

Near the shore the waves become also longitudinal: the small distance from the the surface to the bottom of ocean make the difference.