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

Question

I'm convinced that water waves for example:

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

Answer 1

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.

Answer 2

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.

added:
I described the net transport of energy along the direction of propagation of the waves. In deep waters it is the vertical motion of the surface that is able to do work (on devices that extend more than a wavelength) against the gravitational field.

Answer 3

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.

Answer 4

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.