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?
 A: 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.
A: 
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.
A: 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. 
A: 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!
A: Maybe sea waves are longitudinal at sea but when they hit the shallows of the shore they become transverse waves and take the shape of a wheel and roll towards the shore.
Just guessing this from my years of surfing.   The waves are up & down out in the deep but turn into tubes when they reach the shallows.
A: 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. 
