classical mechanics - 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?

Answer

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.