TITLE: How deep is a ocean wave (the extent of tranverse motion of the water below surface)?
QUESTION [0 upvotes]: While water moves up and down on the surface, does it move the same way below surface also? Or does it fade into a compression wave somewhere below the surface?

REPLY [3 votes]: Water wave is combination of traverse and longitudinal waves with a dispersion relation:
$$c=\sqrt{\left( \frac{g\lambda}{2\pi}+\frac{2\pi \gamma}{\rho \lambda} \right) \tanh \frac{2\pi h}{\lambda}}$$
and displacement profile $$\xi+\eta i=\frac{ga}{kc^{2}} \frac{\cosh[k(y+h)+i(kx-\omega t)]}{\cosh kh}$$

In deep water, the particles move in more circular way, and the amplitude decays with depth.  No perceptible motion deeper than $\dfrac{\lambda}{2}$.
In shallow water, the particles move in more elliptical manner, and they're pure longitudinal at the bottom.

See also another answer here
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