# How deep is a ocean wave (the extent of tranverse motion of the water below surface)?

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?

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.