circle radius is equal to the wave amplitude for
a fluid particle on the free surface. The two semiaxes
of the elliptical motion for finite depth are
horizontal and vertical with the horizontal semiaxis
being the larger.The vertical semi-axis is equal
to the wave amplitude for a fluid particle on the
free surface. When the fluid depth is very shallow,
the horizontal fluid velocity is much larger
than the vertical fluid velocity. This can be seen
by Taylor expanding the finite-depth expressions
of fluid velocity at z= −h and assuming kh to be
small. Further, we can show that the total pressure
is hydrostatic relative to the instantaneous
free-surface elevation when kh→ 0.