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4 How to Determine Wave Parameters
direction of wave propagation
----.
+ll I
A
.. -- - - - - - - - - - - - - - - - - -I
Fig. 4.8: Elliptical path of water particle in waves
- - - . .
~
At the sea bottom (z = - h), the vertical semi-axis B vanishes and the
water particle moves horizontally back and forward along the sea bottom with
amplitude A = (H /2) (gk/w 2 )/ coshkh.
In deep water, when h ~ 00, both semi-axes of the water particle path are
equal, i.'e.:
(4.33)
and Eq. (4.31) becomes:
(4.34)
the equation of a circle with radius A. For points deeper than half the wavelength, Z < -L/2, the radius A ::::::0, and surface waves are unable to induce
any movement of water particles.
Wave Induced Pressure. Total pressure at a given point in the water body
is determined as follows (for derivation see Appendix C.5.4):
p(x, z, t) = Pwg (-z + () - Pwg [1 - Kp(z)] (,
(4.35)
in which:
()
coshk(z + h)
K z - --"':"---,--'P
-
cosh(kh) ,
(4.36)
and ( is the surface displacement given by Eq. (4.13).