and since,
2ffd\
sinh (27rd/L)
L /
cosh (2ttd/L)
therefore,
jrH cosh [2n(z+ d)/L]
2nx
2nt
sinh (2îrd/L)
cos I---*************************************
************** EXAMPLE problem **************
GIVEN: A wave in a depth of d = 40 feet, height of H = 10 feet, and a
period of T = 10 seconds. The corresponding deepwater wave height is
= 10.45 feet.
FIND:
(a) The horizontal and vertical displacement of a water particle from
its mean position when z = 0, and when z = - d.
(b) The maximum water particle displacement at a depth d = 25 feet when
the wave is in infinitely deep water.
(c) For the deepwater conditions of (b) above, show that the particle
displacements are small relative to the wave height when z = - Lo/2
SOLUTION:
(a)
2-20
Lo = 5.12 T* 2 = 5.12 (10)2 = 512 feet,
= 0.0781 .
From Appendix C, Table C-l
2nd\
= 0.6430 .
When z = 0, Equation 2-22 reduces to
2 tanh (27rd/L)