************** EXAMPLE problem
GIVEN: A deepwater oscillatory wave with a wavelength of Lo = 512 feet,
a height of Ho = 5 feet and a celerity of Co = 51.2 ft/sec, moving
shoreward with its crest parallel to the depth contours. Any effects
due to reflection from the beach are negligible.
FIND:
(a) Dérivé a relationship between the wave height in any depth of water
and the wave height in deep water, assuming that wave energy per
unit crest width is conserved as a wave moves from deep water into
shoaling water.
(b) Calculate the wave height for the given wave when the depth is 10
feet.
(c) Détermine the rate at which energy per unit crest width is transported toward the shoreline and the total energy per unit width
delivered to the shore in 1 hour by the given waves.
SOLUTION:
(a) Since the wave crests are parallel to the bottom contours, refraction
does not occur, therefore
= H$. (See Section 2.3. WAVE
REFRACTION.)
From Equation 2-43,
- Ë C = nËC .
2 ° °
The expressions for Eo and E are,
=
PgHO
E° =~r ■
and
where
represents the wave height in deep water if the wave
were not refracted.
Substituting into the above équation gives,
1 c PgH°
= nC PgH*
2 °
8
8
2-29