must be computed from Equation 2-2; in shallow water, tanh(2îrd/L) becomes
nearly equal to 2ird/L and Equation 2-2 reduces to Equation 2-9.
C2 = gd or C = (gel)*4 .
(2-9)
Both Equations 2-2 and 2-9 show the
To a first approximation, the total
may be written as
dependence of wave velocity on depth.
energy in a wave per unit crest width
PgH2L
8
(2-38)
It has been noted that not ail of the wave energy E
is transmitted
forward with the wave; only one-half is transmitted forward in deep water.
The amount of energy transmitted forward for a given wave remains nearly
constant as the wave moves from deep water to the breaker line if energy
dissipation due to bottom friction (K.
wave energy is negligible.
= 1.0), percolation and reflected
In refraction analyses, it is assumed that for a wave advancing toward
shore, no energy flows latérally along a wave crest; that is the transmitted
energy remains constant between orthogonals. In deep water the wave energy
transmitted forward across a plane between two adjacent orthogonals (the
average energy flux) is
(2-73)
where b0 is the distance between the selected orthogonals in deep water.
The subscript o always refers to deepwater conditions. This power may
be equated to the energy transmitted forward between the same two orthogonals
in shallow water
P = nbEC,
(2-74)
where b is the spacing betwegn the orthogonals in the shallower water.
Therefore, (1/2) b0 E0C0 • nb EC, or
Ê _ 1 (l\{bo\(Co\
Êo = 2\;\b\E<2-75’
O
' !
From Equation 2-39,
(2-76)
E =
P = - b E C ,
o
2 ° o o ’
2-66