EM 1110-2-1100 (Part II)
30 Apr 02
1
ρ g H2 L
Ep '
(II-1-56)
16
(c) According to the Airy theory, if the potential energy is determined relative to SWL, and all waves
are propagated in the same direction, potential and kinetic energy components are equal, and the total wave
energy in one wavelength per unit crest width is given by
ρgH 2L
ρgH 2L
ρgH 2L
E ' Ek % Ep '
(II-1-57)
%
'
16
16
8
where subscripts k and p refer to kinetic and potential energies. Total average wave energy per unit surface
area, termed the specific energy or energy density, is given by
2
' E ' ρgH
E
(II-1-58)
8
L
(d) Wave energy flux is the rate at which energy is transmitted in the direction of wave propagation across
a vertical plan perpendicular to the direction of wave advance and extending down the entire depth.
Assuming linear theory holds, the average energy flux per unit wave crest width transmitted across a vertical
plane perpendicular to the direction of wave advance is
1 t%r
T mt
m&d
η
p u dz dt
P'
(II-1-59)
which, upon integration, gives
P ' EnC ' ECg
(II-1-60)
where P is frequently called wave power, and the variable n has been defined earlier in Equation II-1-50.
(e) If a vertical plane is taken other than perpendicular to the direction of wave advance, = E Cg sin
P
θ, where θ is the angle between the plane across which the energy is being transmitted and the direction of
wave advance.
(f) For deep and shallow water, Equation II-1-60 becomes
1
P0 '
(II-1-61)
E C (deep water)
2 0 o
P ' ECg ' EC (shallow water)
(II-1-62)
(g) An energy balance for a region through which waves are passing will reveal that, for steady state, the
amount of energy entering the region will equal the amount leaving the region provided no energy is added
or removed. Therefore, when the waves are moving so that their crests are parallel to the bottom contours
E0 n0 C0 ' EnC
(II-1-63)
or since
II-1-28
Water Wave Mechanics
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