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 Technical Note DOER-N4
May 1999
the dominant force at the sediment-water interface. Therefore the current-only theories must be
modified to include the effects of waves. A method developed by Bijker (1971) is used in this
model to incorporate the effects of waves on the incipient motion of sediments. This modification
is a factor by which the current velocity is multiplied to account for the effects of waves (Swart
1976). The wave effects are included by increasing the current velocity to a value that would be
equivalent to the combined current/wave effects. The methodology used here is the same as that
used in LTFATE (Scheffner et al. 1995). This effective increase in velocity for currents accompa-
nied by waves Vwc is written as a function of the current velocity Vc in the absence of waves as
follows:
12
1 u0
2
$
Vwc = Vc 1.0 + ξ
(1)
2 Vc
where
12
$ f
ξ = C w
(2)
2g
12d
$
C = 18 log
(3)
r
0.194
r
f w = exp -5.977 + 5.213
(4)
a0
(if fw > 0.3, fw = 0.3)
Hgk
HgkT
1
1
$
u0 =
=
(5)
2σ cosh (kd )
4π cosh (kd )
Hgk
H
1
1
a0 =
=
(6)
2σ 2 cosh (kd ) 2 sinh (kd )
$
where u0 is the amplitude of the orbital velocity at the bed (Van De Graff and Van Overeem 1979),
computed according to linear wave theory (Ippen 1966, 28), and a0 is defined as the orbital excursion
(amplitude) at the bed (Swart 1976), computed from linear wave theory (Ippen 1966, 29). In the
r is the hydraulic bed roughness and taken to be 0.197 ft (0.06 m) (Van De Graff and Van Overeem
-1
1979). The terms H, k, σ, and T represent wave height (ft), wave number (ft ), angular frequency
-1
(sec ), and period (sec), respectively. The terms d and g represent water depth (ft) and acceleration
-2
of gravity (ft sec ), respectively.
2
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