2S0
7 Ocean Currents
is expressed as a function of wave-induced bottom velocity. The final governing
equation for longshore current in the Larson and Kraus model becomes:
d [
(
-) dV(X)]
1 dSxy
-
Axy h + ( - - - fb = - - ,
d x '
dx
p dx
(7.44)
in which V is the longshore current velocity, and Sxy is the long-shore component of radiation stress tensor. The first term on the left-hand side of this
equation describes the lateral mixing of current, and in particular the eddy viscosity coefficient, A xy , is a measure of how quickly a longshore current spreads
out in water body by affecting adjacent water particles, initially at rest. It
takes the form (Larson and Kraus, 1991):
(7.4S)
where Ub is the bottom velocity induced by waves (Eq. 4.2S):
Ub = 2L cosh [21l' ( ~+<)] .
gHT
(7.46)
The second term on the left-hand side of Eq. (7.44) represents the longshore
component of the bottom friction, the major retarding force for the longshore
current. When the magnitude of the longshore current velocity is much smaller
than that of the wave orbital velocity, the friction term can be presented as
(Larson and Kraus, 1991):
(7.47)
in which cf is the bottom friction coefficient (usually of order of O.OOS-O.Ol).
The term on the right-hand side of Eq. (7.44) is responsible for the wave-induced
force necessary for the generation of longshore current. It can be presented in
the form:
1
pgH 2
Sxy = 2mE sin(2B) = 1(lm sin(2B),
(7.48)
where m is given by Eq. (4.22). When the angle B is equal to zero (waves
approach perpendicularly to the beach), longshore current ceases. Intensity
of the longshore transport increases with increased angles of incidence. An
example of a comparison of predicted longshore current with field measurements
is shown in Fig. 7.21.
Rip Currents and Edge Waves. There are several mechanisms which are
responsible for the generation of rip currents. The regular spacing of rip currents can be induced by the presence of regularly varying bottom topography
7 Ocean Currents
is expressed as a function of wave-induced bottom velocity. The final governing
equation for longshore current in the Larson and Kraus model becomes:
d [
(
-) dV(X)]
1 dSxy
-
Axy h + ( - - - fb = - - ,
d x '
dx
p dx
(7.44)
in which V is the longshore current velocity, and Sxy is the long-shore component of radiation stress tensor. The first term on the left-hand side of this
equation describes the lateral mixing of current, and in particular the eddy viscosity coefficient, A xy , is a measure of how quickly a longshore current spreads
out in water body by affecting adjacent water particles, initially at rest. It
takes the form (Larson and Kraus, 1991):
(7.4S)
where Ub is the bottom velocity induced by waves (Eq. 4.2S):
Ub = 2L cosh [21l' ( ~+<)] .
gHT
(7.46)
The second term on the left-hand side of Eq. (7.44) represents the longshore
component of the bottom friction, the major retarding force for the longshore
current. When the magnitude of the longshore current velocity is much smaller
than that of the wave orbital velocity, the friction term can be presented as
(Larson and Kraus, 1991):
(7.47)
in which cf is the bottom friction coefficient (usually of order of O.OOS-O.Ol).
The term on the right-hand side of Eq. (7.44) is responsible for the wave-induced
force necessary for the generation of longshore current. It can be presented in
the form:
1
pgH 2
Sxy = 2mE sin(2B) = 1(lm sin(2B),
(7.48)
where m is given by Eq. (4.22). When the angle B is equal to zero (waves
approach perpendicularly to the beach), longshore current ceases. Intensity
of the longshore transport increases with increased angles of incidence. An
example of a comparison of predicted longshore current with field measurements
is shown in Fig. 7.21.
Rip Currents and Edge Waves. There are several mechanisms which are
responsible for the generation of rip currents. The regular spacing of rip currents can be induced by the presence of regularly varying bottom topography