wave height and current setup/setdownCase No... wave height currentCase 4 Feb.
Trang 1(WAVE-INDUCED LONGSHORE CURRENT)
Wave-Induced Longshore Current
Governing Equations for Nearshore Currents
Vertically integrated, time-averaged momentum equations:
F b : bottom friction
L: lateral mixing
R b : wave forcing
+ continuity equation
Trang 21
xy xx
bx
by
S S
R
R
2
(cos 1)
(sin 1)
1
sin 2
16
xx
yy
xy
g C n C
Wind Forcing
cos
sin
D a
sx
D a
sy
C
d
C
d
General formulation:
2
D a
Lateral Mixing
1
1
Trang 32 2
bx f
by f
General expression:
Total instantaneous velocity:
b
b
2
cos cos
2
cos sin
t
T
t
T
Oscillatory wave motion:
Velocity amplitude:
2
2 cosh
m
gHT
u
d
L
L
Driving terms:
f
bx
f
by
c
d
c
d
(triangular brackets denote time-averaging over a wave period)
Trang 4xx
D a
dS
d
Momentum equation, x-direction
(setup/setdown):
Momentum equation, y-direction
(longshore current):
1
sin
dS
Evaluation of bottom friction:
1/ 2
Approximations:
2
2
2
1 sin
by f
weak current
strong current
Square-wave approximation:
2
2
sin
by f
w
Z
1
2
2
Trang 5Duck data (outside surf zone)
C D /c fabout 1.2
Estimation of Wind Drag Coefficient
3
3 ( ) 1.287510 7.5 m/s
( ) 0.8 0.065 10 7.5 m/s
D
D
WAMDI Group (1988):
Validation of Longshore Current Model
Data sets:
• Visser laboratory data
• Kraus-Sasaki field data
• Thornton and Guza field data
Comparison with wave height, mean
water elevation, and longshore current
Trang 6wave height and current setup/setdown
Case No 3
H in =0.089 m, T=1.00 sec, in =15.4 deg
Visser Data
Case No 4
H in =0.078 m, T=1.02 sec, in =15.4 deg
Kraus-Sasaki Data
Shelf-type profile
Trang 7wave height current
Case 4 Feb.
H rms,in =0.56 m, T=14.3 sec, in =7.8 deg
Thornton-Guza Data
Case 5 Feb.
H rms,in =0.45 m, T=12.8 sec, in =9.0 deg
Parameter Values
Laboratory data:
c f = 0.01 – 0.02, 0.5 linear model
c f = 0.005 – 0.015, 0.3 nonlinear model
Field data:
c f = 0.004 – 0.006, 0.5 linear model
c f = 0.003 – 0.005, 0.3 nonlinear model