Acta Oceanol. Sin., 2014, Vol. 33, No. 9, P. 40–46
DOI: 10.1007/s13131-014-0515-5
http://www.hyxb.org.cn
E-mail: [email protected]
Numerical study on water waves and wave-induced longshore
currents in Obaköy coastal water
TANG Jun1*, LYU Yigang1, SHEN Yongming1
1
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian
116023, China
Received 11 October 2013; accepted 24 January 2014
©The Chinese Society of Oceanography and Springer-Verlag Berlin Heidelberg 2014
Abstract
In this paper, the water waves and wave-induced longshore currents in Obaköy coastal water which is located at the Mediterranean coast of Turkey were numerically studied. The numerical model is based on
the parabolic mild-slope equation for coastal water waves and the nonlinear shallow water equation for
the wave-induced currents. The wave transformation under the effects of shoaling, refraction, diffraction
and breaking is considered, and the wave provides radiation stresses for driving currents in the model. The
numerical results for the water wave-induced longshore currents were validated by the measured data to
demonstrate the efficiency of the numerical model. Then the water waves and longshore currents induced
by the waves from main directions were numerically simulated and analyzed based on the numerical results. The numerical results show that the movement of the longshore currents was different while the wave
propagated to a coastal zone from different directions.
Key words: coast hydrodynamics, water wave, mild-slope equation, wave-induced currents, numerical
modeling
Citation: Tang Jun, Lyu Yigang, Shen Yongming. 2014. Numerical study on water waves and wave-induced longshore currents in
Obaköy coastal water. Acta Oceanologica Sinica, 33(9): 40–46, doi: 10.1007/s13131-014-0515-5
1 Introduction
Surface water wave-induced nearshore currents are likely
present on most beaches as a component of the complex pattern of a nearshore circulation. As a wave propagates from a
deep ocean to a shallow water, the wave occurs shoaling, diffraction, refraction and breaking due to the influence of the
bathymetry gradient and land boundary in coast. When the
surface wave breaks on beaches, the wave energy is lost to the
turbulence generated in the process of breaking, and the wave
momentum is transferred into the water column generating
nearshore current. Scientific investigations of hydrodynamics
along the coast have demonstrated that the wave usually breaks
as it approaches the shoreline at an inclination angle, generating the longshore current that flows parallel the beach. The
water waves and wave-induced nearshore currents have an important influence on water exchanging, sediment transport and
pollutant diffusion, and the reliable prediction of water wave
motion and the breaking wave-induced currents in coastal areas is crucial to coastal engineering applications.
The study of coastal water waves and breaking wave-induced nearshore currents, especially longshore currents, is one
of the classic and popular topics in the coastal research. Many
researchers have made many studies and developed theories
for the numerical simulation of wave-induced currents. As the
coastal zone is always a shallow water zone, the wave-induced
currents can be simulated by the shallow water equation or
Boussinesq model, and the shallow water equation is much
more efficient in computation than Boussinesq model which
is usually used in relatively small areas. Longuet-Higgins and
Stewart (1962) were the first to propose that the wave dissipation primarily due to wave breaking in shallow water generates
radiation stress gradients which impose forces on the water column, and Iwata (1970) and Ding et al. (1998) had made more
comprehensive studies on the causes and mechanisms of the
radiation stress and proposed formulas for them. Tang et al.
(2008a, b) modeled the propagation of irregular water waves
and irregular breaking wave-induced nearshore currents based
on the parabolic mild-slope equation and the nearshore current
model. Tang and Cui (2010) simulated the pollutant movement
process in the water waves and nearshore wave-induced currents in combination with the nearshore wave-current model
and the pollutant transport model. Cui and Tang (2011) studied
the water waves and longshore currents formed by the breaking
of obliquely incident random waves at the Leadbetter Beach.
Zheng et al. (2008) simulated a random wave transformation
in strong wave-induced coastal currents based on the wave action balance equation with diffraction effect. Rusu and Soares
(2010) evaluated the performance of two wave-induced nearshore current models in which the water waves were modeled
by SWAN wave model and refraction-diffraction wave model respectively. Nayak et al. (2012) simulated the nearshore wave-induced setup along Kalpakkam coast during an extreme cyclone
event in the Bay of Bengal using the SWAN wave model and the
vertically integrated momentum balance equation in which a
wave-induced setup is balanced by the wave radiation stresses.
Tang et al. (2012) studied the interaction of the water waves with
Foundation item: The National Basic Research Program of China under contract No. 2013CB430403; the National Natural Science Foundation of
China under contract No. 51179025; the Open Foundation of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering under
contract No. 2013491511; the Open Foundation of State Key Laboratory of Ocean Engineering under contract No. 1305.
*Corresponding author, E-mail: [email protected]
41
TANG Jun et al. Acta Oceanol. Sin., 2014, Vol. 33, No. 9, P. 40–46
the wave-induced longshore currents. Though many research
achievements have made on water wave-induced currents,
due to the complicated hydrodynamic factors in shallow water zones, the accurate predictions of waves and wave-induced
currents are still important for the further research, especially in
coastal zones (Liang et al., 2010; Liang et al., 2012).
This paper aimed at studying the coastal waves and the
wave-induced longshore currents in Obaköy coastal water
which is located at the Mediterranean coast of Turkey. The
numerical models consisted of surface water wave and wave
breaking induced current models. In the models, the parabolic
mild-slope equation was applied to modeling the surface water
waves, and the shallow water equation was applied to modeling
the breaking wave-induced longshore currents, where the water
waves provided the radiation stress gradients to drive currents.
The coastal waves and the wave-induced longshore currents
in Obaköy coastal water were studied based on the numerical
results. The rest of the paper was structured as follows. The numerical models were described in Section 2. In Section 3, the
numerical results for the water wave-induced longshore currents were validated by the measured data to demonstrate the
efficiency of the numerical models, and the discussions of the
waves and the longshore currents induced by the water waves
from main directions in Obaköy coastal water based on the
numerical results were also presented. Conclusions were presented in Section 4.
b1 ∂ 2 
∂A  ' 1 ∂Cg 
∂A 
+E +
 A−
 CCg
+
2 ∂x 
ω k ∂x∂y 
∂x 
∂y 
∂ 
∂A 
F '  CCg
=0 ,
∂y 
∂y 
(1)
in which
)
E' =
i k − a0 k Cg +
F' =
=
Db
iCg
2
2
D A +
1 Db
,
2 E
i 
k  b1  k x ( Cg ) x 
,
 a1 − b1  +  2 +
2kCg 
k  ωk


ω
D = k3
2
C ( cosh 4kh + 8 − 2 tanh kh )
,
4
Cg
8sinh kh
KCg
h
(6)
where γ is the wave-breaking ratio, it is usually preferable to 0.6
to 0.8; and L is the wave length.
The incident boundary condition can be specified as
(
)
i  k0 cosθ0 −k x0 + k0 sinθ0 y 
2.1 Parabolic mild-slope equation
The surface water waves are the main driving factor for the
wave-induced nearshore currents, and the reasonable evaluation of the wave-induced currents is indispensable for an accurate simulation of the water waves. If the waves propagate forward over the coastal bathymetry in a main direction, and the
reflection effects are ignored, the parabolic mild-slope equation
can be effectively used to simulate the wave propagation. Kirby
(1986b) has established an parabolic mild-slope equation based
on a minimax principle which can be applied to simulating
wave propagation with a large incident angle, and the equation
incorporating wave-breaking effect can be described as follows:
(
H b = min(γ h, 0.14 L tanh kh) ,
A ( x0 , y ) = A0 e 
2 Numerical models
Cg
where i is the imaginary unit; the positive direction of x is
the wave propagation principal direction; y is the direction
perpendicular to the x-axis; A denotes the complex wave
amplitude; Cg =
∂ ω ∂k , is the wave group velocity; C = ω k ,
is the wave velocity, k is the local wave number, ω is the wave
angular frequency; k is the average of k over the y-direction;
a0, a1 and b1 are the coefficients of the rational approximation
determined by the varying aperture width θ, and defined here
as a0=0.994 733 030, a1=−0.890 064 831 and b1=−0.451 640 568;
h is the still-water depth; E=ρg|A|2/2, is the wave energy, g is
the gravity acceleration, ρ is the water density; Es is the wave
energy where the wave height is stable after wave breaking and
Dally et al. (1985) have the value of E under 0.4h; D is the wave
nonlinear effect term, Db is the wave energy dissipation term;
and K≈0.15, is an experiential coefficient.
In the wave propagation model, it is assumed that the wave
begins to break when the wave height H is greater than the
breaking wave height Hb, and Grasmeijer and Ruessink (2003)
defined Hb as follows:
( E − ES ) ,
(2)
(3)
(4)
(5)

,
(7)
where (x0,y) is the coordinate of the incident boundary; A0 is the
incident wave amplitude; k0 is the wave number of the incident
boundary; and θ0 is the incident wave angle from the principal
direction of the wave propagation. For lateral boundary conditions, Kirby (1986a)used the following expression:
∂A
= ica Aksinθ ,
∂y
(8)
where ca is the wave reflection coefficient on the lateral boundaries, it is usually preferable to 0 to 1.0.
Equation (1) can be discretized by a finite difference method
with Crank-Nicolson scheme and solved by tridiagonal mathematic algorithm in Tang et al. (2008b).
2.2 Wave-induced current model
Coastal wave-induced current is mainly forced by the wave
radiation stresses in the process of the wave propagation, and
it can be simulated by shallow water equations as the coastal
water is always quite shallow. Incorporating the effect of the
bottom shear stresses and the lateral turbulent stresses, the
wave-induced current model can be described as the following
depth-integrated, horizontal momentum balance equations:
∂η ∂
∂
0,
+ U ( h + η )  + V ( h + η )  =
∂t ∂x 
∂y
 ∂S xx ∂S xy
∂U
∂U
∂U
∂η
1
+U
+V
+g
+
+

∂t
∂x
∂y
∂x ρ ( h + η )  ∂x
∂y
1
ρ (h +η )
(τ
ηx
− τ bx ) − Amx =
0,
(9)

−

(10)
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TANG Jun et al. Acta Oceanol. Sin., 2014, Vol. 33, No. 9, P. 40–46
 ∂S yx ∂S yy 
∂V
∂V
∂V
∂η
1
+U
+V
+g
+
+

−
∂t
∂x
∂y
∂y ρ ( h + η )  ∂x
∂y 
1
0,
(τη y − τ by ) − Amy =
ρ (h +η )
τ by =
(11)
where t is the time; η is the mean water level; U and V are the
depth-integral wave-induced current velocities in the x and
y directions respectively; Sxx, Sxy, Syx and Syy are the wave radiation stress components; τbx and τby are the bottom friction
stresses in the x and y directions respectively; τηx and τηy are the
surface friction stresses in the x and y directions respectively;
and Amx and Amy are the lateral mixing stress terms in the x and
y directions respectively.
The wave radiation stresses are essentially the forcing of
wave on the water column driving nearshore currents, and the
reasonable evaluation of the radiation stress is crucial for an accurate simulation of the wave-induced currents. However, it is
not an usually easy task to evaluate the radiation stresses when
the wave field is complicated due to the complicated geography. For example, when the waves are focused behind a shoal,
the conventional theory that evaluates the radiation stresses by
an explicit wave propagation angle fails to evaluate properly the
radiation stresses because it is hard to define a direction of the
wave propagation. Zheng et al. (2000) deduced the alternative
calculating formulas of the wave radiation stresses on the basis of the complex wave amplitude in the parabolic mild-slope
equation to solve these difficulties, and this result in an effective method for calculating the wave radiation stresses using an
intrinsic wave propagation angle that differs from the ones of
using the explicit wave propagation angle. The formulas for the
wave radiation stresses used by Zheng et al. (2000) in the paper
are as follows:
ρ g  ∂A
2
1 
2kh 
2kh
2
+ i kA 2 1 +
+

+ A
4  ∂x
k  sinh 2kh 
sinh 2kh
2
2

2kh / tanh 2kh − 1  ∂A
∂A
2

+ i kA +
− k 2 A  ,
2
 ∂x

2k
∂y


S xx =

2kh / tanh 2kh − 1  ∂A
∂A
2

+ i kA +
− k 2 A  ,
 ∂x

2k 2
y
∂


(13)
*
ρ g   ∂A
 ∂A 
+ i kA 
S xy =
S yx =
Re 
×
4   ∂x
∂
y


1 
2kh  
1 +
 ,
k 2  sinh 2kh  
(14)
where A* is the conjugate complex of A; and the other variables
are the same as above.
The surface friction stresses in the x and y directions are ignored herein, and the following expressions for the bottom friction stresses by Longuet-Higgins (1970) under waves and weak
currents can be used:
τ bx =
4
ρ cf u0U ,
π
Amx
=
∂  ∂U  ∂  ∂U 
,
µ
+ µ
∂x  ∂x  ∂y  ∂y 
(17)
Amy
=
∂  ∂V
µ
∂x  ∂x
 ∂  ∂V 
,
+ µ
 ∂y  ∂y 
(18)
where μ is the lateral mixing coefficient which can be calculated
as the formula
µ = Λu0 H ,
(15)
(19)
where Λ=0.85, is a non-dimension coefficient by Chawla et al.
(1998).
The initial boundary conditions for the wave-induced current model are assumed to be in the state of the rest, and can be
specified as follows: U = 0, V = 0 , η = 0 .
At the onshore boundary and along the lateral open sea
boundaries, the continual boundary condition is adopted:

∂U
∂V
∂η
 = 0 ,  = 0 ,  = 0 , and n is the normal direction of the
∂n
∂n
∂n
boundary.
The wave-induced current model can be solved by a finite
difference scheme with the ADI method. The model was run
until they approximate a steady state, and the stability criterion
can be used by Ebersole and Dalrymple (1980) as follows:
( ∆x ) + ( ∆y )
2
∆t ≤
2
(16)
where u0 is the bottom velocity amplitude which can be guided
by the linear wave theory u0 = 2πaw / T , and aw = H / ( 2sinh kh ) ,
is the amplitude of the bottom wave particle movement, T is
the wave period; cf =0.015, is the empirical friction coefficient
in waves and currents; and the other variables are the same as
above.
The lateral mixing stress terms can be defined as follows:
(12)
2
ρ g  ∂A 1 
2kh 
2kh
2

S yy
=
+
1 +
+ A
4  ∂y k 2  sinh 2kh 
sinh 2kh

2
2
ρ cf u0V ,
π
ghmax
2
,
(20)
where Δx and Δy are the spatial discretization steps in the x
and y directions respectively; Δt is the time step; and hmax is the
maximum water depth.
3 Simulation of waves and wave-induced longshore currents
in Obaköy coastal water
Obaköy coastal zone is a mild-slope bottom zone located
on the Mediterranean coast of Turkey. When the wave travels to
coastal areas, the water depth becomes shallow, the wave breaks
and the wave height and the energy decrease rapidly, then the
greater gradients of the radiation stresses formed during the
wave breaking process, and they usually drive the local water
to flow in these areas. The mean seabed slope in this zone is
about 1/20, and the seabed slope in the nearshore area is about
1/30. The bathymetry of Obaköy coastal zone is shown in Fig. 1
(Balas et al., 2006), where the x-axis direction is set at the north
direction (onshore direction), the y-axis is set at the west direction (alongshore direction). For the zone, the wave propagates
from the dominant wave directions, which are in the range of
43
TANG Jun et al. Acta Oceanol. Sin., 2014, Vol. 33, No. 9, P. 40–46
12
36
14
26
6
36
12
20
10
30
34
18
48
42
4
22
2
4
16
32
22
20
30
0
24
28
8
14
26
100
18
200
6
y/m
2
16
24
28
32
200
100
6
8
38
4
46 4
300
10
500
400
4
40
14
18
16
20
22
24
26
28 32
30
600
300
400
x/m
500
600
700
Fig.1. Bathymetry of the computational area. The water depth is in metre.
the SSW (θ0=−22.5°) and the SE (θ0=45°) directions (Balas et al.,
2006). In the paper, as waves travel from the SE (θ0=45°), the SSE
(θ0=22.5°), the S (θ0=0°) and the SSW (θ0=−22.5°) directions, the
distributions of the coastal waves and wave-induced longshore
currents were numerically simulated and studied based on the
above models. The simulation dimension is 760 m×640 m, and
the deep water wave parameters were selected as, the wave period T0=5.0 s, the wave height H0=3.5 m, to specify the offshore
boundary conditions (Balas et al., 2006). Full transmission and
zero gradient boundary conditions were applied for wave and
current respectively along the lateral boundaries. The incident
deep water wave parameters are shown in Table1. Firstly, the
numerical models were validated by comparisons between the
numerical and experimental results of the wave-induced longshore currents in four sections for the waves approaching from
the SE in Case 1, then they were used to study the waves and
longshore currents induced by waves from SE, SSE, S and SSW
directions in Cases 1, 2, 3 and 4.
The comparisons between the numerically simulated and
measured wave-induced longshore currents in Balas et al.
(2006) for the waves approaching from the SE in Case 1 in four
sections (y=40.0, 200.0, 360.0 and 520.0 m) were shown in Fig. 2.
It can be seen that the numerically simulated longshore current
velocities are in good agreement with the measured data,
and the present models are efficient for modelling the waveinduced longshore currents in the study area.
Figures 3 to 6 showed the numerically simulated wave
heights, the mean water levels and the wave-induced longshore
currents for Cases 1–4. As it was shown in Figs 3a, 4a, 5a and
6a, in the process of the wave propagation from the deep water
zone to the shallow water zone, the wave defocused in the wave
propagation direction behind the shoal resulting in the decrease
of the wave height gradually. As the wave traveled into the very
shallow areas where the wave height is less than the breaking
wave height, wave began breaking and wave height decreased
rapidly, and the wave height was about 0.6h (h is the local water depth) and its distribution was approximately related to the
local water depth contour. These may be due to that the wave
height is usually proportional to the local shallow water depth
contour as the wave breaks. The numerically simulated mean
water level in Figs 3b, 4b, 5b and 6b clearly exhibited the decrease of the water level as the wave approaches the wave breaking zone and the increase of the mean water level as the wave
breaks, and the gradient of the mean water level was also a driving factor for current. Figures 3c, 4c, 5c and 6c showed that the
wave-induced longshore currents were mainly generated in the
wave breaking zone and parallel to the coastline on the whole,
but in some areas the longshore wave-induced currents slightly
deflected corresponding to the asymmetrical water depth and
approximately paralleled to the bathymetry contours, and the
movement of the wave-induced longshore currents was also
different in the four cases for different incident wave directions.
For the wave propagated from the SE and the SSE directions in
Case 1 and Case 2, the longshore currents flowed mainly from
south to north along the coastline and deviated tending to the
offshore zone near the northern boundary, and the movement
Table 1. Deep water wave parameters in the simulation wave-induced longshore current
Case
Incident wave direction
H0/m
T0/s
θ0/(°)
1
SE
3.50
5.0
45.0
2
SSE
3.50
5.0
22.5
3
S
3.50
5.0
0.0
4
SSW
3.50
5.0
−22.5
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TANG Jun et al. Acta Oceanol. Sin., 2014, Vol. 33, No. 9, P. 40–46
2.0
2.0
a
simulated model
experiment data
1.0
0.5
1.0
0.5
0
100
2.0
200
300
400
x/m
500
600
0
700
2.0
c
simulated model
experiment data
100
200
300
d
1.0
0.5
400
x/m
500
600
700
500
600
700
simulated model
experiment data
1.5
V/m∙s−1
1.5
V/m∙s−1
simulated model
experiment data
1.5
V/m∙s−1
V/m∙s−1
1.5
b
1.0
0.5
0
100
200
300
400
x/m
500
600
0
700
100
200
300
400
x/m
Fig.2. Comparison between the numerical and measured data (Balas et al., 2006) of the wave-induced longshore currents for
Case 1. a. Section 1 (y=40.0 m), b. Section 2 (y=200.0 m), c. Section 3 (y=360.0 m) and d. Section 4 (y=520.0 m).
300
500
400
x/m
0.8
100
200
300
400
x/m
500
100
0
0
-0.1
0
700
600
300
200
0.05
100
1.4
1
600
y/m
0.05
-0.1
0.6
1.2
400
-0.05
2.2
2.8
2.6
1.8 2
3.2
3
200
200
1 m/s
0
-0.1
1.8
y/m
3.4
100
-0.1
3.2
y/m
0
300
c
500
0.1
3
3.4
100
0 -0.05
-0.1
3.2
200
0.1
400
2
300
2.6
600
0.25
0.15
0.2
0.05
2.4
400
2.8
-0.1
500
2
3
b
-0.05
1 1.2
1.6 1.8
2.2
2.8
3
500
600
0.6 0.8
a
3.4
600
700
100
200
300
400
x/m
500
600
700
Fig.3. Numerically simulated wave height, mean water level and wave-induced longshore current for Case 1. a. Wave height (m),
b. mean water level (m) and c. wave-induced longshore current (m/s).
300
400
x/m
500
600
1
1.6
0.4 0.6
1.2
0.8
700
-0.05
-0.15
-0.2
-0.2
0.05
100
200
300
400
x/m
500
600
700
400
y/m
0
100
0
0.05
0
1.8
2.8
2.4
2
2.2
200
300
200
3
y/m
3.2
100
1.4
0
2.6
5
-0.0 -0.1
100
3.2
3.4
1 m/s
500
0
2.8
200
-0.2
400
1.6
3
600 c
0.15
0.1
-0.2
2
2.8 3
300
0
500
1.8
3.4
400
b
1.4
y/m
3
3.2
500
600
0.8
1.2
2.4
2 2.2 2.4
3.2
1.6
a
4
3.
600
300
200
100
0
100
200
300
400
x/m
500
600
Fig.4. Numerically simulated wave height, mean water level and wave-induced longshore current for Case 2. a. Wave height (m),
b. mean water level (m) and c. wave-induced longshore current (m/s).
700
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TANG Jun et al. Acta Oceanol. Sin., 2014, Vol. 33, No. 9, P. 40–46
3.2
100
200
1
300
500
400
x/m
600
0.2
700
100
0.15
-0.2
0
100
200
300
400
x/m
0.2
-0.2
500
600
300
200
0.1
-0.15
-0.2
100
0.6
2
1.6
3
3.4
0
-0.2
-0.05 -0.1
0
y/m
3
2.4
1.8
1.4
0.4
3.2
100
-0.05
300
200
1.2
2.2
3.4
3.2
200
0
3.2
300
1 m/s
400
-0.15
2
-0
.2
c
500
0.05
-0.1
-0.2
1.2
3.2
400
600
y/m
500
1.8 .2
2
3.2
3.4
y/m
-0.2
0.1
b
-0.15 -0.2
600
0.6
1.2
3.2
500
400
0.8 0.2
0 -0.05
3.4
a
1.8
2.4 2.8
2.6 3
600
0
700
100
200
300
400
x/m
500
600
700
Fig.5. Numerically simulated wave height, mean water level and wave-induced longshore current for Case 3. a. Wave height (m),
b. mean water level (m) and c. wave-induced longshore current (m/s).
-0.2
b
0.8
5
1
1.4
100
200
300
400
x/m
500
600
-0.1
-0.1
5
1.4
700
0
100
200
300
400
x/m
500
600
0
300
200
0.05
-0.05
25
100
-0.2
-0.25
-0.1
3.2
2.6
2
0.6
3.4
100
0
1.2
400
-0.25
200
3.2
-0
.
200
-0.2
-0
.2
5
300
2.2
2.8
300
y/m
3
c 1 m/s
500
-0.05
400
3.2
3.4
400
y/m
1.6
3
y/m
-0.2
-0.1 -0.15
500
600
0.15 0.1
3.2
500
600
2.2
0.05
0
5
-0.0
1.2
2.6
600 a
700
100
0
100
200
300
400
x/m
500
600
700
Fig.6. Numerically simulated wave height, mean water level and wave-induced longshore current for Case 4. a. Wave height (m),
b. mean water level (m) and c. wave-induced longshore current (m/s).
of the currents were more tending to the offshore zone for the
wave propagation from the SSE direction. For the wave propagated from the S direction in Case 3, the longshore currents,
as compensation currents, flowed to the centre of the concave
shore from both south and north directions along the coastline
and the rip current flowed to offshore from the centre of the
concave shore. For the wave propagated from the SSW direction in Case 4, the longshore currents flowed mainly from north
to south along the coastline and deviated tending to the offshore zone near the southern boundary. Hence, the longshore
currents are different while the wave propagated to the coastal
zone from different directions.
4 Conclusions
Water waves and nearshore currents are important
hydrodynamics in coastal zones. In the process of the wave
propagation from the deep ocean to the shallow water, they
undertake an obvious transformation due to the combination effects of refraction, diffraction and shoaling, and eventually break near the shoreline and generate the currents that
flow in both offshore and alongshore directions. In this paper,
the waves and the wave-induced currents in Obaköy coastal
water which is located on the Mediterranean coast of Turkey
were numerically studied. The numerical models are based
on the parabolic mild-slope equation for the coastal water
waves and the nonlinear shallow water equation for the wave-
induced currents. The wave transformation under the effects of
shoaling, refraction, diffraction and breaking is considered and
the wave provides the radiation stresses for driving current in
the model. The numerical results for the water wave induced
longshore currents were validated by the measured data to
demonstrate the efficiency of the numerical model, and the
water waves and nearshore currents induced by the waves from
different directions were numerically simulated and analyzed
based on the numerical results. The numerical results show
that the movement of nearshore currents is different while the
wave propagated to the coastal zone from different directions.
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