Int. J. MAr. Sci. Eng., 4(1), 15-24, Winter & Spring 2014

ISSN 2251-6743

© IAU

Numerical modelling of induced rip currents by discontinuous

submerged breakwaters

1* M. J. Ketabdari;

2M. BarzegarPaiinlamouki

1 Faculty of Marine Technology, Amirkabir University of Technology, Hafez Avenue, Tehran, Iran 2 Department of marine technology, Amirkabir University of Technology, Hafez Avenue, Tehran, Iran

Received 2 December 2013; revised 14 March 2014; accepted 12 April 2014

ABSTRACT: Submerged breakwaters are one of the shore protective structures. Any discontinuity in these

breakwaters causes changes on current parameters including speed and water surface profile. In this paper,

discontinuous submerged breakwaters were modelled to investigate the changes in the wave and flow pattern. To

investigate the phenomenon, three models including a shore with constant slope, a shore with continuous submerged

breakwater and a shore with discontinuous breakwater were used. Extended Boussinesq Equations were used for

wave generation. The results of the models showed that in the shore without breakwaters transient rip currents are

produced across the shore. By addition of the breakwater, the wave breaking happens on the crest of breakwater

which leads to dissipation of their energy. This in turn creates calm shore currents. However, constructing a gap in

the center of breakwater causes some changes in the system of shore currents. This phenomenon generates a pair of

flow vortices and a powerful return current called rip current. Rip currents not only threaten the life of swimmers, but

also play an important role on the sediment transportation and erosion of the sea bed around the breakwater gap and

may lead to destruction of the whole breakwater.

Keywords: Discontinuous submerged breakwater; Wave breakings; Rip currents; Boussinseq Equations.

INTRODUCTION1 Waves can cause coastal erosion and sedimentation

leading to the change of the shore line. To protect the

shore against waves, submerged breakwaters can be

used. These breakwaters are used in near shore zone

and cause high wave breaking and consequent wave

energy dissipation. Energy damping causes a change

on the sediment regime from erosion to

sedimentation. The sedimentation in the form of

accumulation appears at breakwater's lee side and

conserves the shore line; but if breakwater is

constructed discontinuous, its performance will

change. This gap in the center of breakwater may be

opened for different reasons such as ships traffic

handling. Such a system in the shore can also

naturally be made with the discontinuous sand bars.

Rip currents are powerful one directional current that

flow back towards the sea. Their origin begins from

shore line, then passes the breaking zone and travels

towards the shoaling zone. Rip currents may exist in

any shore when the wave breaking occurs. This

current within the shore set-up zone diminishes

naturally and then slows down towards the sea.

Formation of rip currents and their return velocity

*Corresponding Author Email: ketabdar@aut.ac.ir, mjketabdari@yahoo.com Tel.: 09121344349, 02164543111

depend also on the morphology of the shore line. This

in turn affects the displacement of the sedimentation

sector in surf zone. In the circulation system of shore

currents, rip currents usually are distinguishable by

sediments and suspended materials that carry towards

the sea. Rip currents consist of three principle parts

including feeder, longshore and strong return

currents.

In recent decades, limited studies have been done on

submerged breakwaters. Subjects that are often

studied include the transferred wave energy over

submerged breakwaters (Allsop, 1983; Khaber at al.,

1980). These studies showed that the submergence

depth and geometrical shape of the structure have the

most impact on the passing wave parameters and their

profile. (Koraim et al., 2014) studied the protecting

effects of submerged breakwater on porous seawall

by analyzing its hydrodynamic characteristics. The

results showed that submerged breakwater decreases

the wave reflection and the run-up on the seawall by

about 70 % and 20-60 %, respectively. Studies on permeable submerged breakwaters by

(Dick and Brebner, 1968) showed that breakwaters

with zero crest freeboard relative to water level

reduce the wave energy up to 50%. In a set of

M. J. Ketabdari and M. BarzegarPaiinlamouki

16

experimental studies, (Young and Testik, 2011)

investigated the reflection coefficient for submerged

vertical and semicircular breakwater and concluded

that in general the submerged vertical breakwaters

reflect more energy than submerged semicircular

breakwaters., Using the volume-averaged Reynolds

average Navier-Stokes equations, (Wu and Hsiao,

2013) simulated the interaction between a non-

breaking solitary wave and submerged breakwater.

(Ramen et al., 1977) considered the influence of rigid

rectangular breakwaters on dissipation of wave

energy. They expressed the wave transmission

coefficient in terms of the total wave power.

(Carevice et al., 2009) studied the irregular wave

transmission over the submerged breakwater. They

validated their results by comparing them with the

experimental work of (Johnson, 2006). (Bellotti,

2004) presented a simplified model to estimate

current velocity and changes of water level around

the discontinuous submerged barriers. Another group

of researchers only focused on the rip current

modelling.

In a preliminary research performed by (Shepard and

Inman, 1950), the range of rip current velocity was

obtained between 0-1 m/s. High velocities of rip

currents can influence on sediment transportation in

shores (Komar, 1971; Short, 1999). Field studies on

rip currents have also been performed among them

that of the Palm Shore of Australia is one of the most

important. By taking daily photography and

extracting the information in a period of 2 years,

useful information about this phenomenon was

obtained (Holman at el., 2005).

The analysis of 5-year lifeguard records from 20

beaches in southwest England by (Scott et al., 2014)

showed that high-risk occus around mean low water

on days with long wave period (Tp>10 sec) and low

wave height (Hs< 1 m). Experimental studies

confirmed field observations and showed that the rip

currents velocity reduces by increasing the wave

height and decreasing the surface water level (Fronen

et al., 2002; Haller et al., 2002).

(Johnson et al., 2005) simulated waves and currents

around submerged breakwaters by a phase-averaged

and phase resolving methods. A high order 2DH-

Boussinesq-type model was used to calculate the

waves and flow. The comparison between numerical

results and experimental datapresented a good

compatibility. Other researchers such as (Bellotti,

2004), (Calabrese et al., 2008) and (Sharifahmadian

and Simons, 2014) simulated rip currents and flow

around the submerged breakwater.

In Iran, some researches focused on feasibility of the

rip currents. (Rafi and Maghen, 2007) as well as

(Gholami, 2008) tried to model rip currents in

Mazandaran province coastline. They claimed that in

this shore line in an average of each 800 m there is

the possibility of occurrence of one rip current.

(Shafiei and Barani, 2011) made a research on the

pattern of rip currents in southern costs of Caspian

Sea.

The broad literature as above shows that although

researchers made a great effort on the problem of rip

currents and submerged breakwaters there is a need to

investigate on the relation between discontinuous

manmade submerged breakwters or natural sand bars

and formation of rip currents.

In this paper the effects of existence of a gap in a

submerged breakwater or longshore sandbar on the

current parameter including velocity and wave height

were investigated. For a better understanding of

breakwater’s effects on current parameters, at first a

shore with constant slope without any breakwater was

studied. Then the procedure was repeated with a

continuous submerged breakwater at near shore.

Finally by making a gap in the submerged

breakwater, its influences on velocity and height of

return currents were investigated. A parametric study

was also implemented on the effect of breakwater

height on shore currents.

MATERIAL AND METHODS

Governing equation

Surface waves are the most important phenomenon

that occurs in seas and oceans. Capability for

prediction of the wave transition from deep water to

shallow water and their breaking is one of the vital

matters in understanding the shore process. When

waves propagate towards the ocean, compound

effects due to wave run-up, refraction, diffraction and

wave interaction change the profile of the waves.

These circumstances lead to much different wave

features in shallow water respect to deep water.

Boussinesq Equations are able to model the wave

evolution at shore zone very well. Therefore, for

modelling the currents around the bars and

breakwaters, modified version of Mike 21 BW

Software was used. BW module established

according to the Extended Boussinesq Equations.

Governing equations are as following:

Continuity equation

∂η

∂t+

∂p

∂x+

∂Q

∂x= 0 (1)

Momentum equation in X direction

∂Q

∂t+

∂

∂x(

pQ

d) +

∂

∂y(

Q2

d) + gd

∂η

∂y+

∂Rxy

∂x+

∂Ryy

∂y+

txy

ρ−

∂

∂x(dTxy) −

∂

∂y(dTyy) + Ψy = 0 (2)

Momentum equation in Y direction

Int. J. Mar.Sci.Eng., 4(1), 15-24, Winter & Spring, 2014

17

∂Q

∂t+

∂

∂x(

pQ

d) +

∂

∂y(

Q2

d) + gd

∂η

∂y+

∂Rxy

∂x+

∂Ryy

∂y+

txy

ρ−

∂

∂x(dTxy) −

∂

∂y(dTyy) + Ψy = 0 (3)

Where is the wave elevation relative to the still

water surface, (P, Q) is depth-integrated velocity in

Cartesian coordinate system (x, y) and T is the time.

D is total water depth and h is still water depth. x

and y are dispersive Boussinesq terms. Terms of

Rxx, Rxy, Ryy are additional convective momentum

due to wave breaking that defines as follow:

(Rxx, Rxy, Ryy =δ

1−δ

d

((cx −p

d)2, (cx −

p

d) ∗

(cy −Q

d) , (cxy −

Q

d)2) (4)

Here )t,y,x( is the thickness of surface roller

and )C,C(C yx are the roller celerity

components. Bottom shear stresses are obtained by

following equation:

(tx, ty) =1

2fm

√p2+Q2

d2(p, Q) (5)

Where mf is bottom friction factor. Turbulent is

modelled by eddy viscosity formula as:

txx = 2ν∂

∂x(

p

d) (6)

txy = tyx = ν(∂

∂y(

p

d) +

∂

∂x(

Q

d) (7)

tyy = 2ν∂

∂y(

pQ

d) (8)

In whichν is eddy viscosity.

Grids used in this module are staggered. Water

surface level is located in grid nodes and flux

components are placed between and adjacent to them.

Applied finite difference approximations are used by

the central difference methods as explained by

(Madsen and Sorensen, 1992).

Model set up

To study the effect of discontinuous sandbars and

submerged breakwaters in shore, three tests were

performed. Study domains in this project were1200

*1200 m with an incident regular wave with a height

of 2.7 m.

Propagation of regular waves on constant slope

shore

Wave propagating on the shore deforms. Decreasing

water depth causes an increase in wave height and a

decrease in wave length. These changes lead to wave

breaking near the shore. Waves breaking cause

turbulent in current flow in the breaking zone and

sediment transportation. The models simulated a

shore with constant slope of 3.3% (Fig. 1). A regular

wave with height of 2.7m propagated on shore and

proceeds towards near shore line located in the

coordinate x = 890 m.

Fig. 1: Bed topography in the study domain

Propagation of regular waves on the continuous

submerged breakwater

In the regions that environmental remarks should be

considered, any kind of submerged breakwaters for

protecting the sea shore were used as a suitable

solution. These structures have the ability to dissipate

wave energy in offshore. These structures prevent

from high energy transition toward the beach

avoiding considerable sediment transportation and

changes of shore line.

In order to assess the model and investigate the

discontinuous submerged breakwater influences, in

first step regular wave propagation on a shore with

continuous breakwaterwassimulated. Breakwater was

located at the distance of 174 m from shore and the

difference between water level and breakwater crest

was equal to 1.5m. Shore slope in offshore was equal

to 3.3% and shoreline was located at coordinates x =

890 m.

Propagation of regular waves on discontinuous

submerged breakwater

Discontinuity in longshore structures may be

manmade to create a path for ships transit. This gap

may cause a change in the pattern of shore currents.

This must be considered in the design of the

submerged breakwaters. Such discontinuity in

longshore sandbar can be produced by sedimentation

on offshore naturally. For modelling the

Numerical modelling of induced rip currents by discontinuous submerged breakwaters

18

discontinuous submerged structure, a gap of 60 m

width was created in the middle of breakwater. The

effects of this gap on the current parameters were

then investigated. Features and place of breakwater

was the same as previous test (Fig. 2).

Fig. 2: Changes of sea bed in the shore with discontinuous

breakwater

RESULTS AND DISCUSION

Shore without barrier and with continuous

breakwater

To investigate the influences of shore barriers on

shore currents in this step, shore with constant slope

and shore with continuous submerged breakwater

were investigated. To demonstrate this influence,

changes in water level and current velocity in two

different conditions were evaluated. As mentioned

before, wave propagation towards beach is associated

with decrease of wave celerity and increase of its

height due to bottom friction and continuity

regulation. When the water height reaches to the

critical limit, wave breaking occurs. (McCowan,

1980) showed that the breaking wave height is

estimated as Hb = db, where dbis the water depth in

the breaking point and = 0.78. Other researchers

such as (Dalrymple et al., 1997), Postacchini and

(Brocchini, 2014) and (Zheng et al., 2008) performed

more researches to improve this equation.

Based on the model results in shore without

breakwater, the breaking occurs at a distance of 100

m from shore line. However in the shore with

continuous breakwater, breaking line moves to the

point of 170 m from the shore line (Fig. 3). As it can

be seen in Fig. 3, the incoming wave patterns of two

models are nearly the same before breakwater.

As the waves reach the barrier, breaking occurs and

wave energy dissipates. This in turn creates a

relatively calm current on the shore. In contrast, on

shore with constant slope and without a breakwater,

waves continue to progress, until their height increase

and breaking occurs in a lower depth. In this case,

wave breaking creates somehow non-uniform

currents in near shore. These currents may create

transient rip currents. The transient rip currents are

narrow offshore flows which are associated with a

topographic rip channel. They are temporally and

spatially variable and after a while decays (Johnson

and Pattiaratchi, 2006). Fluctuating nature of current

return velocity can be a reason for development of

these currents in the form of transient. (Johnson and

Pattiaratchi, 2004) alsomentioned such a point during

lagrangian measurements of transient rip currents on

a beach without an offshore bar or significant

longshore variation. They found that offshore

directed flows with speeds 0.2-0.5 m/s occurring at

variable locations. Hence, as can be seen in Fig. 4, the

fluctuations of speed shows that a transient return

current forms in a moment and then cuts off.

Near shore current velocities including littoral and

return velocities in two models are different with each

other due to the difference in height of incoming

waves in this area. For higher wave, the induced

currents have higher velocities. Return current

velocities in coordinates (780 m, 600 m) is compared

for two models in the Fig. 4.

Fig. 3: Comparison of surface water level changes in point y = 890 m for shore with breakwater and shore without

breakwater

Int. J. Mar. Sci. Eng., 4(1), 15-24, Winter & Spring, 2014

19

Fig. 4: Diagram of return velocity (U) and longshore velocity (V); in coordinates (780 m, 600 m)

All dynamic models of rip currents are forced by

alongshore variations of wave height. It in turn leads

to alongshore variations in wave-induced momentum

flux (Kennedy and Thomas, 2004; Longuet and

Stewart, 1964; and Phillips, 1977). (Bowen, 1969),

(Sasaki and Horikawa, 1978) and (Symonds and

Ranasinghe, 2001) described rip currents as an

interaction of the wave field with lower frequency

waves such as edge waves. These longshore waves

generate return currents or rip currents (Johnson and

Pattiaratchi, 2006). However, longshore current

velocities for two models are not much different. This

proves this fact that creation of a powerful rip current

is associated with a strong longshore current.

Therefore, the longshore velocities in these models

are low and a strong rip current does not form on the

shore. However, return velocity in the first model is

much greater than that of the second one. It is

because waves breaking in the second model occurs

at a far distance to shore leading to a less return

velocity than the first model. Comparison of the

results of these two models showed that breakwater

affects the pattern of shore currents accompanied by a

decrease in return currents velocity, which in turn

decreases the sediment transportation.

Shore with continuous and discontinuous

breakwaters

In this section the influence of a gap in submerged

breakwater on current parameter was studied. To

generate longshore variations which are required for

creating rip currents, there are two main basic types

of mechanisms. These models are wave and structural

interaction models (Dalrymple, 1978a and Kevin and

Svendsen, 2002).Wave interaction model originates

within the surf zone because of alongshore gradients

in wave-induced radiation stresses and pressure

(Dalrymple, 1978b; Dalrymple and Lozano, 1978;

Haller et al., 2002 and MacMahan et al., 2010).

Variations in wave heights alongshore can be created

by refraction of waves passing across offshore (Long

and Haller, 2005). The factors effecting on the

structural interaction model include bottom

topography and coastal structures (Belloti, 2004;

Castelle and Coco, 2012 and Xie, 2012).

Created changes on the velocity parameter are shown

in Figs. 5-9. Based on Fig. 5a, the gap leads to severe

changes in shore currents pattern. Wave height

increases due to wave run-up over the breakwater.

But wave height does not increase in the gap vicinity.

Pressure gradient resulted from higher water level on

the breakwater, relative to the water level over the

gap, causes longshore currents (feeding current).

Inthis case pressure gradients occur because of the

difference in wave breaking intensity (Dronen et al.,

2002). These longshore currents then become

convergent and return toward the sea from existing

gap. This action induces a pair of vortices in

coordinates (830 m, 650m) and (830 m, 650 m). This

were also found in the researchers of (Bruneau et al.,

2009) and (Peregrine, 1998).

M. J. Ketabdari and M. BarzegarPaiinlamouki

20

(a) (b)

Fig. 5: Current vector velocity of discontinuous breakwater: a) Experimental data (Haller et al., 1997)

b) Present model at t= 10 min

Fig. 6: Time histories of return velocity (U) and longshore velocity (V); in coordinates (794 m, 536 m) for beach with

discontinuous breakwater

Fig. 7: Inducedvorticity flow around the gap

Int. J. Mar. Sci. Eng., 4(1), 15-24, Winter & Spring, 2014

21

Fig. 8: Time histories of return velocity (U) and longshore velocity (V); in coordinates (714 m, 630 m) for beach with and

without continuous breakwater

Fig. 9: Time histories of return velocity (U) and longshore velocity (V); in coordinates (650 m, 600 m) for continuous and

discontinuous breakwaters

The pattern ofinduced current of present model in

shore have a good agreement with experimental data

of (Haller et al., 1997), both of which

demonstratevorticities opposite of each other as can

be seen in Fig. 5. The return and longshore velocities

in near line shore is shown in Fig. 6.These currents

move toward the offshore through the gap and scatter

after passage of the gap. Fig. 7 clearly shows the

pattern of rip current around the toe of breakwater. As

can be seen in Fig. 7, velocity component in the Y

direction (V, longshore velocity) in the sides of gap

and velocity component in the X direction (U, return

velocity) in the center of the gap have the maximum

values as (Damgard et al., 2002) and (MacMahan et

al., 2005) also mentioned in their researches. For

example, in coordinates (714 m, 630m), velocity

component in Y direction (longshore velocity) in

comparison with velocity component in X direction

(return velocity) has greater values. Velocity in this

point is compared with that of the continuous

breakwater in Fig. 8. This figure clearly shows that

longshore velocity increases significantly but returns

velocity does not change so much in the presence of

gap. The increase of the longshore velocity is due to

the fact that the waves over breakwater break before

reaching the center of gap and move toward the gap

(Dronen et al., 2002). In contrast in coordinates (650

Numerical modelling of induced rip currents by discontinuous submerged breakwaters

22

m, 600 m), conditions are different. At this point,

based on Fig. 9, U velocityis much greater compared

to that of the shore with continuous breakwater

because the water mass ejected seawards through the

gap (Kevin et al., 2002). But longshore velocity does

not change very much.

CONCLUSION

In this research a wide range of simulations was

performed on beach with and without submerged

breakwaters in continuous and discontinuous

conditions. The results showed that in the shore

without breakwater, many transient rip currents along

the shore are generated. However low distances

between them leads to a weak resulting current

velocity. In shore with continuous breakwater,

because of wave breaking over the breakwater and

energy dissipation of incoming waves, uniform

currents are generated near the shore. So there are no

powerful return currents. By adding a gap to

breakwater, shore currents pattern changes.

Two pairs of vorticity flows create in the shore. One

pair is located near the shore and the other is occurred

around the gap. The vortices located near the shore

play an important role in sediment transportation

towards offshore as well as pulling the beginner

swimmers far from the beach towards deep water and

threatening their lives. The power of vorticity flow

occurred around the gap is more than that of located

near the shore. This vorticity flow in turn can be a

threat for breakwater toe. Because of its high power,

the sea bed under the breakwater toe is washed out

leading to instability of the breakwater. Therefore,

marine structure designers must be paid much

attention to this phenomenon in design of

discontinuous breakwaters or existence of natural

discontinuous longshore sandbars. For further

investigation, it is suggested to do a parametric study

on breakwater height and gap width on shore current

system.

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How to cite this article: (Harvard style)

Ketabdari, M. J*.; BarzegarPaiinlamouki, M., (2014). Numerical modelling of induced rip currents by

discontinuous submerged breakwaters. Int. J. Mar. Sci. Eng., 4 (1), 15-24.