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Ocean Engineering 34 (2007) 605–615

www.elsevier.com/locate/oceaneng

The effect of groundwater on topographic changes in a gravel beach

Kwang-Ho Leea,�, Norimi Mizutania, Dong-Soo Hurb, Atsushi Kamiyac

aDepartment of Civil Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, JapanbDepartment of Ocean Civil Engineering, Gyeongsang National University, Tongyoung 650-160, South Korea

cComputer associates, Shinjuku-ku, Tokyo 163-0439, Japan

Received 20 June 2005; accepted 19 October 2005

Available online 19 April 2006

Abstract

In recent years, several attempts to stabilize the beach by control of the percolation of water have been proposed. However,

morphodynamics in the surf zone is still not clear because of the complexity of wave actions and sediment transport. Especially, there is a

little research on gravel beach morphodynamics including wave breaking in the surf zone. The present study investigates experimentally

how groundwater level influences topographic changes in a gravel beach and simulates numerically the wave fields and flow patterns in

the surf zone, considering the porosity of the media and the presence of groundwater. In experiments, water-level control tank was

designed to control the simulated groundwater elevation and the wave flume was divided into two parts to maintain a constant mean

water level. The experimental results show that the berm formed in the upper portion of the shoreline moves up the beach as the

groundwater level falls and the lower the groundwater level, the steeper the beach surface. The numerical model was developed to clarify

these features capable of simulating the difference of groundwater and mean water level. Numerical results showed different flow

patterns due to the groundwater elevation; wave run-up weakens and wave run-down strengthens by the seaward currents caused by

elevated groundwater. These deformations of the flow pattern explain well how the beach profile is affected by the groundwater

elevation.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Morphodynamics; Groundwater; Surf zone; Wave breaking; Wave run-up; Wave run-down

1. Introduction

Coastal sediment transport is generated mainly in thesurf zone, where wave breaking and wave-induced currentsare generated, although a pronounced peak in waveactivity can be found in the swash zone as well (Krauset al., 1982). Waves breaking in the surf zone intensify thelongshore current and undertow, which increase sedimenttransport significantly. In particular, it has been assumedthat flow perpendicular to infiltration and exfiltration on abeach face can influence sediment motion (Nielsen et al.,2001). These phenomena can easily occur on a beach wherethe groundwater does not follow tidal variations, becausedifferences between seawater and groundwater levels mayproduce changes in the volume of infiltration and exfiltra-tion through the beach surface. It is not simple to clarify

e front matter r 2006 Elsevier Ltd. All rights reserved.

eaneng.2005.10.026

ng author. Tel.: +8152 789 3731; fax: +81 52 789 1665.

ss: leekh@civil.nagoya-u.ac.jp (K.-H. Lee).

the effects of infiltration on sediment transport ratesbecause of the mutual relationship between the near-bedvelocity and the downward drag force. Conley and Inman(1994) showed experimentally that the near-bed velocity,which enhances sediment mobility, increases during infil-tration owing to the reduction of the boundary layer. Onthe other hand, infiltration augments the downward dragforce by generating downward pressure gradients thatimpede sediment mobility during the run-up (Hughes et al.,1998; Nielsen, 1997). Nielsen (1997, 2001) proposedapplication of the modified shields parameter to explainthe combined effects of increased shear stress and down-ward drag force due to infiltration under flat bedconditions. These opposite effects of infiltration arereconciled in detail in Butt et al. (2001).Despite these two opposite effects, it might be expected

that sediment transport in the surf and swash zones can beaffected by variation in the rate of percolation of water.Several beach stabilization methods that make use of this

ARTICLE IN PRESSK.-H. Lee et al. / Ocean Engineering 34 (2007) 605–615606

principle have been attempted; examples include the sub-sand filter system, coastal drain system, beach managementsystem and gravitational drainage system. Their usefulnessin sandy beach situations is under investigation by modeland field tests in Japan (Sakai et al., 1997; Nishimura et al.,1998, 1999; Miyatake et al., 1999; Yanagishima et al., 1999;Sato et al., 2000; Sasada et al., 2004).

In addition to the research described above, during thelast two decades many researchers have studied infiltrationeffects (e.g., Sealth, 1984; Baldock and Holmes, 1998, etc.).Most studies, however, have discussed the assessment ofsediment mobility or its direction; few have considered theeffects of wave breaking, the phenomenon that is mainlyresponsible for sediment transport, on beach profilechanges in gravel beaches.

This study has two purposes. The first is to examineexperimentally how groundwater levels, which producevariations in infiltration flow, influence topographicchanges in a gravel beach. The second is to analyze thewave fields and flow patterns in the surf zone numerically,considering the porosity of the media and the presence ofgroundwater, to extend understanding of gravel beachmorphodynamics.

This paper consists of five sections. Section 2 describeslaboratories, such as a water-level control tank designed tomaintain groundwater level. Section 3 briefly describesthe numerical method. Section 4 discusses the resultsobtained from the experiments and numerical analysis. Thelast section outlines the important conclusions from thisstudy.

Fig. 1. Ida beach of Shichri-

2. Experimental setup and procedure

The model used in this study was a very much simplifiedrepresentation of Ida beach, Shichiri-Mihama coast, Japan,which consists mainly of gravel and sand. Fig. 1 shows atypical portion of the shoreline at Ida beach.The laboratory experiments were carried out at Nagoya

University in a wave flume that was 0.7m in width, 0.9m indepth, and 30m in length. A flap-type wave generator wasinstalled at one end of the wave flume. A gravel beach witha slope of 1:7, composed entirely of one kind of bedmaterial (D50 ¼ 5mm, s ¼ 2.65; D50 is median graindiameter and s is specific gravity of the grain), wasconstructed in the wave flume.To control the simulated groundwater, a water-level

control tank made of acrylic plastic was installed behindthe gravel beach. This control tank consisted of twocompartments connected by PVC pipes 25mm in diameter.One compartment (FB) was placed adjacent to the beachand was used for supplying water from the wave flume andmaintaining the water level, the other (BB) was used forpumping out water that overflowed from FB. Nettingreplaced the acrylic side wall of FB adjacent to the beach soas not to impede flow towards the beach, and to preventthe inflow of bed material into the compartment (seeFig. 2).The installation of the water-level control tank caused

problems in maintaining a constant mean water level in thewave flume. To overcome this, the wave flume was dividedlaterally into two parts, one 0.3m wide and the other 0.4m

Mihama coast in Japan.

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Fig. 3. Experimental arrangement for the present study.

Fig. 2. Water-level control tank for considering groundwater.

Table 1

Wave conditions

Wave conditions Experiments Ida beach

Hi (cm) Ti (s) Li (cm)a Hp (m) Tp (s)

Average wave condition 6 1.7 305.2 1.5 8.5

Storm wave condition 12 1.8 326.7 3.7 9

aIncident wave length based on the third-order Stokes wave theory.

K.-H. Lee et al. / Ocean Engineering 34 (2007) 605–615 607

wide, by a wooden partition that started 2.0m from thewave generator. Water was supplied and drained throughpumps between the flume and the water-level control tank,permitting adjustment of groundwater to any desired levelwhile maintaining a constant mean water level in the flume.A schematic diagram of the experimental arrangement isshown in Fig. 3.

Two kinds of regular waves were generated to investigatebeach profile changes, based on a model-to-prototype scaleof 1–25. The wave conditions used were an average wave(Hi ¼ 6 cm, Ti ¼ 1.7 s) and a storm wave (Hi ¼ 12 cm,Ti ¼ 1.8 s), based on wave conditions on the Shichiri-Mihama coast (Table 1). Five groundwater level conditionswere tested, Dh ¼ �10, �5, 0, +5 and 10 cm, where Dh isthe difference between groundwater and seawater levels.The water depth was maintained constant at 40 cm. Tocheck the parameters of the incident wave, water surfaceelevations were measured by capacitance-type wave gaugesin both parts of the divided flumes. Groundwater levelsinside the beach material were monitored by capacitance-type gauges covered with fine netting. The movement ofbed materials while waves were acting on the beach wasalso recorded.

Currents flowed seaward or landward from the water-level tank depending on the level of the groundwater andthe mean water level in the water-level tank. After allowing

time for this flow to reach a steady state, waves weregenerated.

3. Numerical analysis theory

To investigate the wave fields in the swash and surf zonesnumerically, we adopted the numerical wave tank (NWT)method, which directly simulates laboratory experimentaltest conditions. The NWT concept was also used in thisway by Hur and Mizutani (2003) and by Hur (2004). Itcomprises a source for generating waves, an artificial‘‘damping zone’’ to prevent wave reflection at the seawardopen boundary, and a water-level control tank to handlethe groundwater level; the volume of fluid (VOF) method isincorporated to track the free surface. The NWT model

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Unit :

Tank

Impermeableboundary

Wave

Added dissipation zone

Permeable Cellγc =0.37)

slope=1:7

Δh

cm

60 5056

z

x

cell size

2

1

40

470 Ld>2Li

Ld: Length of added dissipation zone

Fig. 4. Definition sketch of numerical wave tank used in the present study.

K.-H. Lee et al. / Ocean Engineering 34 (2007) 605–615608

used in the present study is shown in Fig. 4. Sedimentmovement was not considered and the gravel beach wastreated as a porous medium.

3.1. Governing equation

Assuming a viscous and incompressible fluid with constantdensity flowing through a porous medium (Sakakiyamaand Kajima, 1992), the fluid motion is governed by thecontinuity equation and modified Navier–Stokes equations,given by

qðgxuÞ

qxþ

qðgzwÞ

qz¼ q�, (1)

gvqu

qtþ gxu

qu

qxþ gzw

qu

qz

¼ �gv1

rqp

qx�Mx � Rx þ

1

rqgxtxx

qxþ

qgztzx

qz

� ��

2u3

qgxqn

qx,

ð2Þ

gv

qw

qtþ gxu

qw

qxþ gzw

qw

qz

¼ �gv

1

rqp

qx�Mz � Rz þ

1

rqgxtxz

qxþ

qgztzz

qz

� ��

2u3

qgzqn

qz� bw.

ð3Þ

In the above equations, (x, z) are Cartesian coordinates, the z

axis is zero at sea water level and is negative downward, u

and w are the velocity components in the x and z directions,respectively, t is time, p is pressure, r is the fluid density, g isthe acceleration due to gravity, b is a wave dissipation factorthat equals zero except in the artificial dissipation zone, gx

and gz are the components of surface porosity in thedirections x and z, respectively, gv is the volume porosity,Mx and Mz are the inertial forces, Rx and Rz are the dragforces, and q� is the source term required to generate wavesand supply water to the water-level control tank at the sourceposition (x ¼ xx) defined as

qn ¼qðz; tÞ

�Dxs or Q at each source position ðx ¼ xsÞ;

0 at xaxs;

8><>:

(4)

where q is the flux density, Q is the inflow rate into the wavelevel control tank, and Dxs is the mesh width at the sourceposition. The inflow rate source Q is used to simulategroundwater at the back-beach.More details regarding inertial and drag force terms and

applied boundary conditions can be found in Hur andMizutani (2003).

3.2. Tracking the free surface

The numerical simulation of fluid flows with freesurfaces requires not only the solution of the governingequations but also special treatment of free surfaces, i.e.,tracking of fluid interfaces. Many numerical modelshave been developed in the last four decades to simulatefree surface flows (or immiscible two-phase flows), andthey have been widely used in various fields of study. Webriefly summarize tracking methods for the free surfacebelow.The first approach to tracking a fluid interface is the

well-known marker and cell (MAC) method proposed by JWelch et al. (1965). In the MAC method, the free surface istracked using virtual marker particles that move at eachtime step in accordance with the local fluid velocity. Sincethe initial development of the MAC method, variousimprovements, e.g., SMAC (Amsden and Harlow, 1970),SUMMAC (Chan and Street, 1971), the TUMMACmethods (Miyata et al., 1985; Park et al., 2003) andGENSMAC (Tome et al., 1994, 2001) have been suggested.Although the MAC method allows fluid flows with freesurfaces to be simulated, it also involves several problemswith the virtual marker particles, the finite number ofparticles, and the complexities of the algorithm in threedimensions.Another approach to tracking the fluid interface uses

volume advection techniques, which track the volume ofthe fluid in each cell using a ‘‘color function’’, defined asunity within fluid regions and zero elsewhere. The firstalgorithm to employ these volume advection techniqueswas the simplified line interface calculation (SLIC) methodof Noh and Woodward (1976). Hirt and Nichols (1981)suggested an improvement, the well-known VOF method,and many volume advection techniques have been devel-oped based on their original method, e.g., SOLA-VOF

ARTICLE IN PRESSK.-H. Lee et al. / Ocean Engineering 34 (2007) 605–615 609

(Nichols et al., 1980), NASA-VOF2D (Torrey et al., 1985),NASA-VOF3D (Torrey et al., 1987), RIPPLE (Kotheet al., 1992) and FLOW3D (Hirt, 1988).

In this study, the SOLA-VOF technique was selected.The VOF function (the color function described above)satisfies

qðgvF Þqtþ

qðgxuF Þ

qxþ

qðgzwF Þ

qz¼ Fqn. (5)

3.3. Treatment of a bubble inserted into the fluid

In storm wave conditions, plunging-type breaking waveswill develop in the surf zone. These waves entrap largeamounts of air after breaking. Because the numericalmodel adopted in this study considers only one-phase flow,the large amounts of air entrapped in the fluid would affectthe stability of the model, and result in loss of the freesurface that is specifically required to treat a situation inwhich air is entrapped within the liquid. The Timerdoormethod (CADMAS-SURF, 2001) was used to overcomethis problem.

The Timerdoor method was designed to discharge airfrom the liquid; the upper face of any cell containing air isopened, and air moves to the cell immediately above atspecial time step, Dtbubble. That is, air entrapped in any cellcannot move at each calculation time interval Dt, but afterthe passage of time Dz=wbubble the air rises to the upper cellwith constant upward velocity, Wbubble. This concept isshown in Fig. 5.

After processing entrapped air using the Timerdoormethod, the VOF function is rearranged between the air-entrapped cell (i, k) and the upper cell (i, k+1) as follows:

Fi;kþ1 ¼ Fi;kþ1 �min ð1:0� Fi;kÞ;Fi;kþ1

� �Fi;k ¼ Fi;k þmin ð1:0� F i;kÞ;Fi;kþ1

� ������

(at Dtbubble ¼ Dzk

�wbubble.

(6)

k+1

k

k-1

i

air air

Fi,k

Fi+1,k

Δt

Δt

Δt

Tim

bubble

Fig. 5. Timerdoor method to tre

4. Results and analysis

4.1. Water deformation in the surf zone and the effect of

groundwater level

First, laboratory experiments involving control of thesubsurface water level were conducted under rigid bedconditions, primarily to study wave deformation in the surfand swash zones. Fig. 6a presents the water surface profileat the moment a wave breaks, captured by a video camera.Fig. 6b shows the calculated water surface profile andwater particle velocity field. The computed free surfaceconfiguration in Fig. 4b is plotted as the VOF functionF ¼ 0.5. Figs. 6a and b show a sequence of wavedeformation profiles including wave breaking, and demon-strate that the computed wave surface profiles represent theobserved profiles well. Also, in the computed results, we seethat exfiltration flows out from inside the gravel beachthroughout the wave run-up and run-down, as controlledby the difference between groundwater and mean waterlevels. This process is a little different from that reported byearlier researchers, where infiltration of water into the bedof the swash zone occurs during run-up, and exfiltrationoccurs only during run-down over a more general type ofbeach (Masselink and Hughes, 1998; Conely and Inman,1994). Details of the flow pattern under steady flowconditions will be described for the surf zone in Section 4.3.Fig. 7 shows the mean groundwater levels inside the

gravel beach, obtained from laboratory experiments andthe numerical simulation model, which represented thebeach as a porous medium. Under average wave condi-tions, the numerical results show good agreement with theexperimental results, but under storm wave conditionsthe numerical results overestimate groundwater levels.A possible explanation is that in the laboratory experimentcirculating flow was generated inside the water-levelcontrol tank by water supplied from the wave flume, butthis did not occur in the numerical calculation.

air Fi,k

Fi+1,k

Δt

erdoor

at entrapped air in fluid cell.

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Z(c

m)

-40.0

-30.0

-20.0

-10.0

0.0

10.0

20.050.0cm/sec

-10 10 20 30 40 50 60 70 80

Z(c

m)

-40.0

-30.0

-20.0

-10.0

0.0

10.0

20.050.0cm/sec

-10 10 20 30 40 50 60 70 80Z

(cm

)

-40.0

-30.0

-20.0

-10.0

0.0

10.0

20.050.0cm/sec

-10 10 20 30 40 50 60 70 80

X(cm)

Z(c

m)

-40.0

-30.0

-20.0

-10.0

0.0

10.0

20.050.0cm/sec

-10 10 20 30 40 50 60 70 800

0

0

0

(a) (b)

Fig. 6. Wave breaking in surf and swash zone. (a) Experimental photographs. (b) Snapshots of numerical results.

K.-H. Lee et al. / Ocean Engineering 34 (2007) 605–615610

4.2. Beach profile change

Mizutani et al. (2003) showed that a beach consisting ofcoarse material takes much less time to reach anequilibrium state of deformation than does a fine sandybeach. In our study, it took about 30–50min to reach asteady-state beach profile for each wave condition. Figs. 8aand b show beach profile changes for all of the situationsthat we studied, after 1 h of run time. In every case, theresults demonstrate accretion type deformation, caused byonshore sediment movement through the surf zone; this iscontrary to the erosion type deformation found previouslyfor fine sand (Mizutani et al., 2003). The reason is that thebed material was not carried by the undertow because ofthe relatively high specific gravity of gravel compared tothat of fine sand, which prevented erosion-type deforma-tion from occurring. In Fig. 8a, under average wave

conditions, it is unfortunately difficult to observe thechange in the beach profile produced by variation of thegroundwater level because the relatively small incidentwave caused only a small change in the profile. On theother hand, Fig. 8b under storm wave conditions shows theeffect of groundwater behind the beach, taking account ofthe small scale of the laboratory experiments. Several otherfeatures can be seen in Fig. 8b. First, the berm formed inthe upper portion of the shoreline moves up the beach asthe groundwater level falls, and moves seaward as thegroundwater level rises. Moreover, the higher the ground-water level, the steeper the berm, and vice versa. Thereason is that elevated groundwater decreases wave run-up,because the strong exfiltration flows induced by thegroundwater inhibit the wave run-up of the incident waves.Therefore, the travel distance of bed materials is shorter inthe case of rising groundwater than in the case of declining

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Δh=0cm(CAL)

Δh=+5cm(CAL)Δh=+10cm(CAL)

Δh=0cm(EXP)Δh=+5cm(EXP)Δh=+10cm(EXP)

Porous media

Δh=0cm(CAL)

Δh=+5cm(CAL)Δh=+10cm(CAL)

Δh=0cm(EXP)Δh=+5cm(EXP)Δh=+10cm(EXP)

Porous media

1.6

1.2

0.8

0.4

0.0

-0.4

1.2

0.8

0.4

0.0

-0.4-0.6 -0.4 -0.2 0 0.2 0.4

mea

n/H

im

ean/

Hi

SWL

SWL

Hi=12cm, Ti=1.8s

Hi=6cm, Ti=1.7s

x/Li

ηη

Fig. 7. Mean groundwater level in porous media.

20

10

0

-10

-20-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

x/L

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

x/L

B.P.initial profile Hi=6cm, Ti=1.7s

Hi=12cm, Ti=1.8s

z(cm

)

20

10

0

-10

-20

z(cm

) B.P.

Initial profile

Δh=+10cmΔh=+5cmΔh=0cmΔh=−5cmΔh=−10cm

Δh=+10cmΔh=+5cmΔh=0cmΔh=−5cmΔh=−10cm

(a)

(b)

Fig. 8. Beach profile changes after 1 h.

K.-H. Lee et al. / Ocean Engineering 34 (2007) 605–615 611

groundwater. Second, the lower the groundwater level, thesteeper the beach surface, and vice versa. Third, the mosteroded area is in the vicinity of the wave breaking point in

all cases. This is explained by the fact that waves breakingin the swash and surf zones play an important role insediment transport, as is well known.

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4.3. Flow pattern in the surf and swash zones

To predict the deformation of the beach profile in theswash and surf zones when groundwater is present,observation and representation of flow patterns is useful.Fig. 9 compares the results for computed mean velocitiesaveraged over five cycles of incident waves. Elevatedgroundwater in Figs. 9b and c produces seaward currentsinside the porous medium, which give rise to deformationof the flow pattern in the surf and swash zones. In Fig. 9a,not involving groundwater (Dh ¼ 0 cm), strong wave run-up in the onshore direction appears in the swash zone(�50 cmoxo0 cm) and its direction is predominantly at atangent to the beach slope. Also, infiltration flow normal tothe beach surface is generated in the swash zone andexfiltration flow occurs in the beach surface below the

Fig. 9. Mean water velocity

seawater level (�25 cmoxo100 cm). These seepage flowpatterns inside the general beach in the surf zone aresimilar to the results of Doi et al. (1999). In Figs. 9b and c,wave run-up weakens with increased groundwater eleva-tion and its direction becomes dispersed as compared tothat of Fig. 9a. Infiltration flow (�50 cmoxo0 cm) isreduced and exfiltration flow (�25 cmoxo100 cm) isincreased as the groundwater level rises. On the otherhand, wave run-down below the seawater level (0 cmoxo50 cm) strengthens with increasing groundwater eleva-tion. As seen in Fig. 9, it is clear that seaward currentsinduced by elevated groundwater level affect flow patternsin the beach; they inhibit wave run-up on the beach surfaceand accelerate wave run-down. As a result, in the caseof elevated groundwater, infiltration flow decreases andexfiltration flow increases.

in swash and surf zone.

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These deformations of the flow pattern explain well howthe beach profile is changed by the groundwater in Fig. 8.The wave run-up, weakened by the presence of elevatedgroundwater, cannot move sediment material onshore aseffectively. Thus, in this case, a berm is formed a littleoffshore and its slope is steep. In other cases, themechanism of berm formation can be developed byanalogy from these results. On the other hand, it isexpected that the increase of exfiltration and strong waverun-down from elevated groundwater result in enhance-ment of sediment mobility. This effect can be observed inthe experimental results shown in Fig. 8b. The slope of thebeach profile at higher groundwater levels, below the meanwater level (0ox=Lio0:2 in Fig. 8b), is less than when thegroundwater level is even lower, because strong wave run-down causes sediment materials to move onshore.

Fig. 10. Stream line in s

The situation is further clarified in Fig. 10, which showsstream lines of steady flow in each case; these demonstratethe circulating flow in the beach material that onshoreflows generate above the mean water level, and offshoreflows generate below the mean water level, as is wellknown. However, there is a minor difference, depending ongroundwater level; in Fig. 10a, flow inside the beachmaterial shows an anti-clockwise rotating motion, but itgradually straightens as the seaward currents increase withrising groundwater level.To survey the characteristics of near-bed velocities is

meaningful because the near-bed velocity plays an im-portant in the movement of sediment. Fig. 11 showstangential mean bottom-velocity at sloped beach surface.In figures the minus and plus signs mean onshore directionand offshore direction, respectively. In Figs. 11a and b, the

wash and surf zone.

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-50 -25 0 25 50 75 100 125 150-40

-20

0

20

40

-50 -25 0 25 50 75 100 125 150-40

-20

0

20

40

x(cm)

x(cm)

Vm

ean(

cm/s

)V

mea

n(cm

/s)

(a)

(b)

Hi=6cm, Ti=1.7s

Hi=12cm, Ti=1.8s

offshore

onshore

offshore

onshore

Δh=+10cm

Δh=+0cm

Δh=+5cm

Δh=+10cm

Δh=+0cm

Δh=+5cm

Fig. 11. Mean bottom-velocity at sloped beach surface.

K.-H. Lee et al. / Ocean Engineering 34 (2007) 605–615614

shift points, the direction of the bottom-velocity is changedfrom onshore to offshore or from offshore to onshore,move to onshore and the magnitude of offshore direc-tion velocity strengthens with increasing groundwaterelevation.

5. Conclusions

Changes in the profile of a gravel beach, caused by theeffects of groundwater level on the back-beach, wereinvestigated experimentally and the flow mechanism wasanalyzed using a modified numerical model. This model iscapable of simulating both currents affected by ground-water levels and the effects of large scale breaking waves ona sloping beach. The main results can be summarized asfollows.

1.

The berm formed at the upper portion of the shore linemoves up the beach with decreasing groundwater levelsand moves seaward as groundwater rises.

2.

The greatest erosion takes place in the vicinity of thewave breaking point.

3.

The beach slope below the mean water level is less steepwhen the groundwater level is higher than when thelower groundwater level is low.

4.

The velocity of wave run-up, which moves sedimentmaterials onshore, is reduced by the seaward currentscaused by elevated groundwater.

5.

Strong currents are formed on the beach slope below themean water level.

The numerical model used in the present study did notconsider movable bed conditions because we were con-cerned with understanding the mechanisms that operatewithin the beach when there is a difference between thegroundwater level and the mean water level. A full modelthat includes sediment transport would be required toobtain more exact information about gravel beach profilechanges. But, it is not simple to solve sediment transport,wave and current simultaneously in single model because

ARTICLE IN PRESSK.-H. Lee et al. / Ocean Engineering 34 (2007) 605–615 615

of an increase of calculation capacity of the computer anddifficulty of moving boundary condition at the surfacebetween fluid and sediment. Future research should be paidto develop the full model capable of simulating theinteraction of sediment transport, wave and current inthe NWT.

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