Act Ocenol. Sin., 1, Vol. 37, No. 3, P. 1 3 DOI: 1.17/s13131-1-1197-1 http://www.hyx.org.cn E-mil: hyxe@3.net Numericl simultions of rip currents off rc-shped costlines WANG Hong 1, 3, ZHU Shouxin *, LI Xunqing 1, ZHANG Wenjing 1, NIE Yu 1 1 Institute of Meteorology nd Ocenogrphy, Ntionl University of Defense Technology, Nnjing 1111, Chin College of Ocenogrphy, Hohi University, Nnjing 19, Chin 3 91937 Troops, Zhoushn 31, Chin Received April 17; ccepted 31 My 17 The Chinese Society of Ocenogrphy nd Springer-Verlg GmH Germny, prt of Springer Nture 1 Astrct The rip currents induced y wves off rc-shped costlines re seriously hrmful to humns, ut understnding of their chrcteristics is lcking. In this study, the FUNWAVE model ws used to clculte the wve-induced currents in the Hller experiment nd the idel rc-shped cost similr to Sny Ddonghi, Hinn Province, Chin. The results showed tht the FUNWAVE model hs considerle ility to simulte the rip currents, nd it ws used to further simulte rip currents off rc-shped costlines to investigte their chrcteristics. The rip currents were found to e stronger s the curvture of rc-shped costline incresed. Costl ech slope exerts significnt influence on rip currents; in prticulr, n overly steep or overly mild slope is not conducive to creting rip currents. Furthermore, the rip currents were found to ecome weker s the size of rc-shped cost decresed. When the height nd period of wves increse, the strength of rip currents lso increses, nd, in some cses, wve heights of. m my produce dngerous rip currents. Key words: rip current, rc-shped costline, FUNWAVE model, numericl simultion Cittion: Wng Hong, Zhu Shouxin, Li Xunqing, Zhng Wenjing, Nie Yu. 1. Numericl simultions of rip currents off rc-shped costlines. Act Ocenologic Sinic, 37(3): 1 3, doi: 1.17/s13131-1-1197-1 1 Introduction In the process of wve propgtion from deep to shllow wter, ffected y chnges of topogrphy, the wves roll ck nd rek, sometimes producing reltively strong offshore flows clled rip currents (Bowen, 199). Previous studies hve otined crude estimtes of rip current velocities, such s.3 1 m/s (McMhn et l., ), m/s nd sometimes 3 m/s (Short, 7). Rip currents, which re rpid offshore-directed jets of wter tht originte in the surf zone nd roden outside the reking regions with high speed, not only exert n importnt effect on the trnsport of sediments nd pollutnts (Jin et l., ; Brown et l., 9), ut my lso tke swimmers of ll ility levels into deeper wter within minutes, cusing csulties (Choi et l., 13). Austrli hd out ech drowning incidents ech yer, of which 9% were relted to rip currents (Short, 7). Eighty percent of the ech drowning rescues in the United Sttes were relted to rip currents, nd more thn 1 people died ech yer from ech drowning (Lscody, 199). An rc-shped costline is common type of costline, where rip currents occur frequently, leding to drownings. Dlrymple et l. (11) elieved tht the occurrence of rip currents off n rcshped costline is due to the wve-crest line deformtion tht forms strong nd wek wve energy zones tht cuses the rip currents. There re mny rc-shped costs in Chin tht re prone to rip currents. Though sttistics re incomplete, Ddonghi, which is fmous thing ech in Sny, Hinn Province, hs een the site of hundreds of drownings owing to rip currents; 3 people died t Ddonghi etween nd 13 (Li nd Zhu, 1). However, ecuse of the lck of field oservtion, the chrcteristics of rip currents on such rc-shped eches re still not well understood. Mny scholrs hve nlyzed the chrcteristics of rip currents y conducting physicl experiments in hror pools (Den nd Oh, 199; Hller et l., 1997, ; Hs nd Svendsen, ; Drønen et l., ; Kennedy nd Thoms, ; Cstelle et l., 1). The initil method of rip current field oservtion ws comintion of visul oservtion nd deployment of electronic flow-rte sensors, ut in recent yers GPS flots nd eril photogrphy hve een used more frequently (Wng nd Zou, 1), long with stellite remote sensing (Li nd Zhu, 1) nd the use of dye trcers (Huntley et l., 19). However, ecuse of the instility nd complexly sptil structure of rip currents (Giger et l., 1991), it is difficult to ctlog ccurte descriptions of their chrcteristics y field oservtion. It is lso difficult to ccurtely distinguish etween rip currents nd tidl currents y field oservtion ecuse the rip currents chnge quickly owing to the vritions in tide nd wve ctions. Therefore, some scholrs hve nlyzed the chrcteristics of rip currents using numericl simultions (Chen et l., 1999; Fng et l., 11; Cstelle nd Coco, 1; Be et l., 13; Shin et l., 1; H et l., 1). Chen et l. (1999) tested the effectiveness of FUNWAVE model in rip current simultions y using wve lortory experimentl dt, nd then studying the rip current mechnisms sed on numericl simultions. Be et l. (13), Shin et l. (1), nd H et l. (1) ll used FUNWAVE model to simulte the rip currents t Heunde Bech, Busn, South Kore, tested the simultions y CCTV remotely sensed imgery, nd nlyzed the chrcteristics nd dynmic mechnisms of rip currents on the ech Foundtion item: The Ntionl Nturl Science Foundtion under contrct Nos 113, 17 nd 1371; the Opertion Expenses for Universities' Bsic Scientific Reserch of Centrl Authorities under contrct Nos 11B71 nd 1B1. *Corresponding uthor, E-mil: zhushouxin@vip.sin.com
WANG Hong et l. Act Ocenol. Sin., 1, Vol. 37, No. 3, P. 1 3 sed on numericl simultions. Cstelle nd Coco (1) studied the rip current ptterns on n idel emyed ech sed on the nonliner hydrodynmic model, tested the simultions using video imging, nd studied the evolution of rip currents using the simultions. There re two types of models currently used to simulte rip currents. One is the wve-resolved model, which descries the wve-prticle motions tht llow the wve heights to e determined. The wve verge of the motions of wve prticles results in wve-induced flows nd rip currents. The wve-resolved model minly uses the Boussinesq or Nvier-Stokes equtions. Another type of model is the wve-verged model, which directly descries the wve-verged motions. It uses the wve-verged hydrodynmic equtions, including the rdition stress nd surfce rollers from the wve model, to simulte oth wve-induced flows nd rip currents. It is usully coupled with the wve model. In this pper, the FUNWAVE model sed on the Boussinesq equtions is used to simulte rip currents, nd their chrcteristics off rc-shped costlines re nlyzed sed on the simultions. Test of FUNWAVE model in simulting rip currents In this study, FUNWAVE, nonliner Boussinesq model developed t the University of Delwre (USA), is used to simulte wve-induced currents. It is one of the most dvnced models for simulting wve-induced flows, nd hs een used for the investigtion of rip currents in mny previous studies (Shi et l., 1). Owing to the lck of field oservtion dt, dt from wve lortory experiments, remote sensing, nd photogrphy were used in testing the numericl simultions of rip currents in previous FG DE studies (Chen et l., 1999; Hss et l., 3; Fng et l., 11; Cstelle nd Coco, 1; Be et l., 13; Shin et l., 1; H et l., 1). We lso quntittively tested the numericl simultions of rip currents using Hller s wve lortory experiment dt, nd mde qulittive comprisons to the numericl simultions nd the photogrphy of rip currents on n idel rc-shped cost like Ddonghi Bech. There is no stndrd definition for defining rip currents. Short (7) defined rip current s n offshore flow with speed ove.3 m/s, nd we lso dopt this stndrd. Hller et l. (1997) mesured wve reking nd rip currents on rred ech in lortory experiment. As shown in Fig. 1, the sin of Hller experiment hs constnt wter depth of.33 m. There re three rs, nd the wter depths t the shore toe nd on the crest of the r re.1 m nd. m, respectively. A normlly incident regulr wve with period of T=1 s nd height of H=. m ws induced. The wve height nd men wter level were oserved in the sections of A (y=1.1 m), B (y=. m) nd C (y=7. m) s shown in Fig. 1, nd the wve-induced flows were oserved in the sections of D (x=1. m), E (x=11. m), F (x=1.3 m) nd G (x=13. m). In some previous numericl simultions (Fng et l., 11; Chen et l., 1999), the slope vrition from long-shore uniformity in the plnr ech ws neglected, the slope in Fig. 1 ws simplified s 1:3 nd only n idelized hlf of the thymetry ws used to reduce the mount of computtion. In this study, we lso tke hlf of the experimentl re s the computtionl domin. The topogrphy of the simultion is shown in Fig., in which the slope is verged s 1:3. The grid-spce nd time-step increments re Δx=. m, Δy=.1 m, nd Δt=.1 s. Wves re generted y the source function technique s detiled y Wei et l. 3. m 1. m 1. m cm 7.3 m 1:3 C 1: B 1. m 3. m A. m Fig. 1. Pln view () nd cross-section () of Hller experiment. 9. 9 7. H/m z/m. m/s 7. -. c 1 1 3 3. 1 1 1 1 1 1 11 1 13 1 1 Fig.. Topogrphy nd results of the numericl simultion for Hller experiment.. Numericl topogrphy,. wve height (H), nd c. wve-induced current.
WANG Hong et l. Act Ocenol. Sin., 1, Vol. 37, No. 3, P. 1 3 3 (1999). The wve genertion is locted internlly t x=. m, nd dmping sponge lyer is put ehind the source line to sor outgoing wves reflected y the sumerged r nd the sloping ech. The computed dtsets from to s re used for sttisticl nlysis. The computed wve height is plotted in Fig. : when the wve climed over the snd r to rech shllower wter, the wve height incresed, roke, nd then wekened rpidly. The wves reks on the sumerged r nd ner the shoreline on the rred eches, while t the rip chnnel, wve reking minly occurs ner the shoreline. The simultion results of wve-induced flow re given in Fig. c. There re two strong offshore currents in the rip chnnel, nd the mximum speed of flow velocity is.3 m/s, which is in ccord with rip current chrcteristics. The computed wve height nd men wter level (MWL) long three cross-shore trnsects re plotted in Fig. 3. The experimentl dt nd the numericl results from Chen et l. (1999) nd Fng et l. (11) re lso presented. The long-shore men current (U) nd the cross-shore men current (V) re compred to the experimentl dt nd the numericl results from Chen et l. (1999) nd Fng et l. (11) in Figs nd, respectively. Generlly, the simulted results from this study gree well with the numericl results of Chen et l. (1999) nd Fng et l. (11), nd re very close to the experimentl results of wve height, MWL, nd wve-induced flow. The verge error of wve height etween the numericl results nd the oserved vlues in the three sections y=1.1 m,. m nd 7. m is. cm, nd the verge error of men wter level is. mm. The verge error of long-shore men current t the four sections x=1. m, 11. m, 1.3 m nd 13. m is.3 1 m/s, nd the verge error of crossshore men current is.9 7 m/s. The numericl simultion results from Hller experiment show tht the FUNWAVE model cn qulittively nd quntittively reproduce wves nd wve-induced currents ner shore, especilly the chrcteristics of rip currents. Although there re no on-site mesurements of rip currents t Ddonghi Bech, we cn exmine them using remote-sensingstellite imge nd photogrph. The CCTV imge (Li, 1) in Fig. shows rip currents t Ddonghi Bech with the zone indicted y the dotted line. Another snpshot in Fig. lso presents the rip currents etween two surf zones t Ddonghi Bech. According to the rel depth, nd the rel shpe nd size of the Ddonghi costline, n idel rc-shped costline is designed s shown in Fig. 7, with the costline nd wter depth in the shpe of prol. The re for clcultion mesures 7 1 m, nd the grid spces re Δx=1. m nd Δy=. m. The wve genertion is locted internlly t x= m, nd dmping sponge lyer is lso put ehind the source line. The normlly incident regulr wve with T=7. s nd H=. m is set. The computed dtsets over five periods fter the model hs run for 1 s re used in the sttisticl nlysis. The results of simulted height re given in Fig. 7 nd those of wve-induced flow in Fig. 7c. Figure 7d presents the rnge of rip currents with offshore speed ove.3 m/s. The simulted rip currents cn e explined minly y the wve-induced rdition stress. Mcmhn et l. () used the following equtions to nlyze the mechnisms of rip current: d S xx dx dη = ρ g ( h + η ), (1) dx ds y y dη F = ρ g ( h + η ), y () dy dy where the S xx nd S yy re the rdition stresses, η is the men wter level nd h is the still wter depth, ρ is the density of sewter nd g is the grvittionl ccelertion. Considering the crossshore (x) momentum eqution, the chnges of S xx re lnced y the hydrosttic pressure grdient. Applying liner wve theory in shllow wter, S xx =3/E, where E is the wve energy nd proportionl to the squre of wve height. The S xx results in wve H/cm H/cm H/cm y = 1.1 m rred ech 1. 11. 11. 1. 1. 13. 13. 1. 1. y =. m rred ech 1. 11. 11. 1. 1. 13. 13. 1. 1. y = 7. m rred ech 1. 11. 11. 1. 1. 13. 13. 1. 1. MWL/mm MWL/mm MWL/mm y = 1.1 m rred ech - 1. 11. 11. 1. 1. 13. 13. 1. 1. y =. m rred ech - 1. 11. 11. 1. 1. 13. 13. 1. 1. y = 7. m rred ech - 1. 11. 11. 1. 1. 13. 13. 1. 1. Fig. 3. Comprisons of simulted wve height nd men wter level from this study (solid line), Chen et l. (1999) (sterisks), Fng et l. (11) (circles), nd mesurements (plus signs).
WANG Hong et l. Act Ocenol. Sin., 1, Vol. 37, No. 3, P. 1 3.. x = 1. m x = 11. m.1 U/m s-1 U/m s-1.1 -.1 -.1 -. -... x = 1.3 m x = 13. m.1 U/m s-1.1 U/m s-1 -.1 -.1 -. -. Fig.. Comprisons of long-shore men current (U) from numericl results of this study (red solid line), Chen et l. (1999) (cyn dshed-dotted line), Fng et l. (11) (lue dshed line), nd mesurements (open circles)... x = 1. m x = 11. m.1 V/m s-1 V/m s-1.1 -.1 -.1 -. -... x = 1.3 m x = 13. m.1 V/m s-1.1 V/m s-1 -.1 -.1 -. -. Fig.. Comprisons of cross-shore men current (V) from numericl results of this study (red solid line), Chen et l. (1999) (cyn dshed-dotted line), Fng et l. (11) (lue dshed line), nd mesurements (open circles). Fig.. The snpshots of rip currents t Ddonghi Bech. Arrows indicte the positions of rip currents. set-down outside the surf zone s the wve energy increses due to sholing, nd set-up inside the surf zone s the wves rek nd the energy decreses. Considering the longshore (y) momentum eqution, inside the surf zone, the grdients in the longshore rdition stress nd pressure ct together to produce flow of wter from the regions of high wves to the regions of low wves. As shown in Fig. 7, the wter depth t the oth sides is shllower thn tht t the center of the cost, thus the simulted wve height in Fig. 7 generlly increses from the center to the sides, nd the low wves re ner the section y= m. The longshore currents in Fig. 7c lso flow from the side to the top of the cost, nd then turn offshore. The strong rip currents in Fig.
WANG Hong et l. Act Ocenol. Sin., 1, Vol. 37, No. 3, P. 1 3 1 9 7 3 1 1 9 7 3 1 c. m/s 1 9 7 3 1 1 9 7 3 1 d. 1..3 Fig. 7. Simulted results of rip currents off n idel rc-shped costline.. Contours of still wter depth (unit: m),. simulted wve height (unit: m), c. wve-induced flow (unit: m/s), nd d. rnge of rip currents velocity (unit: m/s). R denotes rip current velocity. 7d re ner the section y= m, with the mximum speed of. m/s nd the mximum width of m. 3 Numericl simultions of the influence of wve height nd period on rip currents Some numericl simultions were crried out y setting the costl terrin s in Fig. 7 nd chnging the incident wve height nd period, the results of which re shown in Tle 1. The first group of simultions retin wve period of T=7. s, ut use incident wve heights of.1,.,.,.7 nd 1. m. The results from the first group of simultions show tht the mximum speed, penetrtion distnce nd re of rip currents increse s the incident wve height increses. The second group of simultions retin n incident wve height of H=. m, ut use wve periods of.,., 7., 1. nd 1. s. The mximum speed, penetrtion distnce nd re of rip currents increse s wve period increses. However, when the wve period increse from 1 s to 1 s, the re of the rip currents is reltively stle. In the cse of wve period T=7. s nd wve height H=. m, lrge rnge of rip currents is still in the simultion results, with mximum speed of 1.9 m/s. Shin et l. (1) simulted the rip currents generted y honeycom-ptterned wve trins in 7 m region with simple slope. They set the incident wve height t. m nd the wve period t. s, nd otined mximum speed of 1. m/s for their simulted rip currents. The results from this study nd of tht of Shin et l. (1) show tht the significnt rip currents my e driven y incident wves of smll height in some specil cses. We lso mde the numericl simultion y the irregulr wve, in which the TMA spectr ws dopted with the significnt wve height of. m nd pek wve period of 7. s. The spreding prmeter of directionl spectrum nd the pekedness prmeter of frequency spectrum were tken s γ=. nd σ θ =1, respectively. The simulted mximum speed of rip currents is 1. m/s, which is 7% of tht in Fig. 7d. So the numericl simultions with regulr wves my over-predict the mgnitude of rip currents. We will oserve the rip currents t Ddonghi Bech lter, then mke more discussions on the numericl simultions with regulr nd irregulr wves. Numericl simultions of the influence of the curvture of n rc-shped costline on rip currents In the ctul physicl re studied, the curvture of rcshped costline is different, nd we rn vrious numericl simu- Tle 1. Sttistics for rip currents of vrious incident wve heights nd periods Group 1 (T=7. s) Group (H=. m) H=.1 m H=. m H=. m H=.7 m H=1. m T=. s T=. s T=7. s T=1. s T=1. s Mximum speed of rip current/m s 1.3 1.9 1.99.7 3. 1.3..1.3 Penetrtion distnce of rip current/m 13 17 9 3 119 1 1 7 Are of rip current/m 19 1 3 1 7 3 1 9 739 7 37
WANG Hong et l. Act Ocenol. Sin., 1, Vol. 37, No. 3, P. 1 3 ltions of rip currents y chnging the rc-shped costline s curvture. The common chrcteriztion of the curvture k of n rc-shped costline (Hsu et l., 199; Li et l., 1) is defined s k=l s /L c, shown in Fig., where L s is the shoreline length nd L c is the emyment width. Five rc-shped costlines with different curvtures re shown in Fig.. The costline is in the shpe of prol, the shoreline length is 1 m, nd the wter depth of the flt ottom is 1. m. However, the emyment widths re L c =, 3,, 1 nd 3 m, which correspond to curvture vlues of.,.3,.,.1 nd.3, respectively. The incident wves re the sme, with wve height H=. m nd period T=7. s. The computed dtsets over five periods fter running the model for 1 s re selected in order to nlyze the wve-induced currents, which re shown in Figs 9, c, e, g nd i. We lso give the rnges of rip currents in Figs 9, d, f, h nd g. The wve-induced currents for these five rc-shped costlines ll flow similrly long the shoreline to the top, nd then turn offshore. However, their intensities ecome weker s their curvtures decrese, with solute mximum speeds of 3.9, 3.9,.79, 1. nd 1. m/s, respectively. The rip currents decrese significntly in intensity nd rnge s the curvtures decrese, with mximum speeds of.9,., 1.99, 1.3 nd. m/s nd rnge res of 9 3, 739, 31 11, 19 1 nd 1 m, respectively. And the penetrtion distnces of rip current re 3,, 13, 1 nd 1 m. In these simultions, when the curvture of costline is.3, the rip currents cn e neglected. 1 9 k =. k =.3 k =. k =.1 k =.3 shoreline length L s emyment width L c 7 3 1 1 3 7 9 Fig.. Terrin detils of rc-shped costline.. Arc-shped costline morphologicl chrcteristics, nd. pln view for different curvtures of rc-shped costline. The simulted results of wve height for the costlines with k=. nd k=.3 re presented in Figs 1 nd, respectively. Induced y the lrge curvture of k=., the high wves re distriuted t the two sides with the mximum height lrger thn 1. m, nd the low wves t the center hve the height lower thn. m. While off the costline with k=.3, the high wves t the two sides only hve the height out 1. m, nd there is no ovious low wves t the center. The grdients of wve height from the sides to the center off the little curvture costline re not so stronger s those off the lrge curvture costline, which result in the differences of rip currents in Figs 9 nd j. Numericl simultions of the influence of costl slope on rip currents Numericl simultions were lso run y setting three rcshped costs with different slopes. As shown in Fig. 11, these rc-shped costs hve the sme wter depth of flt ottom 1 m, ut with different slope. Figure 11 shows cross-section of y= m, the position mrked y red X is the oundry etween wter nd lnd, nd the slopes of the rc-shped costs with the forementioned wter depths re Slope_1=.1, Slope_=., nd Slope_3=.3, respectively. The numericl simultions hve the sme incident wve of height. m nd period 7. s, nd the results over five periods fter running the model for 1 s re used to nlyze the wve-induced nd rip currents. Figures 1, c nd e present the distriutions for the wve-induced currents, nd Figs 1, d nd f present those for the rnge of rip currents. In the numericl simultion with costl slope of.1, the solute mximum speed of wve-induced currents is 9 m/s, nd the mximum speed, penetrtion distnce nd re of rip currents re 1. m/s, m nd 19 m, respectively. And in the numericl simultion with costl slope of., the solute mximum speed of wve-induced current is 3. m/s, the mximum speed, penetrtion distnce nd re of rip currents re.1 m/s, 1 m nd 31 713 m. While in the numericl simultion with costl slope of.3, the solute mximum speed of wve-induced currents is 3.1 m/s, the mximum speed, penetrtion distnce nd re of rip currents re 1. m/s, 1 m nd 33 m. The costl slope not only ffects the intensity nd rnge of rip currents, ut lso hs gret influence on their morphologicl chrcter. The rip currents depicted in Fig. 1 re ggregted s whole, ut re scttered nd distriuted close to the shoreline in Figs 1d nd e. Two dditionl numericl simultions with costl slopes of.31 nd. were run, in which the rip currents hd mximum speeds of 1.99 nd 7 m/s, penetrtion distnces of 13 nd 1 m, nd re rnges of 31 11 nd 3 13 m, respectively. The vlues of wve height increse slowly during the shorewrd propgtion on the lrge slope, the surf zones re close to the costline nd their widths re short, thus the rip currents re wek. While on the smll slope, the surf zones re fr from the costline, which re not conducive to the longshore current ner the costline, mking wek rip currents. Thus, the intensity nd rnge of rip currents first strengthen nd then re wekened s the costl slope increses nd the distnce of rip current decreses s the costl slope increses. In ll of the five simultions in this pper, the rip currents off cost-
WANG Hong et l. Act Ocenol. Sin., 1, Vol. 37, No. 3, P. 1 3 line with slope of. is the strongest. Numericl simultions of the influence of costl size on rip currents Three costs of different size were estlished for rip current simultions. The first is sme s depicted in Fig. 7. The second, shown in Fig. 13, is hlf the size of the first, hs flt ottom with wter depth of. m. The third, shown in Fig. 13, is onefifth the size of the first, lso hs flt ottom with wter depth of. m. In these simultions, the grid spce is 1.. m. We uniformly tke the incident wve to hve period of 7. s nd height of. m for these simultions. Becuse the sizes of the three costs re different, we do not discuss the penetrtion distnce nd re rnges of the simulted rip currents, nd only present their mximum speeds, 1.9, 1. nd.7 m/s, respectively, corresponding to the first, second, nd third costlines. It seems tht the rip currents ecome smller s the costl size decreses.. m/s 7 7. 9 R/m s-1 9 7 Conclusions In this study, the FUNWAVE model ws employed to simulte the rip currents in the Hller experiment nd those t n idel rc-shped cost similr to the Ddonghi Bech. The results show tht the FUNWAVE model is extremely cple to performing the numericl clcultions required for the investigtion of rip currents. Additionl simultions were mde to study the rip current chrcteristics. An rc-shped costline ws found to e fvorle to generte mrked rip currents y common wves. These rip currents re gretly influenced y incident wves, nd their intensity nd rnge increse s wve height nd period increse. The slope of n rc-shped cost is lso shown to hve n effect on rip currents; in prticulr, n overly steep or mild slope is not conducive to the genertion of rip currents. With the sme incident wve, rip currents were found to ecome weker s the size of rc-shped cost decresed nd stronger s its curvture incresed. Since the FUNWAVE model is sed on the fully nonliner 1 1 3 3 1 1 1..3 c 7 7 R/m s-1. m/s. d 9 9 3 3 1 1 1..3 1 1 e. m/s 7 7. f 9 R/m s-1 9 1 1 3 3 1 1 1. 7.3 Fig. 9
WANG Hong et l. Act Ocenol. Sin., 1, Vol. 37, No. 3, P. 1 3 1 9 7 3 1 1 9 7 3 1 g i. m/s. m/s 1 9 7 3 1 1 9 7 3 1 h j. 1..3. 1..3 Fig. 9. Simulted wve-induced currents nd rip currents off rc-shped costlines with different curvture (R denotes rip current).. Wve-induced currents for costline with k=.;. rnge of rip currents for costline with k=.; c. wve-induced currents for costline with k=.3; d. rnge of rip currents for costline with k=.3; e. wve-induced currents for costline with k=.; f. rnge of rip currents for costline with k=.; g. wve-induced currents for costline with k=.1; h. rnge of rip currents for costline with k=.1; i. wveinduced currents for costline with k=.3; nd j. rnge of rip currents for costline with k=.3. 1 9 7 3 1 1 9 7 3 1 1 3 7 Fig. 1. Simulted wve height for costline with k=. () nd k=.3 (). 1 9 7 3 1 section y = m wve genertion depth Slope_1 Slope_ Slope_3 Fig. 11. Mp of costs with three different slopes.. Costline nd section, nd. schemtic of wter depth in section y= m.
WANG Hong et l. Act Ocenol. Sin., 1, Vol. 37, No. 3, P. 1 3 9 1 9 7 3 1 1 9 7 3 1 1 9 7 3 1. Slope_1 c. Slope_ e. Slope_3. m/s. m/s. m/s 1 9 7 3 1 1 9 7 3 1 1 9 7 3 1. Slope_1 d. Slope_ f. Slope_3. 1..3. 1..3. 1..3 Fig. 1. Wve-induced currents (, c nd e) nd rnge of rip currents (, d nd f) for costs with three different slopes (R denotes rip current). 1 1 3 1 3 1 1 1 1 1 3 1 1 Fig. 13. Topogrphy of costs of different sizes.. Cost hlf the size of tht depicted in Fig. 7, nd. cost one-fifth the size of tht depicted in Fig. 7; wter depth is in m.
3 WANG Hong et l. Act Ocenol. Sin., 1, Vol. 37, No. 3, P. 1 3 Boussinesq equtions, which cn reflect the nonliner chrcteristics of surfce wves nd wves reking ner shore, it cn simulte wve-induced flows nd rip currents well. However, it tkes much computtionl time ecuse it requires grid spce tht is fr less thn the wve length nd time step much smller thn the wve period. It is not esy to expnd the clcultion domin to ccount for the influences of costl slope nd size on rip currents. In future studies, we will use the wve-verge model to further investigte the chrcteristics nd dynmic mechnisms of rip currents off rc-shped costlines. References Be J S, Yoon S B, Choi J. 13. Boussinesq modelling of rip current t Heunde Bech in South Kore. Journl of Costl Reserch, : 9 Bowen A J. 199. Rip currents: 1. Theoreticl investigtions. Journl of Geophysicl Reserch, 7(3): 7 7 Brown J, McMhn J H, Reniers A, et l. 9. Surf zone diffusivity on Rip-Chnneled Bech. Journl of Geophysicl Reserch, 11(C11): doi: 1.19/JC1 Cstelle B, Coco G. 1. The morphodynmics of rip chnnels on emyed eches. Continentl Shelf Reserch, 3: 1 3 Cstelle B, Michllet H, Mrieu V, et l. 1. Lortory experiment on rip current circultions over movele ed: drifter mesurements. Journl of Geophysicl Reserch, 11(C1): doi: 1.19/1JC33 Chen Qin, Dlrymple R A, Kiry J T, et l. 1999. Boussinesq modeling of rip current system. Journl of Geophysicl Reserch, 1(C9): 17 37 Choi J, Shin C H, Yoon S B. 13. Numericl study on se stte prmeters ffecting rip current t Heunde Bech: wve period, height, direction nd tidl elevtion. Journl of Kore Wter Resources Assocition, (): 1 Dlrymple R A, Mcmhn J H, Reniers A J H M, et l. 11. Rip currents. Annul Review of Fluid Mechnics, 3(1): 1 1 Den R G, Oh T M. 199. Three dimensionl morphology in nrrow wve tnk: mesurements nd theory. In: th Interntionl Conference on Costl Engineering. Koe, Jpn: ASCE, 191 Drønen N, Krunrthn H, Fredsøe J, et l.. An experimentl study of rip chnnel flow. Costl Engineering, (3-): 3 3 Fng Kezho, Zou Zhili, Liu Zhongo. 11. Numericl simultion of rip current generted on rred ech. Chinese Journl of Hydrodynmics (in Chinese), (): 79 Giger M, Drcos T, Jirk G H. 1991. Entrinment nd mixing in plne turulent jets in shllow wter. Journl of Hydrulic Reserch, 9(): 1 H T, Jun K, Yoo J, et l. 1. Numericl study of rip current genertion mechnism t Heunde Bech, Kore. Journl of Costl Reserch, S7: 179 13 Hs K A, Svendsen I A.. Lortory mesurements of the verticl structure of rip currents. Journl of Geophysicl Reserch, 17(C): 1-1 1-19 Hller M C, Dlrymple R A, Svendsen I A.. Experimentl study of nershore dynmics on rred ech with rip chnnels. Journl of Geophysicl Reserch, 17(C): 1-1 1-1 Hss K A, Svendsen I A, Hller M C, et l. 3. Qusi-three-dimensionl modeling of rip current systems. Journl of Geophysicl Reserch, 1(C7): 317 Hsu J R C, Silvester R, Xi Yimin. 199. Applictions of hedlnd control. Journl of Wterwy, Port, Costl, nd Ocen Engineering, 11(3): 99 31 Huntley D A, Hendry M D, Hines J, et l. 19. Wves nd rip currents on Crien Pocket ech, Jmic. Journl of Costl Reserch, (1): 9 79 Jin Hong, Zou Zhili, Qiu Dhong, et l.. The effects of wve-induced currents on the trnsport of pollutnt outside nd inside surf zone. Hiyng Xueo (in Chinese), (): 1 1 Kennedy A B, Thoms D.. Drifter mesurements in lortory rip current. Journl of Geophysicl Reserch, 19(C): C Lscody R L. 199. Est centrl florid rip current progrm. Ntionl Wether Digest, (): 3 Li Zhiqing, Li Weiqun, Chen Zishen, et l. 1. Influencing fctors nd clssifictions of rc-shped costs in South Chin. Act Geogrphic Sinic (in Chinese), 9(): 9 Li Zhiqing. 1. Rip current hzrds in South Chin hedlnd eches. Ocen & Costl Mngement, 11: 3 3 Li Zhiqing, Zhu Ymin. 1. Bech sfety evlution sed on rip current morphodynmic: cse study of Ddonghi of Sny, Chin. Tropicl Geogrphy (in Chinese), 3(1): 9 1 McMhn J H, Thornton E B, Reniers A J H M.. Rip current review. Costl Engineering, 3(-3): 191 Shi Fengyn, Kiry J T, Hrris J C, et l. 1. A high-order dptive time-stepping TVD solver for Boussinesq modeling of reking wves nd costl inundtion. Ocen Modelling, 3-: 3 1 Shin C H, Noh K, Yoon S B, et l. 1. Understnding of rip current genertion mechnism t Heunde Bech of Kore: honeycom wves. Journl of Costl Reserch, 7: 11 1 Short A D. 7. Austrlin rip systems-friend or foe? Journl of Costl Reserch, S: 7 11 Wng Yn, Zou Zhili. 1. Progress nd prospect of rip currents. Hiyng Xueo (in Chinese), 3(): 17 17 Wei G, Kiry J T, Sinh A. 1999. Genertion of wves in Boussinesq models using source function method. Costl Engineering, 3: 71 99