1 See discussions, sas, and auhor profiles for his publicaion a: hps:// Reproducing laboraory-scale rip currens on a barred beach by a Boussinesq wave model Aricle in Journal of Marine Science and Technology January 1 Impac Facor:.1 READS Available from: Kezhao Fang Rerieved on: 9 May 1
2 Journal of Marine Science and Technology, Vol., No., pp (1) 31 DOI: 1.119/JMST REPRODUCING LABORATORY-SCALE RIP CURRENTS ON A BARRED BEACH BY A BOUSSINESQ WAVE MODEL Ke-Zhao Fang 1, Ji-Wei Yin 1, Zhi-Li Zou 1, Zhong-Bo Liu 1, and Ping Dong Key words: Boussinesq wave model, rip curren, barred beach, domain effec, mean curren. ABSTRACT The pioneering work of Haller  on physically invesigaing bahymery-conrolled rip currens in he laboraory is a sandard benchmark es for verifying numerical nearshore circulaion models. In his paper, a numerical model based on higher-order Boussinesq equaions was developed o reproduce he number of experimens involved in such an invesigaion, wih emphasis on he effec of compuaional domain size on he numerical resuls. A se of Boussinesq equaions wih opimum linear properies and second-order full nonlineariy were solved using a higher-order finie difference scheme. Wave breaking, moving shoreline, boom fricion, and mixing were all reaed empirically. The developed model was firs run o simulae he rip curren under full spaial and ime-domain condiions. The compued mean quaniies, including wave heigh, mean waer level, and mean curren, were compared wih he experimenal daa and favorable agreemens were found. The effecs of compuaional domain size on he compuaion resuls were hen invesigaed by conducing numerical experimens. The Willmo index was inroduced o evaluae he agreemens beween he compued resuls and daa. Iner-comparisons beween he compuaion resuls and measuremens demonsraed ha he compuaional domain size significanly influenced he numerical resuls. Thus, running a Boussinesq wave model under full spaial and ime-domain condiions is recommended o reproduce Haller s experimen. I. INTRODUCTION Rip currens, which are shore-normal, rapid, and inense offshore-direced jes of waer ha originae wihin he surf Paper submied 1/15/1; revised 1//13; acceped 5/9/13. Auhor for correspondence: Ke-Zhao Fang ( 1 The Sae Key Laboraory of Coasal and Offshore Engineering, Dalian Universiy of Technology, Dalian Ciy, China. Deparmen of Civil Engineering, Universiy of Dundee, Dundee Ciy, UK. zone, grealy influence sedimen and polluan ransporaion, hereby affecing he coasal morphology and nearshore waer qualiy. Public safey issues are closely linked o inense rip currens, especially in ouris beaches. For example, in he sae of Florida, rip currens accoun for more han % of all lifeguard rescue effors, and more beachgoers fall vicim o rip currens han o lighing, hurricanes, and ornadoes. Thus, rip currens are lised as he number one naural hazard in he US . These aforemenioned issues illusrae he imporance of rip currens and have iniiaed numerous sudies, as reviewed by MacMahan  and Darlymple . Among he many published research resuls available on rip currens, Haller s experimenal bahymery and layou are ypical . In he experimens, rip currens generaed on a barred beach wih wo incised channels were invesigaed. Many scholars have subsequenly employed he same bahymery and layou o invesigae bahymery-conrolled rip currens [, 9, 1, 15], and hese physical experimens have grealy conribued o our insighs ino he complex rip curren. Haller s experimens also provide an excellen benchmark es for verifying numerical nearshore circulaion models [1, 3, 5-7, 1, 1]. Boussinesq wave models, used by Chen e al. , Nwogu , Lu and Yu , and Fang e al. , can presen good predicions afer careful uning of he involved parameers. Compared wih he real space and ime scales in Haller s experimens, however, laer simulaions were conduced wih cerain simplificaions of he compuaional domain size. The wave basin size in Haller s experimens is 17 m long and. m wide wih a duraion of abou 7 min. By conras, Chen e al. , Lu and Yu , and Fang e al.  only used he op half of he experimenal opography and he simulaion ime was reduced o s. Alhough Nwogu  used he full-size wave basin, he simulaion ime was also limied o s. Resuls from he Boussinesq wave model using he full compuaional domain size have never been repored. The Boussinesq wave model belongs o he phase-resolving ype, which describes wave moion in a wave-by-wave manner and requires considerable compuaion effors. The aforemenioned simplificaions on compuaional domain size are explained in his way.
3 3 Journal of Marine Science and Technology, Vol., No. (1) When using a Boussinesq-ype wave model o reproduce Haller s experimens, he following mus be considered: (1) he simplificaions will ineviably inroduce uncerainies o he compuaion resuls; () compared wih hree-dimensional (3D) models, he compuaional cos of a Boussinesq wave model has already been grealy reduced by inegraion along he waer deph; hus, a relaively compuaion-cheaper model can be used o simulae laboraory-scale rip currens; (3) since fewer domain effecs on he physical phenomena are he main advanage of a numerical model, inroducion of an exra domain effec when a numerical model is used o reproduce laboraory-scale experimens mus be deliberaed on; and () he exen by which domain reducion affecs he numerical resuls from a Boussinesq wave model has ye o be deermined. Previous sudies of Boussinesq-ype simulaions scarcely underline hese problems. The presen sudy addresses he effec of compuaional domain size on he compuaion resuls by conducing numerical experimens. A numerical model based on a se of fully nonlinear Boussinesq equaions is firs developed o reproduce Haller s experimens under full-domain condiions. Then, he validaed model is used o conduc numerical experimens using differen spaial and ime sizes, and he effecs of reducing spaial or ime domains on he numerical resuls are invesigaed. II. MODEL DESCRIPTION AND SIMULATION SETTING 1. Boussinesq-ype Wave Model The governing equaions used in he presen sudy are he exended version of he second-order fully nonlinear equaions of Zou . The wo-dimensional (D) forms of he equaions are βη + ( Λ u ) = f (1) 1 1 u u u G u u + ( ) + g η + = h [ ( h ) ] h ( ) + Bh [ ( u + g η)] + B [ ( h u + gh η)] + R () G = d [( u) u u ( u u )] ηd[ ( u) u u u] η( h+ η) u (3) whereη is he surface elevaion, h is he waer deph, d = h + η is he local waer deph, g is he graviaional acceleraion, and u is he deph-averaged velociy. The coefficiens B 1 and B are se as 9/5 and /59, respecively, afer opimizing dispersion equaions and shoaling properies. The. m z y 3. m 7.3 m 3. m cm 17 m 1. m 1. m Fig. 1. Skech of Haller s experimens. aforemenioned equaions allow a Pade [, ] approximaion of he exac dispersion and are applicable in inermediae waer. As well, he equaions have fully nonlinear characerisics (up o he second order) and can be used o describe he wave moion wih srong nonlineariy. Λin Eq. (1) accouns for he inclusion of porous beaches o ake ino he moving shoreline. f on he righ-hand size of Eq. (1) is he funcion for inernal wave generaion. R in Eq. () is defined as R = R b + R f + R s, where R b represens energy dissipaion caused by wave breaking (including subgrid mixing), R f is he boom fricion, and R s is he sponge layer used o absorb wave energy. All of hese erms are idenical o hose in he FUNWAVE model [1, 11], and readers can refer o ha model or ha by Fang e al. . Two parameers in porous beaches λ and δ, conrol he shape of he slo and are se as λ = and δ =.1. The boom fricion is se as.1 afer uning of he numerical resuls o mach he experimenal daa. The parameers for eddy viscosiy breaking are se o he following values in simulaions: wave breaking iniiaion parameer η I =.3 gh, wave breaking cease parameer η I =.5 gh, ransiion * period T = 5 h/ g, srengh of wave breaking δ b = 1., and mixing urbulence parameer C m =.5. The numerical implemenaion mainly follows he FUNWAVE model [1, 11]. The numerical procedure consiss of solving an algebraic expression for η and ri-diagonal equaions for u along grid lines a he x and y direcions. Deails of such may be found in he sudies of Fang e al. .. Model Seing A plan view and a cross secion of he wave basin in Haller s experimen are shown in Fig. 1, where he origin is locaed a he inersecion poin of he wave maker and one side wall. The wave basin is 17. m long,. m wide, and conains a planar concree beach of 1:3 slope as well as a x x
4 K.-Z. Fang e al.: Reproducing Rip Currens by Boussinesq Wave Model 33 seep (1:5) oe srucure. A longshore bar parallel o he wave maker is locaed beween approximaely x = 11.1 m and 1.3 m wih he bar cres a x = 1. m, resuling in a minimum waer deph of. m on he cres. Two gaps of approximaely 1. m wide, cenered a 1/ and 3/ of he basin widh, are incised o mimic rip channels. The bahymery was inended o be planar and he wo rip channels were inended o be symmeric and equal o each oher; however, bahymeric survey daa clearly show some differences . A more deailed descripion of he experimens is provided in . Only he op half of he bahymery was used for numerical simulaions by Chen e al. , Lu and Yu , and Fang e al. . The proposed model was run for 7 min and he las half of he daa collecion period (19 s) was used for mean quaniy calculaions. These seings are idenical o hose in Haller s experimen, hus creaing a full domain simulaion. In he simulaion, grid sizes along he y and x direcions are.1 m and.5 cm, respecively, and he ime sep is.1 s. Regular waves. m high and of 1. s periodiciy are generaed using inernal source funcion a x =. m, where he waer deph is.33 m. The enire compuaional domain is enclosed by solid walls and sponge layers are placed in fron of walls near he wo ends of he compuaional domain o absorb refleced waves. To evaluae he agreemens beween numerical resuls and experimenal daa for a given quaniy v, he Willmo index  is used. This index is inroduced as d = 1 v n j= 1 n [ y( j) x( j) ] j= 1 y( j) x + x( j) x where x( j) is he measured daa poin, y( j) is he compuaion resul, and x is he mean value of series y( j). Perfec agreemen is indicaed by d v = 1, whereas d v = indicaes complee disagreemen. III. NUMERICAL RESULTS FROM THE FULL DOMAIN SIMULATION Numerical resuls are presened and compared wih he experimenal daa in his secion. The quaniies compared include mean wave heigh (H), mean waer level (MWL), mean cross-shore curren (U), longshore curren (V), and mean flow field. As he measuremens from he experimens cover mos areas of wave basins, heir comparison wih he compuaion resuls will reasonably show he overall performance of he numerical model on reproducing he experimens. 1. Wave Heigh and Mean Waer Level The compued wave heighs, ploed in Fig., show good () H (m) H (m) H (m) H (m) H (m) (a) x = 1. m (b) x = 13. m (c) x = 1. m (d) x = 11. m (e) x = 1. m daa numerical resul Fig.. Comparison of ime-averaged compued wave heighs wih experimenal daa. MWL (mm) MWL (mm) MWL (mm) MWL (mm) MWL (mm) (a) x = 1. m (b) x = 13. m (c) x = 1. m (d) x = 11. m (e) x = 1. m daa numerical resul Fig. 3. Comparison of ime-averaged compued mean waer levels wih experimenal daa.
5 3 Journal of Marine Science and Technology, Vol., No. (1) (a) x = 1. m (b) x = 13. m (c) x = 1. m (d) x = 11. m (e) x = 1. m daa numerical resul Fig.. Comparison of ime-averaged compued cross-shore currens wih experimenal daa (a) x = 1. m (b) x = 13. m (c) x = 1. m (d) x = 11. m (e) x = 1. m daa numerical resul Fig. 5. Comparison of ime-averaged compued long-shore currens wih experimenal daa. agreemen wih he experimenal daa. The increase in wave heigh because of he shoaling process and decrease in wave heigh afer wave breaking are well prediced from relaively deep waer (x = 1. m) o shoreline (x = 1. m). Paricularly, he delayed wave breaking in he rip channel is also well reproduced. The value of d H compued from Eq. () for he wave heigh urns ou o be.915, which demonsraes ha he presen wave model is reasonable. The compued mean waer level (η ), shown in Fig. 3, show good agreemen wih he experimenal daa excep for some underesimaes a x = 1. m and x = 13. m. Before wave breaking, he mean waer level has a negaive value a x = 1. m and x = 11. m, which indicaes a sedown. Afer wave breaking occurs, he mean waer level begins o increase o a posiive value and he maximum value is reached near he shoreline (x = 1. m). The wave seup in he barred region is higher han ha in he rip channel, which will induce a longshore pressure gradien, finally driving he curren o converge and flow ou from in he rip channel o form a rip curren. The index agreemen for mean waer level d η is.93. The high values of d H and d η denoe ha he variaions in surface elevaions are well capured by he numerical model.. Time-Averaged Curren The compuaion resuls for cross-shore mean curren (U) and longshore mean curren (V) are presened in Figs. and 5, respecively. The corresponding values of d U and d V compued from Eq. () are. and.755, respecively. These wo relaively lower values are mainly caused by he discrepancy near he shoreline region x = 1. m, as shown in he figures. The main feaures of rip currens are well reproduced. The offshore-direced currens, i.e., rip currens, are obvious in he rip channel a x = 11. m and x = 11. m. A farher offshore posiions, such as x = 1. m, rip currens are dissipaed because of he mixing mechanism. The rip feeder is also clearly shown in Fig. 5, where he longshore mean currens a he wo sides of he rip channel have opposie signs, indicaing ha hese currens flow in he opposie direcion o converge in he rip channel. The asymmery of mean currens is also demonsraed; such asymmery is mainly due o longshore non-uniformiies of he bahymery and consisen wih observaions of experimens and numerical resuls from a quasi 3D model . Fig. shows more deailed comparisons of he cross-shore curren in he rip channel along hree longshore secions a x = 11.5, 11., and 1 m. The model accuraely capures he ampliude, widh, and longshore variaions in he rip curren and shows excellen agreemen wih he experimenal daa. The index of agreemen for he cross-shore curren is fairly high, wih d U =.955. This high value shows some aracive aspecs of he numerical model, since he mean curren in he
6 K.-Z. Fang e al.: Reproducing Rip Currens by Boussinesq Wave Model (a) x = 11.5 m (b) x = 11. m (c) x = 1. m (a) (b) (c).5 m/s m/s daa numerical resul Fig.. Comparison of ime-averaged compued cross-shore currens in he channel wih experimenal daa Fig. 7. Time-averaged below-rough velociy from he experimenal daa (lef panel), he simulaion (middle panel), and he simulaion a he same poins as he experimenal daa (he hird panel). channel is always he sronges curren. Accurae predicion of he maximum rip curren is exremely crucial for lifeguards or coasal engineers. 3. Mean Curren Field The deph-inegraed curren from he model is displayed in Fig. 7 and compared wih he experimenal daa. The experimenal daa shown here are obained from many repeaed runs of he experimen wih idenical wave condiions bu differen measuring locaions . The classical flow paern of rip currens, i.e., rip feeder, rip neck, and rip head, are well reproduced by he model and appear similar o he measured flow field. The sligh basin cener biased rip header, which is shown by he measuremens, is also reproduced by he model. To faciliae comparisons beween he model resuls and daa, currens from he model obained only a locaions where he measuremens were made are shown in he hird panel of Fig. 7. The figure shows ha he recirculaion cells close o he shoreline have similar dimensions and ha he flow along he offshore edge of he cenral bar is parallel o he shore. The flow paerns in he op and down channels are no idenical, which is mainly due o he sligh non-uniformiies of he bahymery. No measuremens in Haller s  experimens quaniaively suppor his difference bu his asymmery was also observed. Furher analysis of he asymmery will be presened in he following secion using experimenal daa from Tes R in he experimens of Haas e al. , which is designed o supplemen he experimens of Haller .. Mean Curren Field and Movemen of Voriciy Besides he ime-averaged quaniies lised above for comparison, some ineresing insananeous phenomena are also observed in he experimens. The firs is he slow plural of he rip curren during is offshore-direced moion and he second is he asymmery of he rip curren in he op and boom rip channels. Research has shown ha irregulariies in he acual bahymery are responsible for variaions in rip behavior  and ha he slow plural is due o he insabiliy of rip currens [, ]. Furher invesigaions wih respec o hese wo aspecs will be made o demonsrae model s abiliy in capuring hese ime-varying characerisics. Four snapshos of compued voriciy and velociy are shown in Fig., where he quaniies are obained by averaging a series of recorders every wo periods. The unsable feaures of rip currens may be observed from he figures. The voriciy and velociy fields develop fully in he channel and propagae offshore bu he rip coninually meanders from side o side and aenuaes in he process of moving oward deep-waer regions. The aforemenioned asymmery beween he upper and lower channels may also be observed in he figure, where he voriciy and velociy fields are asymmeric. The scale and inensiy of he mean curren originaing from he upper channel are sronger han hose from he lower channel. A similar rend is also observed for long ime-averaged curren fields (Fig. 7). Fig. 9 shows he low-pass filered ime series of cross-shore velociy from he measuremens of Haas e al.  and presen simulaions offshore of he edge of he op (x = 1. m, y = 13. m) and lower (x = 1. m, y =. m) channels. The measuremens show significan differences in he frequency or magniude of he rip evens beween wo locaions. The simulaion presens a similar rend, i.e., rip evens in he op channel occur more frequenly and wih more srengh han hose in he boom channel. Alhough some disinc differences may be observed in he ime series, he measured and long-ime averaged velociies are similar. Boh measuremens and simulaion show ha he rip curren only occurs sporadically.
7 Journal of Marine Science and Technology, Vol., No. (1 ) s = sec 1 15 case half s -. (b) simulaion -..5 = sec s-1 case 3 half 7 min case full s (a) measuremen -1.5 m/s.5 m/s case 1 full 7 min = 1 sec 5.5 Compuaional domain Simulaion ime = sec 1 1 Table 1. Spaial and emporal scale for four cases..5 m/s 1.5 m/s op channel (x = 1., y = 13.) boom channel (x = 1., y =.) Fig. 9. Low-pass filer ime series of he cross-shore velociy of rip currens a x = 1. m, y =13. m (solid line) and y =. (dashed line) from (a) he measuremens of Haas e al.  and (b) he simulaion Fig.. Four insananeous snapshos of simulaed voriciy and velociy vecors. The numerical simulaion shown above illusraes ha he presen model can capure he main feaures of he slow plural of rip currens as well as he difference beween wo rip channels. However, disinc differences may also be found. The ime series shown in Fig. 9 denoes he limied abiliy of he Boussinesq model in accuraely reproducing he emporal variabiliy of rip currens. This limiaion is accepable, considering he following aspecs. Firs, expecing he presen D numerical model o capure he complee deails of a complex 3D process is unrealisic. Second, he main mechanisms ha dominae nearshore circulaion, such as wave breaking, boom fricion, and urbulence mixing, are only reaed by ad-hoc mehods in he Boussinesq model. IV. NEMERICAL EXPERIMENTS The numerical resuls from he full domain simulaion in Secion III demonsrae ha he presen model predics he spaial variabiliy of he wave-induced nearshore circulaion well and capures he main feaures of emporal variabiliy. Thus, we can confidenly run he model using differen spaial and ime domains o reach reliable numerical resuls. 1. Case Seings Four cases wih differen spaial and emporal scales are se for numerical experimens, as shown in Table 1. Case 1: full bahymery and duraion (7 min), which has been compleed in Secion III; Case : he bahymery is idenical o ha in case 1 bu he simulaion ime is reduced o s, which is significanly shorer han ha in case 1; Case 3: half he size of he full bahymery and he simulaion ime is 7 min; and Case : half he size of he full bahymery and he simulaion ime is s. Excep for he spaial and ime scales, all of he remaining parameers and condiions are idenical o hose in case 1. The simulaion imes for cases and are ypical values used by previous sudies [1, 3, 1, 1]. The ime series used for compuing mean quaniies is 19 s for cases 1 and 3, whereas he averaging period for cases and begins approximaely a he ime he firs wave arrives a he shoreline and ends a he compleion of he simulaion .. Comparison of Wilmo Index for Mean Quaniies The Willmo indices of wave heigh, MWL, U, V, and mean cross-shore curren in he channel deermined from he four cases are summarized in Table. The value of dh for case 1 is.915, which is significanly higher han hose in oher cases, indicaing beer agreemen wih he experimenal daa. By conras, case presens a minimum index value of.15, denoing relaively poor predicion abiliy. The compued Willmo indices of MWL for he four cases are almos idenical, indicaing ha good agreemen is obained for all cases.
8 K.-Z. Fang e al.: Reproducing Rip Currens by Boussinesq Wave Model 37 (a) (b) (c) (d) (e) m/s 1.5 m/s 1.5 m/s 1.5 m/s case case case case Fig. 11. Time-averaged velociy vecors obained from (a) he experimenal daa and from (b) case 1, (c) case, (d) case 3, and (e) case. Table. A summary of he index of agreemen for quaniies from four cases. case H WML U V U (in channel) case case case case From he aforemenioned comparisons, we can conclude ha simulaions using full domains presen opimal numerical resuls whereas simulaions using reduced spaial or ime scales presen relaively poor predicions. To fully capure he differences among hese four cases, he profile of he mean cross-shore curren in he rip channel and mean curren field will be furher invesigaed. From he aforemenioned comparisons, we can conclude ha simulaions using full domains presen opimal numerical resuls whereas simulaions using reduced spaial or ime scales presen relaively poor predicions. To fully capure he differences among hese four cases, he profile of he mean cross-shore curren in he rip channel and mean curren field will be furher invesigaed. 3. Mean Cross-shore Curren in Channel and Mean Curren field The numerical resuls of rip currens in he channel from four cases are ploed in Fig. 1 and compared wih he experimenal daa. Case 1 accuraely presens boh he ampliude and he disribuion of he mean curren whereas case 3 gives he poores predicions by underesimaing he srengh of rip currens and disoring is disribuion in he rip channel. Cases and overesimae he ampliude of rip currens and he prediced mean flows are srongly biased. The ime-averaged velociy vecors from four cases are (a) x = 11.5 m (b) x = 11. m (c) x = 1. m daa case 3 case 1 case case Fig. 1. Comparison of compued ime-averaged cross-shore curren in he channel from four cases wih experimenal daa. shown in Fig. 11; hose from Haller s experimen are also shown as a reference. Cases 3 and fail o provide flow informaion of he boom half wave basin because only he op half of he bahymery was used. Comparing he four vecor diagrams wih he experimenal daa, we can see ha cases 1 and predic almos he same flow paern. However, as Fig. 11 shows, case acually presens he wrong profile in he rip channel. Case 3 only gives he local mean curren in he rip channel and fails o predic he offshore-direced rip head. Case presens a significanly biased mean flow and he ampliude of he mean curren is grealy underesimaed.
9 3 Journal of Marine Science and Technology, Vol., No. (1) (a) case 1 (b) case (c) case 3 (d) case Fig. 1. Comparison of compued and low-pass filered ime series of he cross-shore velociy in he rip curren a x = 1. m and y = 13. m.. Furher Analysis and Discussion of Domain Effecs on Numerical Resuls The aforemenioned comparisons show ha he compuaional domain grealy influences he numerical resuls. For he spaial domain, using he op half of he wave basin implies complee symmery of he acual bahymery or, in he very leas, ha irregulariies can be ignored. Boh our numerical experimens and hose of Haas e al.  show ha variaions in he bahymery canno be ignored and ha hey significanly change he flow paerns beween wo rips. Long-erm simulaion resuls obained from using he op half of he basin are also physically incorrec as hey predic a solid wall in he cenerline where he waer region should be, hereby decreasing he simulaion accuracy, as shown in case 3. The compuaional duraion effec on he numerical resuls is furher invesigaed by comparing he low-pass filered ime series of cross-shore currens a he offshore edge of he op channel (x = 1. m, y = 13. m), as shown in Fig. 1. I is ineresing o see ha all of he ime series have an iniial offshore-direced flow even near he beginning of simulaion, which is due o drainage from he iniial surge of waer shoreward when waves begin . If only he firs s is used for simulaion, he ime-averaged quaniy U would be almos idenical for all four cases because of he iniial surge even. However, his resul is no accurae, as shown in he previous secions. Only longerm simulaion can remove he effecs of he iniial surge even, yielding resuls more represenaive of he real rip curren. The experimenal invesigaion of Haas e al.  revealed his phenomenon, where all ime series of measured velociies (Figs., 7, 13, and 1 in ) showed almos idenical iniial surge evens bu long-erm averages resuled in apparenly differen quaniies. Tha also may be he reason why Haas e al.  simulaed Haller s experimen using full spaial and ime domains. Relaively high indices of agreemen are found for cases and in Table, which we believe are no compleely reliable based on he aforemenioned analysis. V. CONCLUSION Domain effecs on he numerical resuls when using a Boussinesq-ype wave model o reproduce Haller s experimens are invesigaed in he presen paper by conducing numerical experimens. A D wave-breaking model based on fully nonlinear Boussinesq-ype equaions is firs developed o reproduce he experimen of Haller. Numerical resuls, including wave heigh, mean waer level, mean longshore, and cross-shore curren, from he full-scale simulaions agree well wih he experimens. Differences in mean curren field in he wo rip channels and he ransien rip curren and voriciy movemen, which have been observed in previous experimens, are also well reproduced by he full-scale simulaion. The overall performance of he presen model illusraes is abiliy o reproduce wave breaking-induced nearshore circulaion. The effecs of differen spaial and ime scales adoped in he simulaion on he compuaion resuls are hen invesigaed by conducing numerical experimens for four cases using differen spaial and ime scales. The Willmo index evaluaes he agreemen beween he numerical resuls and experimenal daa. Deailed comparisons beween he numerical resuls and experimenal daa demonsrae ha he scales significanly influence he compuaion resuls and ha he full-scale simulaion presens he bes numerical resuls and has superior performance compared wih simulaions using reduced spaial or ime scales. Using only he op half of he wave basin is no advisable as variaions in he acual bahymery are ignored and long-erm simulaions are no suppored. To run he Boussinesq model for shor imes is incorrec as he iniial surge of rip curren dominaes he iniial sage of he flow paern. Thus, o reproduce Haller s experimens using a Boussinesq-ype wave model, conducing simulaions under full-scale condiions, which is believed o be consisen wih he inrinsic phase resolving naure of he model, is recommended by he auhors. ACKNOWLEDGMENTS The auhors would like o hank he finical suppor from Naional Naural Science Foundaion of China under Gran 519, Key Laboraory of Coasal Disaser and Defence, Minisry of Educaion, Hohai Universiy. We also would like o hank Dr. Haas Kelvin for providing he deailed surveyed bahymery daa. The valuable commens from anonymous reviewers are grealy appreciaed.
10 K.-Z. Fang e al.: Reproducing Rip Currens by Boussinesq Wave Model 39 REFERENCES 1. Chen, Q., Dalrymple, R. A., Kirby, J. T., Kennedy, A. B., and Haller, M. C., Boussinesq modeling of a rip curren sysem, Journal of Geophysical Research, Vol. 1, No. C9, pp (1999).. Dalrymple, R. A., MacMahan, J. H., Reniers, Ad J. H. M., and Nelko, V., Rip curren, Annual Review of Fluid Mechanics, Vol. 3, pp (11). 3. Fang, K. Z., Zou, Z. L., and Liu, Z. B., Numerical simulaion of rip curren generaed on a barred beach, Chinese Journal of Hydrodynamics, Vol., No., pp (11).. Haas, K. A. and Svendsen, I. A., Laboraory measuremens of he verical srucure of rip curren, Journal of Geophysical Research, Vol. 17, No. C5, pp (). 5. Haas, K. A. and Svendsen, I. A., 3-D modeling of rip curren, The Tweny-Sevenh Inernaional Conference on Coasal Engineering, Vol., No. C7, pp (1).. Haas, K. A., Svendsen, I. A., Haller, M. C., and Zhao, Q., Quasi-hreedimensional modeling of rip curren sysems, Journal of Geophysical Research, Vol., No. C7, pp. 1-1 (3). 7. Haas, K. A. and Warne, J. C., Comparing a quasi-3d o a full 3D nearshore circulaion model: SHORECIRC and ROMS, Ocean Modelling, Vol., Nos. 1-, pp (9).. Haller, M. C., Rip Curren Dynamics and Nearshore Circulaion, Docor Disseraion, Universiy of Delaware, USA (1999). 9. He, L., Video-Based Paricle Image Velocimery of Laboraory Rip Curren, Thesis, Universiy of Delaware, USA (). 1. Kennedy, A. B., Zhang, Y., and Haas, K. A., Rip curren wih varying gap widhs, Journal of Waerway, Por, Coasal, and Ocean Engineering, Vol. 13, No. 1, pp. 1-5 (). 11. Kirby, J. T., Wei, G., Chen, Q., Kennedy, A. B., and Dalrymple, R. A., FUNWAVE 1. Fully nonlinear Boussinesq wave model documenaion and user s manual, Research Repor, CACR-9-, Newwark (199). 1. Lu, J. and Yu, X. P., Model for boh nearshore waves and wave-induced curren based on Boussinesq equaions, Chinese Journal of Hydrodynamics, Vol. 3, No. 3, pp (). 13. MacMahan, J. H., Thornon, Ed. B., and Reniers, Ad J. H. M, Rip curren review, Coasal Engineering, Vol. 53, pp (). 1. Nwogu, O. K., Numerical predicion of rip curren on barred beaches, Proceedings of he h Inernaional Symposium on Ocean Wave Measuremen and Analysis, San Francisco, USA, pp (1). 15. Sapp, B. K., Observaions of Laboraory Rip Curren, Thesis, Georgia Insiue of Technology, USA (). 1. Willmo, C. J., On he validaion of models, Physical Geography, Vol., pp. -19 (191). 17. Zou, Z. L., Higher order Boussinesq equaions, Ocean Engineering, Vol., pp (1999).
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