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1 kë k v r 3 r 4, pp. 76~84, 011 8o Boussinesq t } } z r Boussinesq Modeling of a Rip Current at Haeundae Beach Žƒ}*Ú ~ **Ú~o *** Junwoo Choi*, Won Kyung Park** and Sung Bum Yoon*** k s : Ž plp p m p q rp Ž p p p p r p Boussinesq re p FUNWAVE pn l, Ž s p n kl pk p m. p Žp ržk v l p Ž p q lt pp, p Ž n v p m l e l Ž o lk k p q lt. p pk lk p rp ep p l Ž p l pk rp p v ppp p m. kh : pk, p, Boussinesq re, FUNWAVE, n Abstract : The rip current occurred at Haeundae beach was numerically investigated under directional random wave environment. The numerical simulation was performed using a fully nonlinear Boussinesq equation model, FUNWAVE which is capable of simulating nearshore circulation since it includes the effect of wave-induced momentum flux and horizontal turbulent mixing. The results of numerical simulation show the time-dependent evolution of the wave-induced nearshore circulation system (including rip current) that are caused by nonlinear transformation of directional irregular waves due to unique topography of Haeundae. From the results, it was found that rip current is well generated and developed where relatively lower wave height and relatively deeper water depth along the longshore direction, and sudden and strong events of rip current were observed. Keywords : Rip current, numerical simulation, nonlinear Boussinesq equation, FUNWAVE, Haeundae beach 1. l n l n p krp o pk l k l p ep p , p n nq pk l, 008 e j s s p. p rp pk lkl v, Žp qn qo p kr (instability) l p l Ž l v lk (longshore direction)p (nonuniform) p p k r p (Darlymple, 1975, 1978; Tang and Dalrymple, 1988). v, lk p Ž l v( Ž ) kv yp Ž pln d(waveinduced excess momentum flux)p n p d l pk (rip channel) l n yp p. p pk Shepard (1936), l eq mp, l l p r p pn l rp ƒ vp n p l (m, Bowen, 1969; Bowen and Inman, 1969; Noda, 1974; Darlymple and Lozano, 1978). p pn pk l plp (radiation stress) p pn Ž p p pn (Haas et al., 003; Yu and Slinn, 003; Choi and Yoon, 011) Boussinesq re p pn (Chen et al., 1999; Johnson and Pattiaratchi, 006) l v p. l p pn l n nql pk p l l (, 011). Ž - p l p r r p p Ž Ž p p r plp p l r *** l o } k l e (River, Coastal & Harbor Research Division, Korea Inst. of Construction Tech., Goyang, , Korea. jwchoi@kict.re.kr) *** k o (Dept. of Civil & Environ. 171 Sa-3-dong Sangnok-gu, Ansan, , Korea.) *** k (Corresponding Author: Sung Bum Yoon, Dept. of Civil & Environ. 171 Sa-3-dong Sangnok-gu, Ansan, , Korea. sbyoon@hanyang.ac.kr) 76

2 Boussinesq re p pn n pk p 77 qnp l. p p Žp n, Ž p p r plp l rrp pp (Choi et al., 009), rp e p o p, p rp p p. pm, Ž p el Boussinesq re p plp p r v k v rep p q rp plp p rr p pp, e p p rp p. Žp o p primitive valuablep l rp pk p l o (o, 010). p pn l pnl, Hammack et al.(1991), Haller et al. (000)m Dronen et al. (00) p e p l }k pp, MacMahan et al.(004a,b) p q p l l p. p sl pk p p s p l pk p e p p l p p. ƒ vp s p r p sq v, kr plv p erp rp, pk p er q m p n l., n m p l (pocket beach)p n, vp Ž p k kyp d r l p Ž l p t p s p lk eˆ, p v lk, p ol l s pk p ƒ v n yp pk eˆ. l l s pk l o n l p n q n Ž, Žp o p pl r pk pp p Boussinesq re p FUNWAVE(Wei et al., 1995; Kirby et al., 1998; Chen et al., 1999; Chen et al., 000; Kennedy et al., 000; Chen et al., 003; Johnson and Pattiaratchi, 006) pn l n p lk p p m. Ž o lk n k p v p l kr p opp p r pk l ep vt l m. n lk l q q p v tp kv n l e n r rp l pp, q rnp o parameterizationp r rp vp ˆp. l l p p l n l rp pk p p p, kp p p e l p p Ž.. l l n p FUNWAVE o~ Ž p el p Wei et al.(1995)l Boussinesq rep v rep n. p Boussinesq rep rp 3 o Euler rep r r m r k p } rp pn e r l o, qo om o p v o p Ž p rp n l m. Chen et al.(003)p r rp o p v rep n rel r rp p p ~ l p m. v rep l rep p. z u α 1 α h hη η + ( + ) ( u α ) 6 + ( ) = z α + -- ( h η) [ ( hu α )] η t h + η l η qo o, h r e, u α z = z α = -0.53h l p o, = ( x, y), ~q t e p p. v rep n rep p. (1) = 0 () u αt ( u α )u α g η V 1 V V 3 R b R s R f l, V 1 = ---- ( u (3) αt) + z α [ ( hu αt) ] V = z α ---- u α t + η η ( hu αt) 1 ( z α η) ( u α ) [ ( hu α )] -- ( z α η + )( u α ) ( u α ) hu α {[ ( ) + η u α ] } l g t, V 1 m V Boussinesq, V 3 lv m (vorticity) ˆ. R b, R s, R f Ž,, ˆ p, FUNWAVE p p r o l p p (Kirby et al., 1998; Chen et al., 1999; Chen et al., 000; Kennedy et al., 000)., sž p pn Žp sž o d p l qo(random) o p t t~ qo e lp l sž (Wei et al., 1999; Johnson and Pattiaratchi, 006; Choi et al., 009). p p p v l p l l p. q np e. (4)

o A (array A)p } e k p p, B (array B) D (array D)p lk (longshore direction) snl l v p rp p (rip channelp p p ), C (array C)p lk snl l v p rp p l r m. l l pk t p k v S Ž Fig.

3 78 tnë o Ëo 3. set-up pl n n lkv p Fig. 1l ˆ l. p o pp s orp r mp, x p l yp 4 nlv p r l v p e m. q x =.0m y =3.0m 948,600 p q n m. l ˆ v kp x =150m sž mlp m, sž yl k 140 m p mlp r m. sn p k 00 mp pp v p l t r s p n p m. p t r s p pn o l kl l s p rp n p, p s p n l Ž rl m rl mlp tp pl. Fig. 1l ˆ r (A, B, C, D) p p o pp r r p lkv p e k l l v (cross shore direction)p pv p r m. o A (array A)p } e k p p, B (array B) D (array D)p lk (longshore direction) snl l v p rp p (rip channelp p p ), C (array C)p lk snl l v p rp p l r m. l l pk t p k v S Ž Fig.. Input frequency-directional spectrum with a significant wave height H = 1.5 m, a peak frequency f = 0.1 Hz, a peak direction θ = 4 deg. (i.e., waves from south to north) using JONSWAP spectrum for frequency distribution and cosine-power spreading function for directional distribution. l l p ee m. S Ž p opž 1.5 m, ~ t 10p Ž sž o l JONSWAP tž m cosine- pn l tž - d p Fig. m p m. JONSWAP ~ v (peak enhancement parameter) 3.3p, vt 15 n m. S Ž p q o d p ~ p -4 p kl l } v p r p. p d p p Ž l v,400 p Ž p l qo(random)o p tl sž m. pm p opž.5 m, ~ t 10p d p p Ž sž l p ee l e m. p o e q 0.1 m. sž p Ž k 3.85p t v, el e 18ml k 3mp Žqp. lk l n tn l p p 0.003p n m, p p r p r p p r n m. p o l Intel Core i7(950)p PC n m. 4. m Fig. 1. Topography of Haeundae beach for numerical simulation and numerical gauge array locations A, B, C and D (unit : m). 4.1 m o n kl p l } l o n FUNWAVE p Ž o lk p p v p. p o n Ž,, l k p l n tn m p t p parameterizationp o, emlp p o r s p p v o e r r e q q mp n.

Boussinesq re p pn n pk p 79 kv v q q p r erp, r rp e s., n nq lkr l nl ( le n, 009)l n lk p e l r r rp pl, l p p m l r r ˆ p p k. p rl re p e p S Ž p opž.5 m, ~ t 10p Ž p l.

Žp opž o l ~ t tp Žl e lp pn p p rpv, e l }p ˆ p m p k Ž l o 300 e lp p pn l p p zerothmoment wave height l opž t m. H sig = 4.0 η l η qo o, ( ) 300 e p. p ˆ Fig. 3p p Žp rž p n q lt p.

p p Fig. 5(a), (b) (c) sžeq (5) Fig. 3. Plane distributions of (a) free surface displacement and (b) significant wave hight (m) resulted from t = 60 min after wave generation begins (incident =.

4 Boussinesq re p pn n pk p 79 kv v q q p r erp, r rp e s., n nq lkr l nl ( le n, 009)l n lk p e l r r rp pl, l p p m l r r ˆ p p k. p rl re p e p S Ž p opž.5 m, ~ t 10p Ž p l. n p llv qo om opž p Fig. 3l re m. qo o Ž eˆ 60 p p p, opž kp Ž o pn l p. Žp opž o l ~ t tp Žl e lp pn p p rpv, e l }p ˆ p m p k Ž l o 300 e lp p pn l p p zerothmoment wave height l opž t m. H sig = 4.0 η l η qo o, ( ) 300 e p. p ˆ Fig. 3p p Žp rž p n q lt p., q o o ˆ Fig. 3(a)l k x=750m, y= 600 ml o t} l p l r, rž Ž p q ˆ p. Ž ˆ Fig. 3(b) v l p Ž prp r e l t Ž v p p Ž Žp p p p. SŽ, opž.5 m, ~ t 10p Ž v rp n lkp rž, Ž o lk p e p Fig. 4m Fig. 5l ˆ l. p p Fig. 5(a), (b) (c) sžeq (5) Fig. 3. Plane distributions of (a) free surface displacement and (b) significant wave hight (m) resulted from t = 60 min after wave generation begins (incident =.5 m). Fig. 4. Vector plot of wave-induced currents resulted from a laboratory experiment where the shading indicates the bathymetry (Busan Metro City - Haeundae District, 009). Fig. 5. Vector plots of wave-induced currents obtained at (a) t = 15 min, (b) t = 30 min, and (c) t = 45 min after wave generation begins (incident H sig =.5 m).

80 tnë o Ëo, 15, 30, 45 300 kp l o p e p. v rp Ž p kp rž, lkl Ž, Ž p ln o p p rp pr p v, p Ž o lk p eˆ p k p. Fig. 4l ˆ e m, Fig. 5(a)l ˆ lk p k n o p k p.

5 m). The broken lines in (a) indicate the region where relatively intense wave-breaking occurs. p sž eq 45 Fig. 5(c)m p mr k l m. 4. n mg k rp p opž.5m, ~ t 10p S p Ž v rp n lkp rž n n pk p p pl.

5 80 tnë o Ëo, 15, 30, kp l o p e p. v rp Ž p kp rž, lkl Ž, Ž p ln o p p rp pr p v, p Ž o lk p eˆ p k p. Fig. 4l ˆ e m, Fig. 5(a)l ˆ lk p k n o p k p. k x = 750 m, y = 600 ml o t} l p Ž o (Choi et al., 009) rp p l lt p. l, p pp r rp n l lk p q q p Ž p. Fig. 6. Plane distributions of (a) free surface displacement and (b) significant wave hight (m) resulted from t = 60 min after wave generation begins (incident H sig = 1.5 m). The broken lines in (a) indicate the region where relatively intense wave-breaking occurs. p sž eq 45 Fig. 5(c)m p mr k l m. 4. n mg k rp p opž.5m, ~ t 10p S p Ž v rp n lkp rž n n pk p p pl. k l 3.0 m p p Ž p l np v lp p Ž, kr eˆ p p pk q o, np Ž opž 1.5 m, ~ t 10p S Žl l p rp m. Fig. 6l Ž eˆ 60 p p qo o m kp Ž o pn l opž e m. k rl re p m p, p Žp rž v l p p q lt p. Fig. 6(a)l Ž re m. p Žmlp 300 e p e l l 0.5%p Ž mlp Žmlp t l e p. Fig. 7l sžeq, 5, 60, kp l o p e l v r p Ž rž p m p Ž o lk p ˆ l. Fig. 5l ˆ.5m opž p n k p k p., y = 700 mm 1,50 m r p o l k pk p. p o kl l p o r 4 p array n, pk (rip channel) sq p m Bm Dp o p, p o p Ž Fig. 6l p Ž rp l p Fig. 7. Vector plots of wave-induced currents resulted at (a) t = 5 min, (b) t = 60 min, and (c) t = 95 min after wave generation begins (incident H sig = 1.5 m).

Boussinesq re p pn n pk p 81 pp p pp, Žml Ž ( o p snl l) rp k l n l p l o pp k p. p sž eq 95 Fig. 7(c)m p mr k l m. pr 4 p arrayl p q. Fig. 8l kl l 4 p array A, B, C, D o l l p l t = 75, 80, 85, 90 l p qo om opž v m e m.

6 Boussinesq re p pn n pk p 81 pp p pp, Žml Ž ( o p snl l) rp k l n l p l o pp k p. p sž eq 95 Fig. 7(c)m p mr k l m. pr 4 p arrayl p q. Fig. 8l kl l 4 p array A, B, C, D o l l p l t = 75, 80, 85, 90 l p qo om opž v m e m. ep Žp Ž Žp Ž p l Ž p. v p rp v l bar p v k p eq p r lv p p. arrayl Ž l l array Bl 5 p Ž r p r (unsteadiness)p p. p pk lkl v p r l p Ž p Ž, p p (Fig. 9(b)p w Ž )l ˆ l p p. Fig. 9l array A, B, C, D o l p ( η ), l kv o (cross shore velocity, V cs ), lk o (longshore velocity, V ts )p v m e m. l ˆ p p e t = 80, 85, 90, 95 l 300 kp p array o l l,, l ll. r, arrayl ˆ p q k v setup setdownp q ˆ p. lkv (cross shore direction) o p kp p array o l k p p ˆ, pp p n p ˆ. lk (longshore direction) o p kp p array o l y p p, pp p y p p ˆ. Array Bm Cl o p e r p arrayp o l rp, Ž rž p, l p ˆ lkv o p Ž l m p t Fig. 8l ˆ Ž p e r l m p t p Ž. Fig. 9l ˆ pp p lkv o p n p ˆ p p pk Ž pp p. Array Bl e rp n p p v rp n yp pk. k, 5 o p kr ppˆ r pk p p Ž l o p. 0 o p pn l arrayl p o e e l k. Fig. 10p array A, B, C, D o l p 0 o (<η >), lkv o (cross shore velocity, <V cs >), lk o (longshore velocity, <V ls >)p v m e p. kl m p p e t = 80, 85, 90, 95 l array o l l,, l p ll. 0 o 300 om e l e p p. l lk ˆ 0 lk o <V cs > array Bp p rn 300 lk o V ls m d, l r p p ˆ p. pk p p Fig. 8. Free surface displacement (top panels), significant wave height (middle panels) and bathymetry (bottom panels) along (a) array A, (b) array B, (c) array C, and (d) array D at t = 80 min ( ), t = 85 min ( ), t = 90 min ( ), t = 95 min ( ) (incident H sig = 1.5 m).

(bottom panels) along (a) array A, (b) array B, (c) array C, and (d) array D at t = 80 min ( ), t = 85 min ( ), t = 90 min ( ), t = 95 min ( )(incident H sig =1.5m). Fig. 10.

7 8 tnë o Ëo Fig. 9. Cross-shore distribution of 5 min-averaged surface elevation (top panels), cross shore velocity (first middle panels), longshore velocty (second middel panels) and bathymetry (bottom panels) along (a) array A, (b) array B, (c) array C, and (d) array D at t = 80 min ( ), t = 85 min ( ), t = 90 min ( ), t = 95 min ( )(incident H sig =1.5m). Fig. 10. Cross-shore distribution of 0 sec-averaged surface elevation (top panels), cross shore velocity (first middle panels), longshore velocity (second middle panels) and bathymetry (bottom panels) along (a) array A, (b) array B, (c) array C, and (d) array D at t = 80 min ( ), t = 85 min ( ), t = 90 min ( ), t = 95 min ( )(incident H sig =1.5m).

8 Boussinesq re p pn n pk p 83 Fig. 11. Time history of a wave height (top panels), 0 sec-averaged cross shore velocity (first middle panels) and longshore velocty (bottom panels) at 5 0m from the shoreline along array A ( ), array B( ), array C( ), and array D( )(incident H sig =1.5m). lkv o (<V cs >) e l e p. lkv o (<V cs >) n array Bp n, t = 85 minp k l 80~110 m lv l 0.5 m/s r pk, 5 p t= 90 minl k p 0~60 m lv e 1.0~.0 m vlp pk p r mp, e 5 p t=95 minl pk v p ˆ pk p r p q ppp k p. p r pk p t p o p (Fig. 11)l k p 50 m lv o p o p e l e m. Fig. 11p array A, B, C, D k p 50 m lv o l pn l 0 kp o pn opž, 0 lkv o (cross shore velocity, <V cs >), lk o (longshore velocity, <V ls >)p e l ˆ p. l opž 0 kp e lp pn l pp zeroth-moment Ž pn l r m. H m0 = 4.0 η l <( )> 0 e p rp. k r l l o p p kp l p o. v, pp p lkv o <V cs >p n p ˆ pk ˆ Ž pp p. l e opž e l Žp e l Ž k pp, array Al Ž arrayp nl k }l Ž l ~rp ˆ. lkv o <V cs >p n, e l (6) p p k p., array Bl lkv o <V cs >p e l rp 0.5m/s pk p rp p k p. Ž e l, rp p Ž arrayl pk p p k p. lk o <V ls >p n, array Bl lk e l p, v lk p p e l p v, r~rp p p sq. 6. m lkp Ž p v Boussinesq rep v rep Žp plp p q rp FUNWAVE p pn l n pk lk p p, e m r rp q p p m. p p k v m p rp ep Ž rp v v lk (rip channel) l pk rp p v ppp p pl. p r rp pk p p p plp, p re Ž l l k p r r p o Ž ( ) p p n, p o r r e q q n., pk p pk (rip channel)p q q p r p v q n p Ž. p rp lk p ep rp p lk sq l pk p p

9 84 tnë o Ëo epv, Žp pr el p Ž p p sq, tv l p Ž p e Ž lk p m p p q l pk r l., l p Ž pr d ppp qo pn l e lp Ž s p v rp sže e p p., er qp n e l d q~ pp r pk l e r l o l e Ž lk r ˆp o p rp. p pp ere 1 p o k 3 p e p n l. ee m p o p pn l p p kv erp l n, l l m p p pn l k e ml p p, ee r m l m kp er kp p. m l Š k l lp l vol p ld. y p~, ptn, pr (010). n nqp pk p. k k v, 3(1), le n (009). n nq lkr l nl (r6 e, r7 e ). o, q, o, tn (010). n pk l p. k k v, 19, Bowen, A. (1969). Rip currents 1. Theoretical investigations. J. Geophys. Res., 74(3), Bowen, A. and Inman, D. (1969). Rip currents. Laboratory and field observations. J. Geophys. Res., 74 (C3), Chen, Q., Dalrymple, R., Kirby, J., Kennedy, A. and Haller, M. (1999). Boussinesq modelling of a rip current system. J. Geophys. Res., 104, Chen, Q., Kirby, J.T., Dalrymple, R.A., Kennedy, A. and Chawla, A. (000). Boussinesq modeling of wave transformation, breaking and runup. II: d. J. Wtrwy., Port, Coast. and Ocean Eng., 16 (1), Chen, Q., Kirby, J.T., Dalrymple, R.A., Shi, F. and Thornton, E.B. (003). Boussinesq modeling of longshore current. J. of Geophys. Res., 108(C11), Choi, J., Lim, C.H., Lee, J.I. and Yoon, S.B. (009). Evolution of waves and currents over a submerged laboratory shoal. Coastal Engineering, 56, Choi, J. and Yoon, S.B. (011). Numerical simulation of nearshore circulation on field topography in a random wave environment. Coastal Engineering (in press). Dalrymple, R.A. (1975). A mechanism for rip current generation on an open coast. J. Geophys. Res., 80, Dalrymple, R.A. (1978). Rip currents and their causes. 16th international Conference of Coastal Engineering, Hamburg, Dalrymple, R.A. and Lozano, C. (1978). Wave current interaction models for rip currents. J. Geophys. Res., 83 (C1), Dronen, N., Karunarathna, H., Fredsoe, J., Sumer, B.M. and Deigaard R. (00). An experimental study of rip channel flow. Coast. Eng., 45, Haas, K., Svendsen, I., Haller, M. and Zhao, Q. (003). Quasithree-dimensional modeling of rip current systems. J. Geophys. Res., 108 (C7), 317. Haller, M., Dalrymple, R. and Svendsen, I. (00). Experimental study of nearshore dynamics on a barred beach with rip channels. J. Geophys. Res., 107 (C6), doi:10.109/001jc Hammack, J., Scheffner, N. and Segur, H. (1991). A note on the generation and narrowness of periodic rip currents. J. Geophys. Res., 96 (C3), Johnson, D. and Pattiaratchi, C. (006). Boussinesq modelling of transient rip currents. Coastal Engineering, 53, MacMahan, J.H., Reniers, A.J.H.M., Thornton, E.B. and Stanton, T.P. (004). Infragravity rip current pulsations. J. Geophys. Res., 109, C MacMahan, J.H., Reniers, A.J.H.M., Thornton, E.B. and Stanton, T.P. (004). Surf zone eddies coupled with rip current morphology. J. Geophys. Res., 109, C Noda, E.K. (1974). Wave induced nearshore circulation. J. Geophys. Res., 79 (1974), Shepard, F.P. (1936). Undertow, rip tide or rip current, Science, 1, pp Tang, E.S. and Dalrymple, R.A. (1989). Nearshore circulation: rip currents and wave groups. Advances in Coastal and Ocean Engineering. Plenum Press, New York, Wei, G., Kirby, J., Grilli, S.T. and Subraymanya, R. (1995). A fully non-linear Boussinesq model for surface waves: I. Highly non-linear, unsteady waves. J. Fluid Mech., 94, Wei, G., Kirby, J. and Sinha, A. (1999). Generation of waves in Boussinesq models using a source function method. Coast. Eng., 36, Yu, J. and Slinn, D. (003). Effects of wave-current interaction on rip currents. J. Geophys. Res., 108 (C3), 3088, doi:10.109/ 001JC o r p: 011 1o 31p r }ˆ: 011 3o 1p q rp: 011 7o 3p

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44(3)-16.fm Korean Chem. Eng. Res., Vol. 44, No. 3, June, 2006, pp. 270-276 지능형헬스케어욕조시스템개발을위한온수온도변화 r ~r l o l l e l 561-756 r rte v v 1 664-14 (2006 3o 9p r, 2006 6o 20p }ˆ) Change of the Warm Water emperature for