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. 007 008 1, 009 010 4 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, 411-71, Korea. jwchoi@kict.re.kr) *** k o (Dept. of Civil & Environ. 171 Sa-3-dong Sangnok-gu, Ansan, 46-791, Korea.) *** k (Corresponding Author: Sung Bum Yoon, Dept. of Civil & Environ. 171 Sa-3-dong Sangnok-gu, Ansan, 46-791, Korea. sbyoon@hanyang.ac.kr) 76
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 + ( ) = 0 1 + 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 ) 1 + -- 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)
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. n p llv qo om opž p Fig. 3l re m. qo o Ž eˆ 60 p p p, opž 60 300 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. 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 60 300 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, 95 300 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. 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).
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).
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
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