CHAPTER 283 Cross-shore Structure of Longshore Currents durng Duck94 Falk Feddersen 1, R.T. Guza 2, Steve Elgar 3, and T.H.C Herbers 4 Abstract The cross-shore structure of the mean longshore current on a barred beach s nvestgated wth observatons from the Duck94 feld experment. Maxma of the hourly-averaged longshore current are most frequently located ether slghtly nshore of the bar crest or near the shorelne. At low tde the longshore current maxma are located closer to the bar crest, and the current s stronger and narrower than at hgh tde. The tdal cross-shore dsplacement of the longshore current maxmum s qualtatvely consstent wth the observed radaton stress, S, although the maxmum currents are dsplaced shoreward of the maxmum S gradents at both hgh and low tde. Ths spatal lag suggests that some mechansm (such as wave rollers) delays the transfer of momentum from waves to the mean low. Bathymetrc longshore nhomogenetes may also affect the cross-shore structure of the longshore current. Introducton Selected observatons from the DELILAH feld experment at Duck N.C. suggest that the maxmum of the mean longshore current, v, occurs between the crest of the sand bar and the trough between the bar and the shorelne (Fgures 8-11 of Church and Thornton, (1993)), and that longshore current varablty s coherent wth the approxmately 1 m semdurnal tdal fluctuatons n water level (Thornton and Km, 1993). However, the generalty of these results over the wde range of wave (Long, 1996), wnd, and bathymetrc (e.g. pronounced sandbars and alongshore nhomogenetes (Lppmann and Holman, 1990; Gallagher, 1996)) condtons observed at Duck s unknown. Here the cross-shore structure of v s further explored wth observatons from the Duck94 feld experment. 1 2 Graduate Student, Scrpps Insttuton of Oceanography, 0209, La Jolla Ca,92037-0209, falk@coast.ucsd.edu Professor, Scrpps Insttuton of Oceanography, 0209, La Jolla Ca, 92037-0209, rguza@ucsd.edu 3 Professor, Washngton State Unversty, Pullman Wa, 99164-2752, elgar@eecs.wsu.edu 4 Assstant Professor, Naval Postgraduate School, Monterey Ca, 93943, heroers@zee.oc.nps.navy.ml 3666
CROSS-SHORE STRUCTURE 3667 Duck94 Observatons The experment ste s located on a long straght barrer sland exposed to the Atlantc Ocean. Drectonal propertes of sea and swell (ncludng the wave radaton stresses, S ) were estmated wth data from a 2-dmensonal array of 15 bottom-pressure sensors located n 8 m water depth operated by the Feld Research Faclty (FRF) of the U.S. Army Corps of Engneers (Long, 1996). Longshore currents, wave-nduced bottom pressures, and the locaton of the sea floor were observed wth colocated bdrectonal electromagnetc current meters, pressure sensors, and sonar altmeters (Gallagher et al., 1996) deployed on a cross-shore transect extendng 750 m from the shorelne to 8 m water depth (Fgure 1). The sensors were sampled at 2 Hz for approxmately two months. At each pressure sensor-current meter par, hourly values of S were crudely estmated usng lnear theory. 0 100 200 300 400 Cross-Shore Poston (m) Fgure 1. The cross-shore locaton of current meters (A), and measured bathymetry relatve to sea level on August 25 (sold lne) and October 26 (dashed lne). An addtonal current meter at cross-shore locaton 749 m n 8 m water depth s not shown.
3668 COASTAL ENGINEERING 1996 Condtons durng Duck94 are shown n Fgure 2. In 8 m water depth, the sgnfcant wave heght (H.) ranged between 0.2 m to 4 m and the mean wave angle between ±50, so that the total ( e.g. frequency-ntegrated ) ncdent wave radaton stress S Ip (where p s the water densty) n 8 m depth ranged from -0.7 to 0.5 m 3 /s 2 (fgures 2a-c). The mean (e.g. centrodal) wave frequency ranged from about 0.08 to 0.2 Hz (not shown). Maxmum mean longshore currents (n each hour-long record, v max ) ranged from 0.1 to 1.4 m/s (Fgure 2d). The bar crest, orgnally located 80 m from the mean shorelne, gradually mgrated 120 m offshore (Fgure 2e, after Gallagher, 1996). Fluctuatons n mean water level were about 1 m at sprng tde. The slope of the beach foreshore s about 1/10 (Fgure 1), so tdal fuctuatons n the locaton of the mean shorelne are about 10 m. Tdal currents n depths less than 8 m are less than 0.03 m/s (S. Lentz, personal communcaton 1996). Results The sand bar s expected to strongly effect the longshore current, so a normalzed cross-shore coordnate s defned as, where x s the cross-shore coordnate, x. s the cross-shore locaton of the bar bar crest, and x 02 s the cross-shore locaton of the most nearshore sensor uv02. The dstance from sensor uv02 to the mean shorelne was typcally less than 10 m. Depths at uv02 (x'= 0) ranged from about 0.2 to 1.2 m. In ths coordnate system, the bar crest s always located at x'= 1, but the locaton of the trough s not constant because of varablty n the shape of the cross-shore seafloor profle (e.g. Fgure 1). The locaton of the longshore current maxmum, v max, s broadly dstrbuted and roughly bmodal n the normalzed coordnate system (1) (Fgure 3, after Gallagher, 1996 ). Maxma most often occur ether slghtly nshore of the bar crest (0.65 s. x'sl.2) or near the shorelne (x'< 0.3). Rarely does 7^ occur seaward of the bar crest, even when large waves were breakng well seaward of the bar (x' > 2). The few maxma located well seaward of the bar crest typcally are weak (.v mn ~ 0.3 - m/s) and approxmately correspond to tmes of strong buoyancy drven flows (Renne and Larger, personal communcaton 1996). The stronger longshore currents (v^ > 0.8 m/s) are assocated wth large offshore S (Fgures 2c and 2d) and occur near the bar crest (0.65 < JC'<1.2). Weaker maxma (0.25-0.7 m/s) occur typcally near the shorelne (0 < *'<0.3) or near the bar crest, wth few maxma n the regon n between. Many of the larger v ma ( - 0.6 m/s) n the regon 0 < x' < 0.3 occur after the sandbar mgrated far offshore n md-october (Fgure 2e).
CROSS-SHORE STRUCTURE 3669 l x (0 E > 1.5 1.0- o.5 -; -.3 ft ; r t '. ;' '". t J!! (d) V >= : t -^ o 250,c I 200 o.n CO 150 E o 100 LL 0 O 50 C & w b 10 20 30 40 Days From Sept 1 (e) 50 60 Fgure 2. Hourly values of (a) sgnfcant wave heght H s n 8 m depth (b) devaton of the mean ncdent wave angle from shore normal (postve angles correspond to waves from the northern quadrant) (c) S Ip n 8 m depth (d) maxmum hour-averaged longshore current v mu (e) bar crest locaton (dashed) and the cross-shore locaton of v mm. v max s plotted only f there were at least fve actve current meters and v mu s 0.25 m/s. Out of 1464 possble values, 572 hourly maxma pass these crtera. The few maxma occurrng more than 250 m from shore are not shown n (e).
3670 COASTAL ENGINEERING 1996 1.5 5". 1 o.5 > :4Y : -I*'' 2 3 4 5 Normalzed Locaton of Vmax (a) 1.2 1-42 0.8 E, «E 0.6 > 0.2 1 : : ;;H f I : 'Pt*. I* : * 0.2 0.6 0.8 1 1.2 1.4 Normalzed Locaton of Vmax 1.6 1.8 (b) Fgure 3. Magntude of the maxmum of the hourly averaged longshore current n normalzed cross-shore coordnate, x' (1). the upper panel shows the entre cross-shore regon. The regon 0 < x < 2 s enlarged n the lower panel.
CROSS-SHORE STRUCTURE 3671 Tdes domnate the varablty of the local water depth, and thus affect wave shoalng, breakng, and the longshore current. When v max s near the bar crest (0.65 <. x'sl.2), the locaton of v max s tdally modulated (Fgure 4). At hgh tde, v nua s rarely located seaward of x'= 0.8, whereas at low tde v s near x'= 1. Tdal effects on the locaton of v m are smaller when v, s max max max near the shorelne (x'< 0.3). Tdal dfferences n the cross-shore structure of v are further llustrated n Fgure 5. The current profles at low tde exhbt a number of smlar features; v max s located close to x'= 1, and the current falls off rapdly shoreward of the maxmum. Close to the beach, v s approxmately 1/4 of v max In contrast, at hgh tde v s farther shoreward (around x'= 0.7, consstent wth Fgure 4) and weaker. The current profle s broader, and near the shorelne v s about 1/2-2/3 of v. The observed v tdal varaton s consstent wth max the phase relatonshps between v and sea-level at tdal frequences found by Thornton and Km (1993). Wave-breakng nduced gradents n sgnfcant wave heghts are greater durng low tde than hgh tde ( 0.8 < x'< 1.5 n Fgure 6), resultng n smaller waves shoreward of the sandbar at low tde (H sjg ~ 0.7 m) relatve to hgh tde (H ~ 1.0 m). The dfferences wthn the low (Fgure 5a) and hgh (Fgure 5b) tde crossshore structure of v are prmarly owng to dfferences n the condtons over the two days spanned by the observatons. The bar was relatvely statonary movng 7 m, H t n 8 m depth ranged from 1 to 2 m (Fgure 6), the mean ncdent wave angle from 15 to 45 degrees, and SJp from 0.2 to 0.5 m 3 /s 2. Smlar qualtatve features n the tdal varaton of v were observed at other tmes when the longshore current was strong for several tdal cycles (e.g. Sept 2-5 and Oct 10-16). The modeled tdal varaton of H s and v, for waves and bathymetry representatve of Fgures 5 and 6, are shown n Fgure 7. The wave heghts are modeled usng Church and Thornton (1993), wth free model parameters selected to best ft the observed wave heghts. The qualtatve features of the observed H s. dstrbutons (Fgure 6) are reproduced by the model (Fgure 7a), except close to the shorelne. The longshore current predctons are made usng the modeled H varaton and observed (n 8 m depth) drectonal wave propertes n the Thornton and Guza (1986) longshore current model. A drag coeffcent of 0.015 results n smlar magntudes for the modeled (Fgure 7b) and observed (Fgure 5) currents. Smlar to prevous results (e.g. Church and Thornton, 1993 and others), the modeled longshore currents have the famlar problem of predctng a flow wth two maxma, one seaward of the bar crest and one near the shorelne, wth no flow n the bar trough. The modeled low and hgh tde maxma occur at A:'=1.25 and JC'=1.1 respectvely, farther offshore than observed (Fgure 5). In physcal unts, the dsplacement of the maxmum s about 30 m.
3672 COASTAL ENGINEERING 1996 0.2 0.6 0.8 1 1.2 1.4 Normalzed Locaton of Vmax 1.6 1.8 Fgure 4. Locaton and magntude of v mm, observed wthn about 1.5 hours of tdal extrema n normalzed cross-shore coordnate. There are 157 low tde (+) and 108 hgh tde (o) values. Two commonly gven reasons (among many) for the model falure are: (1) There may be a spatal lag n the transfer of momentum from the waves to the mean flow, possbly assocated wth wave rollers (Svendsen, 1984; Dally and Brown, 1995; and many others). (2) Longshore nhomogenetes n the bathymetry and wave feld may result n nonlnear terms or longshore pressure gradent terms n the longshore momentum equaton (e.g. Putrevu et al., 1995). Some of the observatons are consstent wth the lag hypothess, and there are other examples where alongshore nhomogenetes are lkely domnant. The cross-shore varaton of S for the successve low and hgh tde cases (Fgure 5 and 6) s shown n Fgure 8. At low tde, strong S^ gradents are observed seaward of the bar (1 s x'^1.5, Fgure 8a), whereas shoreward of the bar crest, S s relatvely constant. The shoreward dsplacement of the observed longshore current maxma (Fgure 5a) relatve to strong S gradents (Fgure 8a) s consstent wth a spatal lag n the transfer of momentum to the mean longshore current. At hgh tde, the regon of strong S x gradents s
CROSS-SHORE STRUCTURE 3673 slghtly seaward of the bar crest (0.9. JJ'^1.25, Fgure 8b), and seaward of the locaton of v max (x'~0.7) agan ndcatng a spatal lag n the transfer of momentum to the mean flow. The tdal dfferences n the cross-shore structure of v (.e. the the broadng of Vat hgh tde, Fgure 5) may be related to tdal varatons n the laggng mechansm. 1.2 - A. 1.0 ^ 0.8 I -> 0.6 / ft- * \ * : v fr r\ :/ ty. > :A Low Tde 0.2 SK- / V ^U '_' *- SIP*:- - - - -;_ zt: (a) I 1 1 1.2 1.0 Hgh Tde: > 0.6 :...m.. *...: : / *»...",.%'.*-.-*\^ ; 0.2 / ':"'* v..^..^...^.^ w v W *--* * ^ : ^*- X : s " ~*~ - * - *'~ -*-"- 0.5 1.0 1.5 2 2.5 Normalzed Cross shore Coordnate - -.r -^ * (b) 1 3.0 Fgure 5. Mean longshore currents n the normalzed cross-shore coordnate x (1) durng October 10 and 11. (a) 3 low tdes (b) 4 hgh tdes.
3674 COASTAL ENGINEERING 1996 2.0 1-1- -" 1 '1 " 1.8-1.6-1.4 1.2 l.cn I 0.8 0.6 s s? : *" : 0.2 - :.,./....<... w jt -T&, -3K-. m _y?.^jn-.r. W *- ' --* 'm' **** ' f- 1 ' ' ' - ' ^ '^_' '. *W,*..* ' -_-* -*r--~-- 4. -*- ; Low Tde : 1 1 : (a) v ' 2.0... 1.8 1.6-1.4-1.2. o> 1.0' f:-^m5r..^5. "^^ ; ; /<- -J7-. : / * " _ - k.^-r-.- _.* _.- - -*-..-*.-- X 0.8h 0.6 ; Hgh Tde 0.2 0.5 1.0 1.5 2.0 2.5 Normalzed Cross Shore Coordnate 3.0 (b) Fgure 6. Sgnfcant wave heght n the normalzed cross-shore coordnate x (1) durng October 10 and 11. (a) 3 low tdes (b) 4 hgh tdes.
CROSS-SHORE STRUCTURE 3675 2.0 X 1.5 1.0 0.5 (a) 0.5 1 1.5 2 2.5 Normalzed Cross shore Coordnate Fgure 7. Modeled (a) sgnfcant wave heghts (b) mean longshore currents (c) model bathymetry n normalzed cross-shore coordnate (1). Sold curves represent low tde and dashed curves are hgh tde. The ncdent wave parameters are representatve of condtons n Fgure 5 and 6: H. = 1.5 m and 0 = 25. sg An example of longshore currents lkely affected by longshore bathymetrc nhomogenetes s shown n Fgure 9. Although the waves were energetc (H sl = 3 m n 8 m depth), they were nearly normally ncdent (the mean ncdent wave angle n 8 m depth was 2 ) and thus S^ n 8 m depth was small ( about 0.1 of S wth less energetc but more oblquely ncdent waves n Fgure 8). The observatons suggest that S and S gradents are small everywhere (Fgure 9b), and that wave breakng began (x >200 m, Fgure 9a) far
3676 COASTAL ENGINEERING 1996 " - T - 1 0.35 0.3 Low Tde 22 CO, 0.2 OT 0.15 s*~ - _ r- - * 0.1 0.05 sr-- " ^ 0 j«=# s^ 1 (a) 0.35 0.3 Hgh Tde : -* ceo-25 J2 CO E, 0.2 CO 0.15 0.1 * " " - * - - * /V~~ ~* * " Aj, %-" SKr..". " - * - *-- ^^Tff -* : -*- - - - -* 0.05 0.5 1.0 1.5 2.0 2.5 Normalzed Cross-shore Coordnate 3.0 (b) Fgure 8. S Ip for the cases (October 10 and 11) shown n Fgures 5 and 6 n the normalzed cross-shore coordnate*' (1). (a) low tde (b) hgh tde. The accuracy of S^ estmates s lmted because of uncertantes n current meter response and orentaton, and because errors n lnear theory may be sgnfcant n the surfzone. Only two low tde profles are shown because of unavalable data.
CROSS-SHORE STRUCTURE 3677 offshore of the locaton of v max (x» 25 m, Fgure 9c). The observed longshore current jet (Fgure 9c) near the shorelne s nconsstent wth model predctons (based on Thornton and Guza, 1986) of neglgbly small currents (not shown). Tme elapsed vdeo mages (R.A. Holman, personal communcaton, 1996) suggest that the bathymetry was longshore nhomogeneous. Three dmensonal bathymetrc surveys were not avalable because of the stormy condtons, however, the frst post-storm survey (October 20) dd reveal strong longshore nhomogenety. Sancho et al. (1996) demonstrated that ths nhomogeneous bathymetry can cause pressure gradents and nonlnear terms to become mportant n the longshore momentum balance. I I I I E 2 "vt 1 - *--*-*--* -*--*- *'*'*''.: (a) 0.05 * to E, CO -0.05 *- A..j*r. * :.*..--.*., (b) CO E. > 0.2 H!! I ~--x " :w (c) 1 1 1 Q- Q -4 "~\ 1 1 1 1 (d) 50 100 150 200 250 300 350 Dstance From Shorelne (m) Fgure 9. Observed cross-shore varaton of (a) sgnfcant wave heght (b) S Ip (c) longshore current v (d) bathymetry on 0500 October 10.
3678 COASTAL ENGINEERING 1996 Conclusons Observatons spannng a wde range of bathymetrc and wave condtons show that the probablty dstrbuton of cross-shore locaton of longshore current maxma s bmodal. Maxma typcally occur near the crest of the sand bar or near the shorelne (Fgure 3). At both hgh and low tde, the observed currents (Fgure 5) are qualtatvely consstent wth the observed S (Fgure 8), although wth a spatal lag, perhaps assocated wth wave rollers. The 1 m tdal fluctuatons n sea level affect the cross-shore structure of the longshore current (Fgure 4). At low tde, the current jet s stronger, narrower, and located closer to the bar crest than at hgh tde (Fgure 5). The reason for the tdal changes n the longshore current structure s unknown, however tdal changes n the wave forcng are surely mportant. Clearly more quanttatve work s necessary. The observed varaton n the cross-shore structure of the longshore current across a tdal cycle s a robust feature (see also Fgure 12 of Thornton and Km, (1993)), and one step n the verfcaton of a roller model would be to reproduce qualtatvely the observed tdal varaton of the longshore current. Fnally, although the magntude of the effects of longshore bathymetrc nhomogenetes s not known, there are cases where they domnate the longshore current (Fgure 9). Acknowledgments The array of current meters, sonar altmeters, and pressure sensors was deployed and mantaned by staff from the Center for Coastal Studes. Brtt Raubenhemer and Edth Gallagher helped collect the data. Excellent logstcal support was provded by the FRF. We thank Edth Gallagher for provdng sonar-altmeter based depth profles and Rob Holman for provdng the vdeo mages. Ths research was supported by ONR and the NSF CoOP program. Falk Feddersen receved tranee support from the Natonal Sea Grant College Program, NOAA, U.S. Department of Commerce. References Church, J.C. and E.B. Thornton, Effects of breakng wave nduced turbulence wthn a longshore current model, Coastal Eng., 20, 1-28, 1993. Dally, W.R. and C.A. Brown, A modelng nvestgaton of the breakng wave roller wth applcaton to cross-shore currents, J. Geophys. Res., 100, 24,873-24,883,1995. Gallagher, E.L., Observaton of sea oor evoluton on a natural barred beach. SIO PhD thess, 62pp. 1996. Gallagher, E.L., W. Boyd, S. Elgar, R.T. Guza, B. Woodward, Performance of a sonc altmeter n the nearshore, Marne Geology, 133, 3, 241-248, 1996.
CROSS-SHORE STRUCTURE 3679 Lppmann, T.C., and R.A. Holman, The spatal and temporal varablty of sand bar morphology,/. Geophys. Res., 95, 11,575-11,590,1990. Long, C.E., Index and bulk parameters for frequency-drecton spectra measured at CERC Feld Research Faclty, June 1994 to August 1995, Mscellaneous Paper CERC-96-6, U.S. Army Engneer Waterways Experment Staton, Vcksburg, MS, 1996. Putrevu, U., J. Oltman-Shay, and I.A. Svendsen, Effect of alongshore nonunformtes on longshore current predctons, /. Geophys. Res., 100, 16,119-16,130, 1995. Sancho, F.E., LA. Svendsen, A.R. Van Dongeren, and U. Putrevu, Longshore nonunformtes of nearshore currents, Coastal Dynamcs 1995, 425-436, 1996. Svendsen, LA., Wave heghts and set-up n a surf zone, Coastal Eng., 8, 303-329, 1984. Thornton, E.B. and R.T. Guza, Surf zone longshore currents and random waves: feld data and models, J. Phys. Oceanogr., 16, 1165-1178,1986. Thornton, E.B., and C.S. Km, Longshore current and wave heght modulaton at tdal frequency nsde the surf zone, /. Geophys. Res., 98, 16,509-16,519, 1993.