Research Facility, Duck, North Carolina, USA, 3 WaveForce Technologies LLC, Kill Devil Hills, North Carolina, USA

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1 PUBLICTIONS RESERCH RTICLE Key Points: Novel observations of intense hurricane wave conditions in the nearshore environment are presented and indicate high rates of momentum longshore currents shear against wind-driven shelf currents for a local hurricane, generating intense surf zone eddies Waves generate alongshore, crossshore, and rotational flows with strong horizontal mixing and crossshore advection in the surf zone Correspondence to: R. P. Mulligan, mulligar@queensu.ca Citation: Mulligan, R. P., and J. L. Hanson (6), longshore momentum transfer to the nearshore zone from energetic ocean waves generated by passing hurricanes, J. Geophys. Res. Oceans,, , doi:./ 6JC76. Received FEB 6 ccepted 5 MY 6 ccepted article online 8 MY 6 Published online 8 JUN 6 VC 6. merican Geophysical Union. ll Rights Reserved. longshore momentum transfer to the nearshore zone from energetic ocean waves generated by passing hurricanes Ryan P. Mulligan and Jeffrey L. Hanson,3 epartment of Civil Engineering, Queen s University, Kingston, Ontario, Canada, U.S. rmy Corps of Engineers, Field Research Facility, uck, North Carolina, US, 3 WaveForce Technologies LLC, Kill evil Hills, North Carolina, US bstract Wave and current measurements from a cross-shore array of nearshore sensors in uck, NC, are used to elucidate the balance of alongshore momentum under energetic wave conditions with wide surf zones, generated by passing hurricanes that are close to and far from to the coast. The observations indicate that a distant storm (Hurricane Bill, 9) with large waves has low variability in directional wave characteristics resulting in alongshore currents that are driven mainly by the changes in wave energy. storm close to the coast (Hurricane Earl, ), with strong local wind stress and combined sea and swell components in wave energy spectra, has high variability in wave direction and wave period that influence wave breaking and nearshore circulation as the storm passes. uring both large wave events, the horizontal current shear is strong and radiation stress gradients, bottom stress, wind stress, horizontal mixing, and cross-shore advection contribute to alongshore momentum at different spatial locations across the nearshore region. Horizontal mixing during Hurricane Earl, estimated from rotational velocities, was particularly strong suggesting that intense eddies were generated by the high horizontal shear from opposing winddriven and wave-driven currents. The results provide insight into the cross-shore distribution of the alongshore current and the connection between flows inside and outside the surf zone during major storms, indicating that the current shear and mixing at the interface between the surf zone and shallow inner shelf is strongly dependent on the distance from the storm center to the coast.. Introduction The east coast of North merica is frequently struck by hurricanes [Muller and Stone, ] with strong surface winds that generate large surface waves, high storm surges, and strong currents. These storm conditions endanger human lives and can have a devastating effect on the economy of the coastal environment, as demonstrated by recent events like Hurricane Katrina in 5 and Hurricane Sandy in that resulted in high death tolls and billions of dollars in property damage. The frequency and intensity of tropical storms, the deadliest and costliest being major hurricanes [Goldenberg et al., ], have pronounced interannual variability in the North tlantic Ocean. Future climate warming will likely cause the globally averaged intensity of tropical cyclones to shift toward stronger storms [Knutson et al., ] and a longer period for storm formation each year, making observing and understanding storm-driven physical processes critical to our ability to determine and minimize the risks associated with coastal hazards. The waves generated by a hurricane evolve as storm passes from narrow-banded unimodal swell to a broadbanded bimodal spectral distribution (swell and wind sea), and change to swell in the wake and far from the storm [Lenain and Melville, 4]. The energy distributed into the swell and wind sea bands of hurricane wave spectra are related to the distance from the storm to given observation site [Hu and Chen, ] and therefore, depending on the distance of a storm to the coast, nearshore areas can receive very different ocean wave conditions. Hurricanes that are close to a coast have strong local winds that generate a mixed sea and swell, and rapid directional changes in winds and waves create a more chaotic sea surface that extends into the nearshore zone. Waves from a tropical cyclone that enter a coastal bay [Mulligan et al., 8] have sea and swell waves that can be nearly equally important components of the wave energy spectrum, with swell directionally constrained by the shape of the coast and wind-generated sea that changes direction rapidly. Storm waves deliver high levels of energy to the coast that break with high dissipation rates in the nearshore zone [Elgaretal., 997], generating longshore currents and driving coastal circulation. These currents provide a MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 478

2 .4. y x F E C B 8m 4 37 o N 36 o N. FRF Pier 4 W o N o N 3 34 o N 3 77 o W 3 76 o W 3 75 o W o W Figure. Location map of uck, NC (inset), six acoustic sensor stations F north of the FRF pier, the 8 m array of pressure sensors (8 m), meteorological sensor location W at the end of the pier, and rotated cross-shore (x) and alongshore (y) coordinate system. The bathymetry shown (m, NV88 datum) was surveyed on November. means of transport for sediments, effluents, or any other suspended materials discharged into coastal water, and can induce morphological changes [e.g., Hansen and Barnard, ]. Longshore currents develop in response to the wave momentum flux generated by wave breaking in shallow water [Bowen, 969; Longuet-Higgins, 97], drive horizontal mixing [Svendsen and Putrevu, 994], and generate current shear [Bowen and Holman, 989; Ozkan-Haller and Li, 3]. The mean velocity distribution of these wave-driven currents depends on the incident wave conditions, bottom friction [Feddersen et al., 3], morphological features that influence breaking [Reniers and Battjes, 997], and momentum from other sources such as wind [Feddersen et al., 998] and geostrophic circulation on the continental shelf [Lentz et al., 999]. However, wave breaking and momentum transfer between waves and currents are complex phenomena that are still not well understood. In particular, the outer edge of the surf zone is a dynamic region where wave-driven currents interact with wind-driven flows. The interaction of currents in this zone results in an unknown balance between several forces that generate strong shear, turbulence, and mixing by eddies at a range of scales that are important drivers of fluid and sediment exchange. In this paper, we describe detailed wave and current measurements across a m wide transect in the nearshore zone during hurricane conditions. The focus of the study is on two energetic ocean wave events generated by passing hurricanes, that differ significantly by the distances from the shoreline to the storm centers resulting in different wind and wave conditions at the coast. We hypothesize that the relative differences between the characteristics of wind and swell components controls current shear and consequently momentum exchange in the complex region around the break point where the surf zone interacts with the shallow shelf. This is tested by calculating the temporal and cross-shore spatial variability of flows in the surf zone to determine the sources, magnitudes, and rates of alongshore momentum transferred from the waves to the nearshore region during hurricanes.. Observations.. Coastal Observing System n observing system for waves and currents spans the nearshore region at the U.S. rmy Corps of Engineers Field Research Facility (FRF) at the sandy beach at uck, North Carolina (NC), shown in Figure. This consists MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 479

3 z (m) before Bill (988) after Bill (996) before Earl (78) after Earl (96) x (m) Figure. Bathymetric elevation profiles along the sensor transect before and after each storm event, with respect to the NV88 vertical datum and the local FRF horizontal coordinate system. of six acoustic wave and current sensors at sites F (four Nortek WCs at outer sites -; two Nortek quadopp Profilers at inner sites E-F) that are cabled to shore along the 56 m long FRF pier and are located in nominal water depths of, 4, 5, 7, 9, and m [Hanson et al., 9]. In the local FRF coordinate system where x, y are cross-shore and alongshore positions, the mean tide shoreline in located at x 5 m and the sensors are located at x 5 33, 375, 446, 66, 98, and 33 m. The WCs operate at an acoustic frequency of. MHz, measure current profiles with a vertical resolution of.5 m and sample the currents over min ensembles, four times per hour. The quadopps operate at an acoustic frequency of. MHz, measure current profiles with a vertical resolution of.5 m and sample the currents over min ensembles, four times per hour. Bulk wave statistics are computed from the directional spectra, estimated using the Maximum Likelihood Method from the pressure ( Hz), acoustic surface tracking (4 Hz), and velocity measurements ( Hz) at each sensor over 7 min wave bursts every hour. In addition, directional wave spectra are estimated from the 8 m array of pressure sensors located at a nominal depth of 8 m (Figure ) using the Iterative Maximum Likelihood Method [Long and Oltman-Shay, 99]. Mean hourly wind data are observed using an RM Young marine wind monitor located at the end of the pier (Figure, site W), with resolution of. ms and 8. Bathymetry is surveyed using the LRC (Lighter mphibious Resupply Cargo), at an average horizontal resolution of. m (Figure )... Storm Events Nearshore observations from two storms, namely Hurricane Bill and Hurricane Earl which occurred in the North tlantic Ocean in ugust 9 and September respectively, are compared in this study. These storm events were similar in intensity: both were category two hurricanes on the Saffir-Simpson Hurricane Wind Scale with maximum sustained winds over 43 ms and both storms were similar in size (55 75 km radius to maximum winds) as they passed offshore of NC [Landsea and Franklin, 3; Landsea et al., 5]. However, the storms moved northward at very different distances from the shoreline with the eye of Hurricane Bill passing 6 km from shore and the eye of Hurricane Earl occurring within km of the coast. s a result, the wind and wave conditions were very different at the FRF. uring these storms, observations were made at four sensor sites ( ) for Hurricane Bill and at all six sensor sites ( F) for Hurricane Earl (sensors at E, F were installed between these storms in ugust ). Bathymetric profiles before and after each event are shown in Figure, and indicate that the storms induced major changes to nearshore morphology. However, the morphological changes are mainly associated with the inner bar location within 3 m from the shoreline in mean water depths less than 4 m, thus influencing breaking and circulation in the inner surf and swash zones. The focus of the present study is on data collected across the surf zone and outside it in mean depths ranging from 5 to m (Hurricane Bill) and to m (Hurricane Earl) where the morphology change is minimal. Sea surface elevation spectra are shown in Figures 3a and 3b at the maximum energy conditions for each storm, where time is referenced to the decimal day of the year (Y). The directional spectra indicate major low frequency (.5. Hz) energy peaks (swell) with very different higher frequency (..3 Hz) characteristics. Hurricane Bill had greater energy in a narrower frequency and directional band, while Hurricane Earl was broad-banded with high directional spreading. The frequency spectra (Figures 3c and 3d) show evidence of nonlinear energy transfer (increase in first, second, and higher harmonics particularly for Hurricane Bill), wave breaking (energy dissipation) and wind sea (f.5 Hz for Hurricane Earl). MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 48

4 a) b) E(m /Hz/deg) 8 5 E(m /Hz) c) : H s =3.7m B: H =4m s C: H s =3.6m : H s =3.3m E(m /Hz) d) : H s =4.7m B: H s =4.4m C: H s =3.9m : H =3.4m s E: H s =.8m F: H =.m s f(hz) f(hz) Figure 3. Sea surface elevation spectra for two events: directional energy spectra measured by the WC at site for the maximum energy conditions for (a) Hurricane Bill (Y 34.9, 9), and (b) Hurricane Earl (Y 46.38, ). irections are in degrees relative to true north and frequency is given by the radial coordinate. Frequency energy spectra for the maximum energy conditions at sites shown in Figure for (c) Hurricane Bill, and (d) Hurricane Earl. The wind and wave time-series for these storms are indicated in Figure 4. Hurricane Bill had light local winds (up to 6 ms ), longer peak wave periods (T p ) up to 7 s and smaller significant wave heights (H s )upto 3.7 m observed at site. Hurricane Earl had very strong winds (up to 5 ms ), shorter T p (5 s that reduced to 8 s as the storm passed), and higher H s up to 4.7 m at site. The mean wave direction a (with respect to offshore normal) remained steady from 8 to 38 at site throughout Bill; while it rapidly shifted from 48 to 8 at during the passage of Earl (Figure 4h). Observed water level elevations at site are shown in Figure 5, including both the tide and storm surge. Residual water levels, determined by applying a low-pass butterworth filter to the observed pressure signal, indicate that the storm surge was much greater for Hurricane Earl (.3 m) than for Hurricane Bill (<.5 m). This is in general agreement with previous studies, since the distance from the hurricane center to the coast strongly influences the storm surge [Irish et al., 8]. The velocity observations (Figure 5) indicate near-uniform vertical profiles (not shown) but very strong differences in horizontal magnitude for Bill and both magnitude and direction for Earl between the sensors sites across the transect. Bill generated a very strong depth-averaged alongshore current up to. and.8 ms at C and, respectively, with very weak flow (.5 ms ) at and B (Figure 5b) suggesting that the limit of the surf zone and alongshore current extended to between sites B and C. Earl had northward depthaveraged alongshore currents up to.5 and. ms at C and respectively (Figure 5e) that were aligned with the wave direction (with stronger flows up to. and.4 ms in the inner surf zone at E and F, respectively). uring Earl opposing southward alongshore flow of. and.8 ms was measured at the outer sites and B that were aligned with the wind direction. Observations from both events indicate strong gradients in wave energy and depth-averaged alongshore current velocity ( ms changes in v over only several hundred meters), suggesting high horizontal shear that can drive mixing in the outer surf zone. The time-averaged cross-shore velocity (Figures 5c and 5f) reached.3.4 ms in the offshore direction at MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 48

5 U w (ms ) H s (m) a) Hurricane Bill U V (U +V ) / b) c) B C e) Hurricane Earl U V (U +V ) / f) g) B C E F T p (s) d) h) α ( o ) Y, Y, Figure 4. Nearshore wind and wave observations from two hurricane wave events: (a, e) wind speed and rotated wind velocity components; (b,f) significant wave height; (c, g) peak period; and (d,h) wave angle (relative to offshore normal) for (left) Hurricane Bill and (right) Hurricane Earl at the stations shown in Figure. The shaded region denotes H s >. m. several sites for both storms, suggesting advection across the surf zone. The cross-shore velocities indicate an offshore mass flux that could be caused by a rip-current; however, a stable rip at this location over the duration of both storm events is unlikely. More likely is a balance between the onshore mass flux above the trough elevation (Stokes drift) and the offshore mass flux below the trough elevation (undertow) that is measured by the sensors (discussed further in section 3.4). The wave and current observations were spatially interpolated in the x-direction to illustrate the time evolution of cross-shore variability of significant wave heights (H s ) and wave energy gradients (dec g cos a=dx) over the 7 min wave burst periods, and of alongshore velocity (v) and horizontal shear of the alongshore current (dv/dx) over the min velocity ensemble periods. These are shown in Figure 6 for both storm events. The cross-shore extent of the decrease in wave energy flux and increase in alongshore current magnitude toward shore indicates wave breaking. The surf zone width determined by high-image intensity from rgus camera data [Mulligan et al., ] also indicates breaking. The alongshore current in the inner surf zone is directed northward for both events, extending over 6 m from shore at the time corresponding to the peak significant wave height. Southward wind-driven currents outside the surf zone during Hurricane Earl oppose the alongshore current (Figure 6g). Even though Hurricane Bill has higher current speeds, high horizontal shear of the alongshore current is similar for both events (Figures 6d and 6h) and extends over m from shore. 3. Evaluation of Momentum Terms For the case of vertically averaged flow (u, v) in the horizontal (x, y) plane over the total depth h (mean water depth plus the time-varying surface water level, g), the fluid momentum equation in the y-direction with wave forcing included can be written as: MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 48

6 a) Hurricane Bill observed residual d) Hurricane Earl observed residual η (m) u (ms ) v (ms ) b) c) Y, 9 B C B C e) f) Y, B C E F B C E F Figure 5. Water level and current observations from two hurricane wave events: (a, d) mean observed and residual water levels (site ); (b, e) depth-averaged rotated alongshore velocity (northward flow indicated by v); and (c, f) cross-shore current velocity (eastward flow is indicated by u) for (left) Hurricane Bill and (right) Hurricane Earl at the stations shown in Fig.. The shaded region denotes H s @x sw y qh sb y qh sa y qh v () where g is gravitational acceleration, q is fluid density, and t is time. The terms on the left-hand side represent the local fluid acceleration and nonlinear advection. The forcing terms, on the right-hand side of equation () include the pressure gradient due to changes in water level g, wave-induced radiation stress gradients (s w ), bottom friction (s b ), atmospheric wind stress (s a ), and mixing parameterized by a horizontal eddy viscosity or lateral mixing coefficient m. In this study, we investigate the depth-averaged alongshore momentum balance and evaluate each term individually using the observations to examine cross-shore (x-direction) spatial variability in alongshore (ydirection) flow. We make the assumption that that gradients in the alongshore direction are small [Feddersen and Guza, 3]. This is further supported by recent work by Wilson et al. [3], who showed that even slight alongshore variations in bathymetry causes alongshore-nonuniform wave forcing, but advection dampens alongshore variability and results in more alongshore uniform circulation. The rearranged alongshore momentum equation then reduces to: 5 sw y qh sb y qh sa y qh @x () By considering the alongshore current v(x) as a continuous function with cross-shore distance x, spatial derivatives and second derivatives can be approximated by a central difference technique using the observations on each side of x at distances x / and x vðxx =Þvðxx ðx x Þ= (3) erivatives of v(x) can be evaluated by approximating the differential equation using the central differences in observations between the sensor locations, as long as x =; x = are small relative to the total distance. The distances between sensor locations in the cross-shore array are 7 3 m and the surf zone MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 483

7 Figure 6. Cross-shore (x) time evolution of the significant wave height (H S ), wave energy gradient (dec g cos a=dx), alongshore current velocity (v), and alongshore current shear (dv/dx), spatially interpolated from observations for two storm events: (a d) Hurricane Bill; (e h) Hurricane Earl. Vertical lines indicate the sensor locations and time is referenced to 5 daysfor Y (9) in Figures 6a 6d, and 5 days for Y () in Figures 6e 6h. Note that sensors - were deployed during Bill and all sensors -F were deployed during Earl. width is typically 5 m during large, long period, wave events as determined by camera image intensity observations. The distances between adjacent sensors range from 5 to 5% of the surf zone width, indicating that that the central difference approximation is useful over these length scales to evaluate the momentum terms for major storm wave events. 3.. Radiation Stress Gradients Wave momentum flux is described by the gradients in radiation stress, the effects of the waves on the mean current due to the divergence of the stress tensor, with the alongshore component given by: s w y yx yy where the radiation stress S is a tensor proportional to the wave energy E and therefore wave height [Longuet-Higgins and Stewart, 96]. lthough there are no observations at sites distributed alongshore, the assumption of alongshore uniformity is valid for wave energy at the 8 m depth with negligible differences in energy between the WC (site B) and the 8 m pressure sensor array (distance of 5 m apart in the alongshore direction) and yy =@y. The radiation stress term for the onshore flux of alongshore momentum is estimated from the directional wave measurements used to determine the directional energy spectra E(f,a) following Pawka et al. [983]: MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 484

8 ð ð S yx 5qg Eðf; aþ nðfþ sin acos a da df (5) f a where a is the locally observed wave angle, f is wave frequency, and n(f) is the ratio of group speed c g to phase speed c. Radiation stress gradients are determined using the central difference approximation between the observation sites. 3.. Bottom and Winds Stresses The nonlinear bottom stress is estimated using the velocity observations, with the alongshore component written as: s b y 5qc dhj~ujvi (6) where c d is a bottom drag coefficient, v is the alongshore velocity, j~uj is the total maximum current speed resulting from the combination of wave orbital and mean current velocities, and hi denotes time averaging over many wave periods. The mean currents are determined from the min averaged velocity observations, the maximum wave orbital velocities are determined from the variance of the velocity spectra, and the total maximum current speed is determined using the maximum of these two values. Breaking wave-induced turbulence and spatial variation in roughness element height can result in higher drag coefficients in the surf zone. Previous studies have considered different drag coefficients inside and outside the surf zone [Lentz et al., 999; Feddersen and Guza, 3] and Kumar et al. [3], for example, obtained a cross-shore variable drag coefficient using regression analysis to account for wave-enhanced roughness in shallower water. In the present study, we apply a cross-shore constant drag coefficient of c d 5.3 that results in high correlation (R 5.8 for Bill; R 5.93 for Earl) between the bottom stress and radiation stress gradient terms inside the surf zone. This also results in reasonably good correlation between bottom stress and wind stress well outside the surf zone (R 5.67 for Earl), which has been shown in other studies to be the dominant balance on the shelf [Church and Thornton, 993; Lentz et al., 999]. The atmospheric wind stress is estimated by s a y 5q ac j~ujv (7) where q a is the density of air, c is an atmospheric drag coefficient, j~uj is the total wind speed, and V is the alongshore wind velocity component. We apply a spatially uniform canonical value of c 5.3, although the surface drag coefficient may vary depending on wind speed [Smith, 988], particularly for hurricane strength winds [Powell et al., 3] Horizontal Mixing Surf zone mixing is determined by the cross-shore gradient of the depth-integrated turbulent momentum flux, typically specified as proportional to the mean alongshore current shear [Feddersen et al., 998]. The horizontal mixing coefficient is often parameterized according to water depth and shallow water wave speed: p m5c x h ffiffiffiffiffi gh (8) for which values of C x could range from. to. across the surf zone and account for mixing caused by the turbulence generated by wave dissipation [Svendsen and Putrevu, 994]. However, this estimate of the horizontal eddy viscosity coefficient is independent of the scale of eddies generated by wave breaking. To better account for the strong influence of eddies in the surf zone, we compute the horizontal eddy viscosity by calculating the rotational velocity v rot (x) at each site. Following Lippmann et al. [999], lowfrequency vortical motions are estimated by removing irrotational infragravity wave energy from the observed velocity via: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð v rot ðxþ5 ð~u ~v g h ~p Þdf (9) IG where ~u; ~v; ~p are the cross-shore, alongshore, and pressure spectra, respectively, integrated over the infragravity wave band for frequencies f from.4 to.3 Hz. The rotational velocity at each sensor is shown MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 485

9 v rot (ms ) a) B C v rot (ms ) b) B C E F Y, Y,.5 c) ν (m s ) 3.5 d) ν (m s ) x (m).5 x (m) Figure 7. Horizontal rotational velocity v rot at each site for: (a) Hurricane Bill; (b) Hurricane Earl; and evolution of the cross-shore variation of horizontal eddy viscosity m for: (c) Bill; (d) Earl. in Figures 7a and 7b, with the highest values of over.4 ms at site during Hurricane Earl, indicating intense eddies near the edge of the surf zone. Clark et al. [] used the rotational velocity approach to estimate horizontal diffusivity of a dye tracer in the surfzone, k xx, finding that the diffusivity is well correlated with the low-frequency horizontal rotational velocity scale: k xx 5av rot ðxþl x () where a is a constant of O(), taken to be.4 analogous with Von Karman s constant for wall-bounded shear flow, and L x is the surf zone width. In the present study, we estimate L x by the distance from the shoreline to the breaking index c 5.7, where c5h rms =h and H rms is the root-mean-squared wave height. This results in a surf zone that is over 5 m wide during Hurricane Bill, verified by measuring the distance to the offshore limit of wave breaking from optical imagery [Mulligan et al., ] collected with the rgus camera system. Brown et al. [9] showed that the eddy diffusivity for material suspended in the surf zone (k xx ) is very well correlated (R 5.95, slope.88) with the horizontal eddy viscosity (m) in the surf zone based on the average breaking wave dissipation and turbulence production as a function of input wave energy flux and surf zone width. Therefore, the rotational velocity of eddies driven by wave breaking dominate the lateral mixing process and can be used to estimate the horizontal mixing coefficient in the surf zone: m k xx () The resulting cross-shore variation in horizontal eddy viscosity is shown in Figures 7c and 7d. The high values during Hurricane Earl are due to the high rotational velocities, suggesting very intense eddies at the MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 486

10 outer edge of the surf zone where the northward mean alongshore current shears against the southward mean wind-driven along shelf flow. The horizontal shear is significantly larger than other velocity shears on an alongshore uniform beach, and is an important term in the alongshore momentum balance [Van ongeren and Svendsen, ]. To estimate the second derivative of observed alongshore velocity with respect to cross-shore distance, we use the central difference approximation (equation (3)) twice. The gradient calculation results in a significantly reduced cross-shore domain compared to the other terms, but the results cover the outer surf zone for the storm events dvection and cceleration Terms In the present study, the cross-shore advection of alongshore momentum is evaluated by considering two components: the mean Eulerian current u and the Stokes drift u st. The observed cross-shore currents u during the two storms (Figures 5c and 5f) indicate that the mean Eulerian flow observed by acoustic sensors under the wave trough elevation is directed offshore (undertow). The Stokes drift is a waveinduced mass flux that is directed onshore, resulting in onshore-directed advection of alongshore momentum. Recent field observational studies [e.g., Kumaretal., 3] have considered the vortexforce representation of wave-averaged effects on currents, where the force results from the interaction between the vorticity of the flow and the Stokes drift [Craik and Leibovich, 976]. The vorticity generated by wave breaking therefore contributes to the momentum of the flow Clark et al. [] and can be a primary cross-shore dispersion mechanism. The Stokes velocity is determined from the directional wave properties using: u st 5 gh rms cos a () 6ch where c is wave celerity and the total cross-shore advection is estimated from the net cross-shore velocity as the sum of the mean Eulerian flow and the Stokes drift velocity: u T 5uu st (3) Cross-shore advection of the alongshore current is determinedfromtheproduct of the cross-shore velocity component and the central difference approximation to the partial derivative of v with respect to x, resulting in a reduced cross-shore domain compared to the other terms. The resulting opposed cross-shore advective terms are shown in Figure 8 after spatially interpolation in the x-direction, and under the alongshore uniform assumption nearly cancel out (the total advection term is shown in Figures 9e e). Local fluid acceleration can also be an important contributor to momentum in the surf zone [Whitford and Thornton, 996]. In this study, we estimate this time-dependent acceleration from the difference in mean velocity per unit time at each sensor. 4. Results and iscussion 4.. Evolution of Momentum Each term in equation () is spatially interpolated in the x-direction to estimate the time-dependent evolution of cross-shore variability in alongshore momentum, shown in Figure 9 for Hurricane Bill and Figure for Hurricane Earl. For both storm events, the dominant momentum terms inside the surf zone are radiation stress gradients and the bottom friction indicating the first-order importance of wave breaking in nearshore circulation. This has been shown in previous studies; however, the contrast between storms in the present study indicates yx =@x=qh has higher variability for Hurricane Earl, where warm colors in Figures 9a and a represent a negative shoreward gradient (wave breaking) and cool colors represent a shoreward positive gradient (wave shoaling). In the case of Hurricane Bill (distant offshore storm), wind stress is negligible and the outer surf zone is dominated by radiation stress gradients, bottom friction, mixing, advection, and local acceleration. For Hurricane Earl (storm center close to the coast), the wind stress that drives flow on the shelf contributes to the current shear (Figure 6h) and therefore drives both stronger horizontal mixing (Figure d) and cross-shore advection (Figure e), as well as influencing the bottom stress by reducing it to a zero mean between the MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 487

11 .5 a) u st v/ x b) u v/ x.5 (m s ) 5 x c) u st v/ x d) u v/ x x (m) 5 x (m) Figure 8. Evolution of the cross-shore advection of alongshore momentum (ms ) from the Stokes drift u st and the mean Eulerian current u for: (a)-(b) Hurricane Bill; and (c)-(d) Hurricane Earl. opposing flows (Figure b). Rapid changes in the directional wave energy distribution as the local storm passes therefore drive significant changes in the radiation stress gradients, leading to very different nearshore conditions compared to the distant storm. In the outer part of the surf zone and beyond it, horizontal current shear is strong and several momentum terms are nearly equally important. This region can extend a significant distance seaward of the surf zone (e.g., 3 5 m outside the surf zone for these storm events). The horizontal mixing, for example, is proportional to the rotational velocity induced by surf zone eddies and the rate of change of the current shear. This can be high outside the surf zone, especially as observed during Hurricane Earl in Figure d, when all six sensors were operational and the wave-driven alongshore and wind-driven alongshelf currents (Figure 6g) flowed in opposing directions. Strong offshore-directed mean Eulerian velocities below the wave troughs of u ms were observed during Hurricane Earl. This undertow drives higher cross-shore advection of momentum outside the surf zone during this storm event. The advection, which depends on also on the horizontal shear is high (Figure e) when the wave angle is close to normally incident, and the total cross-shore flux (mean current and Stokes drift) is directed offshore. MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 488

12 Figure 9. Evolution of the cross-shore variation in the leading alongshore momentum terms (ms ) arranged according to equation () for Hurricane Bill. Vertical lines indicate the sensor locations and time is referenced to 5 days for Y in 9. This analysis indicates the cross-shore spatial variability of important alongshore momentum terms and that a combination of radiation stress gradients, bottom friction, wind stress, horizontal mixing, and crossshore advection can dominate the outer surf zone. Time-series of the sum of all terms over the cross-shore evaluation region for each storm and the individual alongshore momentum terms at two cross-shore locations are shown in Figure. This further indicates that momentum at selected locations in the inner surf zone (e.g., x 5 53 for Bill; x 5 36 for Earl) is governed mainly by the wave momentum flux and bottom stress, in agreement with previous studies. In the outer surf zone (e.g., x5 73 for Bill; x5 76 for Earl), the cross-shore advection and horizontal mixing terms become relatively more important. The time series of horizontal mixing peaks before and after the peak in the radiation stress gradient, suggesting that it is most intense at the edge of the surf zone since the width of the surf zone changes and passes through this location over time. The local wind stress is also important during Hurricane Earl (Figure f), particularly near the outer edge of the surf zone and on the inner shelf, and is only in balance with bottom friction well outside the surf zone (e.g., x > m, Figures b and c). The evaluation of the individual momentum terms that depend on coefficients (e.g., c d, c ) are difficult to exactly determine, considering that they are rapidly changing and can all be the same order of magnitude in the outer surf zone. However, integration of all the momentum terms across the measured region of the surf zone, shown by R x in Figures b and e, indicates closure of the momentum balance. It is notable that at any cross-shore location the momentum does not necessarily balance, but the cross-shore integrated near-balance is dominated by () radiation stress gradients and bottom friction inside the surf zone where these two terms are typically an order of magnitude greater than the others, () wind stress and MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 489

13 Figure. Evolution of the cross-shore variation in the leading alongshore momentum terms ms arranged according to equation () for Hurricane Earl. Vertical lines indicate the sensor locations and time is referenced to 5 days for Y in. bottom friction on the shallow shelf, and (3) by a combination of all terms, including horizontal mixing and cross-shore advection, in complex region around the break point where the surf zone interacts with the shallow shelf. 4.. Other Considerations The Coriolis acceleration [Lentz et al., 999] and Stokes-Coriolis acceleration (effect of Earths rotation on surface waves) [Kumar et al., 3] terms are calculated from the depth-averaged cross-shore mean velocity and the depth-averaged cross-shore component of the Stokes drift velocity respectively. Both the Coriolis and the Stokes-Coriolis acceleration terms are an order of magnitude smaller than other terms (the inertial frequency f s at this latitude) since hurricane wind and wave forcing change rapidly compared to inertial forces from Earth s rotation. These terms are much smaller so are not shown, but are likely of higher relative importance in deeper water on the shelf [ Ozkan-Haller, 4]. longshore gradients in momentum (partial derivatives with respect to y, equation ()) are not evaluated since velocity measurements at sensors distributed alongshore were not obtained for these storm events. lthough wave energy differences between measurements at the 8 m depth (site B and 8 m, Figure ) are negligible for these storms and Feddersen and Guza [3] show that the alongshore currents are alongshore uniform for wave heights generally less than m, strong horizontal current shear can generate intense eddies resulting terms that are similar in magnitude [Long and Ozkan-Haller, 5]. future goal would be to obtain nearshore current observations for hurricane wave events from sensors distributed in both the alongshore and the cross-shore directions. MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 49

14 Σ all terms (m s ) a) 3 x x (m) (ms ) 3 x x = 53 m 3 b) Σ x S xy / x/ρh τ y b /ρh τ y w /ρh ν x/ x u T v/ x v/ t x x = 73 m 3 c) Σ all terms (m s ) d) 3 x 3 (ms ) 3 x x = 36 m 3 e) (ms ).5.5 x 3 x = 76 m f) x (m) Figure. Time-series of the cross-shore distribution of the total sum of all momentum terms ms, and the dominant alongshore momentum terms at two cross-shore locations for (a,b,c) Hurricane Bill and (d,e,f) Hurricane Earl. R x (grey line in Figures b and e) represents the integration of all terms in the cross-shore direction over the cross-shore evaluation region for each storm. Note the change in y axis scales between locations. 5. Summary and Conclusions Novel observations of intense hurricane wave conditions in the nearshore environment are made using a m wide cross-shore array of acoustic wave and current sensors, indicating high rates momentum transfer from waves to flows in the surf zone. For two major hurricanes that are far from (light local wind) and close to (high local wind speed, e.g., up to 5 ms ) to the coast, large waves (H s m) generate very strong alongshore flows (up to ms ) however the distance from the storm to the coast results in different nearshore conditions. Waves from the distant storm have higher lower frequency energy (swell) with lower variability in wave direction as the storm passes. In contrast, waves from the local hurricane have bimodal higher-frequency energy (swell and wind sea) from several directions with rapid changes in wave direction as the storm passes. These rapid changes in wave forcing conditions influence the nearshore circulation response and in particular the speed, timing, and width of alongshore currents in the surf zone. The evolution of alongshore momentum across the nearshore region is evaluated from the observations. Radiation stress gradients are typically in near-balance with bottom stresses inside the surf zone where the waves are breaking, in agreement with previous studies. Other momentum terms including advection, horizontal mixing, and wind stress play important roles at different spatial locations across the nearshore region. In the outer surf zone, which extends a distance on the order of the surf zone width seaward of the surf MULLIGN ET L. NERSHORE MOMENTUM URING HURRICNES 49

15 zone, horizontal mixing, and advection are particularly strong and wind stress is in balance with bottom stress further offshore on the inner shelf. Horizontal mixing during the local hurricane, estimated from the high (over.4 ms ) rotational velocities in the surf zone, was very strong suggesting that intense eddies are generated by the high horizontal shear between the opposing alongshore and along-shelf flows. Local fluid acceleration is found to be important but smaller than other terms, and Coriolis and Stokes-Coriolis accelerations were found to be an order of magnitude smaller and negligible in the surf zone compared to other terms. The nearshore circulation during storms with large waves is typically dominated by forcing from wavebreaking that generates alongshore, cross-shore, and rotational flows. The observations presented in this study indicate that the wave-generated alongshore currents can drive high horizontal shear between the wind-driven shelf currents from a local hurricane. The current shear generates intense eddies, increases the importance of horizontal mixing, and advection across the nearshore region, and results in a combination of momentum terms are the same order of magnitude in the outer surf zone. cknowledgments This research was supported by a Natural Science and Engineering Research Council of Canada (NSERC) iscovery Grant to the first author, and funding for the instrumentation was provided by the U.S. rmy Corps of Engineers. The data used in this work are archived by the U.S. rmy Corps of Engineers at the Field Research Facility (FRF) in uck, NC, and can be accessed at We thank anonymous reviewers for insightful comments on the original manuscript. 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