Field Measurements of a High-Energy Headland Deﬂection Rip Current: Tidal Modulation, Very Low Frequency Pulsation and Vertical Structure

: Headland rips, sometimes referred to as boundary rips, are rip currents ﬂowing against natural or artiﬁcial obstructions extending seaward from the beach, such as headland or groynes. They can be driven either by the deﬂection of the longshore current against the obstacle or by alongshore variation in breaking wave height due to wave shadowing in the lee of the obstacle. The driving mechanism therefore essentially depends on the angle of wave incidence with respect to the natural or artiﬁcial obstruction. We analyze 42 days of velocity proﬁle measurements against a natural headland at the high-energy meso-macrotidal beach of Anglet, southwest France. Measurements were collected in 6.5–10.5-m depth as tide elevation varied, during the autumn–winter period with offshore signiﬁcant wave height and period ranging 0.9–6 m and 8–16 s, respectively, and the angle of wave incidence ranging from − 20 ◦ to 20 ◦ . Here we analyze deﬂection rip conﬁgurations, corresponding to approximately 24 days of measurements, for which the current meter was alternatively located in the rip neck, rip head or away from the rip as wave and tide conditions changed. Deﬂection rips were associated with large offshore-directed velocities (up to 0.6 m/s depth-averaged velocities) and tide modulation for low- to moderate-energy waves. The vertical proﬁle of deﬂection rips was found to vary from depth-uniform in the rip neck to strongly depth-varying further offshore in the rip head with maximum velocities near the surface. Very low frequency motions of the rip were dramatic, ranging 10–60 min with a dominant peak period of approximately 40 min, i.e., with longer periods than commonly reported. The strong offshore-directed velocities measured well beyond the surf zone edge provide new insight into deﬂection rips as a dominant mechanism for water and sediment exchanges between embayed (or structurally-controlled) beaches and the inner-shelf and/or the adjacent embayments. current magnitude and ( m , n ) direction against the headland projected into a cross-shore/alongshore local reference frame ( > 0 Northward, < 0 Southward).


Introduction
Headland-bay and structurally-controlled beaches are ubiquitous worldwide [1]. Natural or artificial obstruction extending seaward from the coastline can directly impact the incident wave field and, in turn, wave-driven currents (e.g., [2]), sediment transport pathways (e.g., [3]), beach morphodynamics (e.g., [4,5]) and temporal and spatial modes of shoreline variability (e.g., [6,7]). Over the last decades, a lot of efforts have been made to improve our understanding of shoreline change along headland-bay and structurally-controlled beaches. In particular beach rotation, which can Deflection rip behavior is therefore critical to our understanding of water and sediment exchanges between the embayed beach and the inner-shelf and/or the adjacent embayments. However, to the best of our knowledge, there are very few continuous Eulerian flow measurements within the headland rip neck and rip head, and no measurements have been collected during high-energy conditions. One of the two notable exceptions is the unpublished PhD work of Coutts-Smith [21] who deployed current meters during two years offshore an embayed beach in New South Wales, Australia, and captured some high-energy rips, which were assumed as headland rips. The maximum surface flow reached 1.3 m/s in 15-m depth during a severe storm (H s about 6 m), with typical rip flow pulsing at periods 10-15 min. However, the relationships with an offshore wave and tide conditions were not systematically addressed, and the time-averaging of the velocities was unclear. The second exception is a field experiment that was recently conducted in October 2018 at Anglet beach, southwest France, described in [31] and from which some of the data presented here builds on.
Overall, little is known about the dynamics of deflection rips. Their pulsing characteristics, depth variability and whether they are modulated by the tide like channel rips further away along the beach (e.g., [32][33][34]), are virtually unknown. This paper aims at paving these knowledge gaps using direct field measurements of headland rip in a high-energy meso-macrotidal beach in southwest France, here focusing on the deflection regime which was well captured by our currentmeter. The present analysis builds on some of the data collected during the experiment presented in Mouragues et al. [31] and on additional measurements subsequently collected at the same beach. In this paper we analyze 42 days of continuous current profiles acquired at 1 Hz in 6.5-10.5 m depth against a natural headland. After analysing rip flow characteristics with regards to bulk wave parameters and tide conditions, an in-depth description of two representative deflection rip events are carried out.

Field Site
La Petite Chambre d'Amour (PCA) beach is located at the southern end of Anglet beach on the French Basque Coast, southwest France ( Figure 2a). It is a high-energy beach exposed to waves generated in the North Atlantic by extra-tropical low-pressure systems tracking eastwards [35]. Waves come primarily from the W-NW direction, and incident wave energy is strongly seasonally modulated, with an annual mean significant wave height and peak period of H s = 1.57 m (up to 10 m during severe storms) and T p = 10 s, respectively [36]. The tide regime is mostly composed of semi-diurnal components, giving near-sine oscillations of the Still Water Level (SWL) with an average period of approximately 12 h and 20 minutes. The tidal regime is meso-macro, with tide range varying between 1 and 4.7 m.-macro. Tide-induced currents are weak along the Anglet shores and the waves are by far the dominant, but tidally-modulated, driver of the nearshore hydrodynamics [37]. PCA beach is the most southern stretch of the 4-km long sandy embayment of Anglet, which is bounded by the approximately 500-m long Saint-Martin rocky headland in the south and by the Adour river training wall in the North. In between, six groynes have been implemented over the last decades to constrain shoreline variability. PCA beach is composed of medium to coarse (D50 ≈ 2 mm) sand with a steep beach face (≈1/10). For more information on Anglet beach setting and beach morphodynamics, the reader is referred to Huguet et al. [38], Rodriguez-Padilla et al. [39].

Data and Methods
The present dataset gathers the data collected during two successive field deployments: (1) on 8-25 October 2018 in the frame of the large-scale field experiment described in Mouragues et al.  (Figure 2b). The initial intention was to deploy the profiler at the same location for both campaigns but the deployment conditions encountered in 2019 do not allow to safely approach the shore. The small shift between 2018 and 2019 locations should not significantly affect the measurement analysis, in particular in the case of well-developed deflection rips analysis hereafter. For both campaigns, the instrument was deployed on a weighted (150 kg lead) tripod structure. The velocity profile was measured continuously at 1 Hz over 0.2-m cells. The blanking zone was set to 0.1 m. The position of the bottom cell is estimated to approximately 0.65 and 0.3 m above the sand bed at the start and the end of each deployment, respectively. The continuous dataset of 1 Hz velocity profiles was first subdivided into 2-h bursts. While longer duration would have been preferable to increase the number of degrees of freedom, the 2-h duration is the best compromise to capture both the dominant low-frequency fluctuations of the signal and the tidal dependency. On each 2-h burst, the instantaneous velocity profiles were first processed to discard from the analysis cells that were intermittently emerged at the passage of a wave trough. This was carried out by detecting from embedded pressure data the minimal elevation reached during each burst, and restricting the analysis within the water column below this elevation. Velocities were then projected into a cross-shore/alongshore local reference frame: the cross-shore component is aligned with the shore-normal (300 • in nautical convention) direction, positive offshore, while the alongshore component is shore-parallel (30 • in nautical convention), positive northward: where u E and u N are respectively the eastward and northward velocity components provided by the profiler, u and v the alongshore and cross-shore velocity components and α the shore-normal direction (in Nautical convention). Depth-averaged velocity components, hereafter denoted U and V for the alongshore and cross-shore components, respectively, were computed by averaging the flow velocities from the bottom cell to the surface: where N is the number of immersed cells. A discrete Fourier transform was computed on the depth-averaged velocity components without any windowing to preserve the low-frequency content. The resulting spectra were then smoothed using a 0.00065 Hz moving average. Time-averaged velocity profiles were obtained by averaging the velocity data in each cell either over the complete 2-h burst or using a 2-min moving average in order to low-pass filter out the gravity wave orbital component and to highlight the low frequency pulsations. Still-water level was obtained from the Bayonne-Boucau tide gauge located near the entrance of the Adour river and operated by the Service Hydrographique and Oceanographique de la Marine (SHOM). Offshore directional wave measurements were collected by an offshore wave buoy moored in approximately 50-m depth offshore of Anglet. In order to relate the offshore wave forcing with the rip development, we computed the longshore wave power P l defined as: where ρ is the seawater density, g the gravity acceleration and H s and T e are the significant wave height and energetic period (ratio between −1 and 0-order moments of the spectral density) measured at the wave buoy, respectively. The angle of wave incidence θ is positive (negative) for northern (southern) waves, that is, for a wave direction larger (lower) than 300 • . The mean direction at the buoy is used for the calculation. Accordingly, the longshore power ranges from −25 to 10 kW/m, with more energetic wave events recorded during 2019 (Figure 3g,h), meaning that both shadow rip and deflection rip configurations occurred during the course of the deployments. Overall, the deflection rip regime (P l > 0) was observed during approximately 24 cumulative experiment days. During both deployments, one complete neap-spring tide cycle was covered, with tidal range varying from 1.1 to 3.9 m and from 1.3 to 4.6 m during the first and second deployment, respectively (Figure 3i,j). Wind conditions (not shown) were weak to moderate during both field campaigns, with mean values of approximately 3.0 and 3.7 m/s, respectively, with wind events coming primarily from the W-NW sector. There was no severe storm wind event as the time-averaged wind speed never exceeded 12 m/s. (e,f) mean wave direction (>300 • Northward, <300 • Southward); (g,h) longshore wave power; (i,j) measurement depth; (k,l) 2-h-averaged current magnitude and (m,n) direction against the headland projected into a cross-shore/alongshore local reference frame (>0 Northward, <0 Southward).

Headland Rip Flow
This large range of tide/wave forcing conditions resulted in a large variability in headland rip current activity (Figure 3m,n). Periods of a few days with no rip activity are observed, with magnitude of depth-averaged flow below ≈0.1 m/s, readily coinciding with periods with H s < 2 m. Long periods of rip flow activity are also observed, coinciding with periods of waves with H s > 2 m and/or with oblique incidence with a preferred northern incidence (P l > 0, deflection rip configuration), with no apparent influence of wind conditions. Time-and depth-averaged rip flow speed reached 0.6 m/s (Figure 3l). This peak does not coincide with the H s peak on 5 March 2019, but with the peak of positive longshore power observed on 11 March 2019, highlighting the importance of wave incidence. When active, the rip flow direction is well-defined within the 270-290 • (nautical convention) sector, meaning that the rip flows offshore along the headland with a slight westward inflexion. Results also show that, when active, rip flow velocity is strongly modulated by the tide, with rip flow speed maximized for lower tides, while the flow direction is not readily affected. Figure 4 provides insight into the relationship between the cross-shore/longshore components of the headland rip current and the longshore power P l , which allows identifying the conditions for the deflection rip development. Following the basic conceptual scheme presented in Figure 1, a deflection rip is expected for positive longshore power (P l > 0) corresponding to waves coming from the north. For these deflection rip configurations, rip flow speed strongly increases and deviates westward with increasing P l . Results also suggest that rip flow activity increases with decreasing tidal elevation ( Figure 4b) and offshore wave height (Figure 4d). Figure 5 further shows that tide modulation depends on incident wave energy. For H s < 3 m, deflection rip is active only between low-and mid-tide, with maximum activity around mean low water level (Figure 5a,b). Tidal modulation disappears for high-energy waves (Figure 5c) when rip flow activity is maintained even for higher tide elevation (e.g., see from 11 March 2019 in Figure 3n). . Scatter plot of depth-averaged and 2-h-averaged alongshore (a,c) and cross-shore (b,d) flow components against longshore power P l . Positive/negative longshore power corresponds to northern/southern waves, positive/negative alongshore velocity component U corresponds to northward/southward current and positive/negative velocity component V corresponds to off/onshore flow. In the top and bottom panels the water depth and significant wave height are colored, respectively. The present analysis focuses on the deflection regime for P l > 0 (right parts of the subplots).

Representative Rip Flow Events
Results show that the longshore wave power dictates the rip flow regime, with additional influence of wave height and tidal elevation. To explore the detailed rip flow response, two representative events in moderate-and high-energy deflection configuration were selected and further analyzed below in terms of temporal and vertical structure.

Moderate-Energy Deflection Rip
This event on 23 October 2018 ( Figure 6) is characterized by an average wave height, period and direction of 1.6 m, 7.8 s and 322 • , respectively, for the 2-h low-tide burst (SW L = −1.5 m, left-hand panels in Figure 6) and 1.7 m, 8.5 s and 314 • , respectively, for the 2-h high-tide burst (SW L = 1.4 m, right-hand panels in Figure 6). At high tide, the headland rip is not active with both 2-min averaged flow components well below 0.1 m/s. By contrast, the headland rip is active at low tide with an offshore-directed velocity averaging around 0.2 m/s despite the fact that the current profiler was sitting in approximately 7-m water depth and located far offshore of the outer surf zone edge. The 2-min averaged cross-shore flow velocity also shows a striking pulsing behavior, with an energy peak at 0.00067 Hz, corresponding to very low frequency (VLF) motions with a dominant period of approximately 25 min (Figure 6c). The mean cross-shore current is also highly variable across the water column, with mean flow velocity almost linearly increasing from 0 near the bottom to approximately 0.3 m/s near the surface. By contrast, the alongshore component of the rip current shows pulsations at a wider and shorter range of periods and is nearly depth-uniform.

High-Energy Deflection Rip
This event on 10 March 2019 is characterized by an average wave height, period and direction of 3.5 m, 10.8 s and 302 • , respectively, for the 2-h low-tide burst (SW L = −1.6 m, left-hand panels in Figure 7) and 3.5 m, 11.5 s and 305 • , respectively, for the 2-h high-tide burst (SW L = 1.3 m, right-hand panels in Figure 7). In contrast with the previous event, the headland rip is active at both low and high tide, with a time-and depth-averaged offshore-directed velocity of approximately 0.5 m/s and 0.3 m/s, respectively. At low tide the current meter is in approximately 7.1-m depth and is therefore located within the outer surf zone. Both the 2-min averaged alongshore and cross-shore flow velocity components show a strong pulsing behavior, with energy peaks at approximately 0.00069 and 0.00041 Hz, corresponding to very low-frequency motions with a dominant period of approximately 24 and 40 min for along and cross-shore components, respectively. At high tide, lower frequency pulsing is also observed with a more pronounced cross-shore pulsation than for low tide. Both components are fluctuating in the same frequency band (about 0.00041 Hz, i.e., 40 min). The rip flow is also more depth variable at high tide, when the currentmeter is located well offshore of the surf zone edge. In contrast with the low tide situation of the moderate-energy deflection rip described previously, here both the cross-shore and alongshore components are depth variable, with mean flow velocity roughly linearly increasing from the bottom to the surface where it almost reaches 0.5 m/s. At low tide the current profile is nearly depth uniform, with the development of an (incomplete) bottom boundary layer.

Discussion
The above analysis emphasizes the complex and contrasting behaviors that headland rips can exhibit in high-energy meso-macro tidal settings. In particular, the primary driving mechanism of headland rip is critical to rip flow activity. Our results indicate that headland rips driven by the deflection of the alongshore current against the structure are the most intense. In addition, this type of rip was the only one for which offshore-directed depth-and time-averaged velocities were measured far beyond the surf zone. This is in line with previous modeling work [29] and drifter measurements [17] in lower energy environments showing that mean flow speed and exit rates are both greater under deflection rip configuration than under shadow rip configurations, with the latter often dominated by a circulatory flow regime [27]. It is therefore hypothesized that boundary rips driven by the deflection of the alongshore current can be a dominant mechanism for water and sediment exchanges between the embayed beach and the inner-shelf and/or the adjacent embayments.
The present study also indicates that deflection rip flow speed consistently increases with increasing longshore wave power. However, it is expected to eventually saturate as offshore wave height further increases. Scott et al. [16] showed that if the ratio of the headland length to the surf zone width decreases below 1.25 the amount of deflected alongshore current decreases. This means that as offshore wave height further increases with the surf zone edge reaching or exceeding the headland tip, the amount of deflected current does not further increase. It must be noted that this 2018/2019 winter was characterized by the absence of a severe storm, with the most energetic event captured with H s ≈ 6.5 m and near-shore normal incidence, thus preventing exploration of a potential saturation of deflection rip velocity as offshore wave height further increases. Additional deployments and/or modeling experiments will be required to address rip flow characteristics during severe storms (H s > 8 m), for which waves break well offshore of the headland at PCA.
Headland rips have received little attention so far compared to, for instance, channel rips. While tide modulation of channel rips has been documented fairly well, showing, most of the time, maximized rip flow activity around lower tide levels (e.g., [32][33][34]), tidal modulation of headland rips has never been explored. Similar behavior to channel rips is observed at PCA for moderate-wave energy conditions during which the deflection rip is only active at low tide ( Figure 6). Although one can expect that at high tide the current meter was located too far away from the rip, resulting in a biased tide modulation, a drifter experiment conducted that day confirms that maximum headland rip flow activity was observed at low tide [40], in line with the measurements collected by our current meter. Although slight tidal modulation was also observed for the high-energy deflection rip event shown in Figure 7, on average no clear tidal modulation was observed (Figure 5c). Interestingly enough, for high-energy conditions it is expected that deflection rip flow becomes maximum at high tide. Steeper surf zone slope and more prominent offshore extent of the headland as the entire surf zone migrates landward should result in more alongshore current to be deflected [16]. This will need to be further explored using numerical modeling and/or denser Eulerian measurements against the headland, in order to capture a much wider wave height/longshore power spectrum. Previous work also indicates that, in the laboratory and for highly alongshore non-uniform bar bathymetry, the vertical profile of channel rips varies from depth-uniform in the rip neck to depth-varying further offshore in the rip head [41]. Such vertical structure of the rip flow has never been measured in the field, because of the lack of velocity profile measurements in the neck and the head of the rip, and also because the horizontal dimensions of rip circulation are large compared to the surf zone water depth. This statement does not stand for the deflection rips observed at PCA. As deflection rips consist in narrow jets extending well beyond the surf zone in deeper water (>10 m), the vertical dimension becomes non-negligible. Here, using the wave and tide modulation of the surf zone location as a proxy to study the spatial structure of the rip we found that, in line with the laboratory work on channel rips, the deflection rip flow is nearly depth-uniform in the neck and becomes increasingly sheared seaward through the rip head (Figure 7). Deflection rips are associated with large VLF fluctuations, with periods ranging 10-60 min. The VLF motions with periods > 30 min, which is much longer than VLF motions typically observed in various rip current systems (e.g., [42][43][44]), are closer to the recent observation of Elgar et al. [45] who referred to these surf zone eddy motions to as extremely low-frequency motions (ELF). The relationships between wave/tide forcing conditions, the mechanism of boundary rip generation, and VLF flow response was further analyzed. Significant amplitudes of VLF fluctuations were systematically computed over successive 2-h bursts, integrating the spectral density of variance for velocity (along-shore, cross-shore and magnitude), and plotted against mean flow velocities, tide elevation and longshore wave power. The selected frequency band was 0.0002 < F < 0.0033 Hz, i.e., to account for periods between 5 min and 1h20, in line with the observed dominant VLF/ELF motions. Figure 8 shows a clear discrimination between deflection (reddish bubbles) and shadow (yellow-blue bubbles) configurations. For deflection rips, the VLF/ELF motions of the cross-shore component increases with increasing mean cross-shore component (r 2 = 0.62). The correlation is also significant for the alongshore component (r 2 = 0.55) and particularly for the flow magnitude (r 2 = 0.8). This correlation indicates that the VLF/ELF motions are related to the shear instabilities of the rip current, as an increase in velocity shear should increase instability intensities. This contrasts with previous observations of channel rips showing that VLF amplitude is poorly correlated with the mean flow speed but more significantly correlated with incident wave energy [42]. The cut-off frequency between infragravity and VLF bands is typically set arbitrarily to values such as 0.004 or 0.005 Hz, or even 0.008 Hz [46]. Given the long wave periods (up to 16 s) that were encountered during our measurement periods, it is likely that some infragravity energy has been taken into account in Figure 8. However, computations using other upper-frequency limits, e.g., F = 0.0083 Hz and F = 0.0017 Hz, corresponding to periods of 2 and 10 min, showed similar outcomes to the results discussed here. At this stage the underlying mechanism driving these VFL and ELF flow motions is unclear and should be further investigated through detailed process-based modeling. Figure 8. Significant amplitude of very low frequency (VLF) fluctuations (above 5min period) vs mean current for the cross-shore (a) and along-shore (b) components and magnitude (c) for the depth-averaged velocity. Longshore power and tidal elevation are depicted by color levels and marker size (the larger, the higher), respectively.

Conclusions
The present study used 42 days of velocity profile measurements collected from one current profiler along a natural headland at PCA beach, southwest France, in order to study headland rip activity. The current meter was alternatively located in the rip neck, rip head or away from the rip as wave and tide conditions changed. Strong headland rips driven by the deflection of the alongshore current against the headland were observed, associated with large offshore-directed velocities and tide modulation. Deflection rip flow structure varied from nearly depth-uniform in the rip neck to strongly depth-varying further offshore in the rip head with maximum velocities near the surface. VLF motions of the rip flow were strong, with periods ranging 10-60 min and a dominant peak period about 40 min, i.e., extending in the ELF range defined by Elgar et al. [45]. The velocities measured in this study (up to 0.6 m/s in > 10-m depth under < 4 m obliquely incident waves) confirm that, by contrast to undertow, deflection rips can potentially transport large quantities of sediment offshore well beyond the depth of closure, which is estimated to be approximately 14 m at this site [40], as storm waves can well exceed 8 m. Such a dataset provides new insight into headland rips as a dominant mechanism for water and sediment exchanges between the embayed beach and the inner-shelf and/or the adjacent embayments.