Atmospheric-hydrodynamic coupling in the nearshore

Authors


Abstract

[1] Natural beach shorelines commonly present morphological rhythmic or non-rhythmic features of varying geometrical characteristics. Traditionally, their formation is believed to be due to wave-induced processes, a line thoroughly investigated during the last few decades. However, these natural beach formations are frequently bounded by coastal cliffs (or capes) and are affected by intense winds, a fact not previously considered. This paper presents the results of a field survey, demonstrating the existence of atmospheric-hydrodynamic coupling in the nearshore region outside of the breaking zone at Carchuna beach (Motril, Spain), where the atmospheric conditions are influenced by a lateral geographic obstacle (Cape Sacratif).

1. Introduction

[2] Coastal cliffs are common along many of the world's coastlines [Komar, 1998] and can be defined as “steep slopes that border ocean coasts” [Masselink and Hughes, 2003]. A variety of cliff profiles are found in nature (e.g. Spanish South Mediterranean coast; Oregon coast; UK coast) with different geometrical characteristics (i.e. height and seaward protruding distance with respect to the mean coastline alignment). Thus, it is common to find natural beaches bounded by various typologies of coastal cliffs or capes. Also, embayed or laterally constricted beaches frequently show shoreline morphological features of different cross-shore and longshore dimensions [Komar, 1998], where a variety of cuspate shoreline forms may be observed ranging from large scale cuspate forelands to short scale beach cusps.

[3] In the past, special attention has been focused on beach cusps on both sandy or gravel beaches mainly due to their periodicity and their intriguing cuspate shape [Guza and Inman, 1975; Inman and Guza, 1982; Coco et al., 1999; Masselink et al., 2004]. The formations are believed to be generated by wave action [Komar, 1998; Holland and Holman, 1996] and the physical processes that can initiate their formation have been thoroughly investigated. Guza and Inman [1975] considered that longshore periodic gravity waves trapped close to the shoreline by refraction (edge waves) can form a standing pattern with a periodic sequence of high and low amplitudes in the alongshore [Coco and Murray, 2007]. However, the existence of edge waves is still a matter of controversy, as various authors present evidence of their occurrence [Huntley and Bowen, 1973; Coco et al., 1999], while others disagree [Holland and Holman, 1996; Masselink et al., 2004].Werner and Fink [1993] proposed a model based on morphodynamic feedbacks and self-organization that successfully predicts the beach cusp spacing with respect to the length of the swash zone flow excursion; signatures of the validity of this model were clearly detected by Coco et al. [2003].

[4] Similar shapes, but with larger spatial scales, can be found in features such as alongshore shoreline sand waves, cuspate bumps, crescentic bars, spits or giant cusps [Ashton and Murray, 2006a; Coco and Murray, 2007], but little attention has been given to their formation in comparison to beach cusps. In addition to the previously described mechanisms, Ashton et al. [2001] demonstrated how the relationship between alongshore sediment flux and deep-water wave approach leads to an instability in the plan-view shoreline shape. This instability can generate different shoreline shapes depending on the particular offshore wave climate [Ashton and Murray, 2006a, 2006b].

[5] Other mechanisms that can lead to the formation of cuspate features have been proposed by Ortega-Sánchez et al. [2003], who studied the irregular large scale cuspate features observed at Carchuna beach (Spanish south-east coast). They found that their formation is associated to the alongshore wave height modulation near the coast due to wave energy propagation over submarine fluvial valleys. However, in theory, other mechanisms may also be present at the beach that can modify the existing morphology; for example, the arrival of waves from alternative directions and with varying characteristic peak harmonic frequencies can non-linearly interact and excite secondary infragravity oscillations [Hasselmann, 1962]. After wave breaking, these forced oscillations can be released as free waves and propagate to the shore. For certain angles of incidence these shoreward propagating waves can become trapped and confined to the shore, as is the case of edge waves.

[6] Accordingly, previous studies have examined the formation of cuspate features due to wave-induced hydrodynamic processes, but not the possibility that these hydrodynamic processes are forced by the nearshore atmospheric variability (wind and pressure) due to the presence of natural cliffs or capes that bound the beach. Quevedo et al. [2008] examined how pulsating pressure fields associated with the wind flow on the lee side of geographic obstacles could generate edge waves on the inner continental shelf. They applied this new physical process to Carchuna beach and the results indicate a possible reinforcing of the existing morphology. However, neither detailed hydrodynamic nor atmospheric measurements that supported their theory were included. This paper presents the results of a field survey, performed at Carchuna beach, where the hydrodynamic and atmospheric properties are measured simultaneously. Results confirm the influence of the atmospheric processes induced by the local topography in the nearshore hydrodynamics.

2. Field Site and Physical Processes

[7] Carchuna beach is a 4 km long mixed sand and gravel beach located on the south –eastern Spanish Mediterranean coast (Figure 1) and can be considered as a straight beach bounded by a cape at one end (Figure 1a, H1). The beach presents a complex shoreline morphology, characterized by four large scale irregularly spaced cuspate features limited by seaward protruding horns and a peculiar bathymetry comprised of fluvial valleys to the west of the Cape. The beach experiences the co-existence of a number of physical processes (wave refraction patterns over submarine fluvial canyons, progressive or quasi-stationary edge waves trapped between the horns, offshore high angle waves instabilities, wind-wave coupling) that may define its morphology [Ortega-Sánchez et al., 2003, 2008; Quevedo et al., 2008].

Figure 1.

Location and bathymetry of Carchuna beach. Figure 1c presents an overhead photo of the studied embayment indicating the instrument positions.

[8] The field site is adequate to study the nearshore wind-wave interaction due to the presence of Cape Sacratif on its western boundary, a geographic obstacle with principal dimensions in the order of O(100 m) with respect to the mean shoreline orientation, both in the vertical (height, H) and horizontal (normally seaward, D) directions. For winds originating from the direction of the cape, the wind is forced to flow over and around the land extrusion, which perturbs the leeward air flow. According to Quevedo et al. [2008], the air flow around the cape (Figure 2, left) can generate a large-scale Von Kármán vortex street that travels over the sea surface downstream of the cape. The basic frequency of these vortices fv is derived from the Strouhal number, S = D fv/U10 = 0.21, (hereinafter referred to as S) where D is the principal dimension of the obstacle and U10 is the general flow velocity. On the other hand, at some point downstream, the air flow over the cape (Figure 2, right) reattaches to the sea surface forming a wake of trapped vortices [Good and Joubert, 1968; Nezu and Nakagawa, 1989] which induces a quasi-standing atmospheric pressure field with maximum suctions separated by a distance L ∼ 4–6H.

Figure 2.

Scheme of the perturbed air flow behind an obstacle. The vortex shedding effect (left) and the re-attached flow (right).

[9] This produces an atmospheric pulsating pressure field on the sea surface associated with both vortex shedding and re-attached flow. By solving the linear shallow water equations in a semi-infinite beach with a parallel and rectilinear bathymetry similar to that of Carchuna beach (Figure 3, left), Quevedo et al. [2008] suggested that the sea response to a pulsating pressure field was an edge wave with the kinematics characteristics of the pressure field fluctuations. For the case of a discrete spectrum of edge waves, only certain waves satisfy the edge wave dispersion equation for the inner continental shelf morphology of Carchuna (Figure 3, right). The superposition of edge waves of the same period produces standing or partially standing oscillations, whose net mass transport in the boundary layer may create a complex rhythmic morphology [Holman and Bowen, 1982], reinforcing the generation of shoreline features and acting as positive feedback.

Figure 3.

Beach profile similar to that of Carchuna Beach (left) and edge wave dispersion relation (right).

3. Field Measurements

[10] An intensive one week field survey consisting of simultaneous atmospheric and hydrodynamic measurements was performed at Carchuna beach between 7th to 14th of March, 2008 to (1) give insight into the atmospheric and hydrodynamic processes present on Carchuna beach, (2) confirm (or not) results from previous studies and discuss their possible influence on the morphology and (3) describe the hydrodynamics outside a large scale shoreline cuspate embayment. The principal results of the survey are described by S. Bramato et al. (Atmospheric and hydrodynamic interaction outside a natural coastal embayment, submitted to Continental Shelf Research, 2008). The nearshore hydrodynamics are obtained using a cross-shore and longshore array of wave and current meters at six locations (AW1, AW2, AD1, AD2, V1 and V2; Figure 1c) outside a 735 m long embayment limited by horns H3 and H4 (Figure 1a). AW1 was placed at 8 m depth in the middle of the embayment, while the remaining instruments were placed in a longshore array at 5 m depth. The current profiler devices (AW1, AW2, AD1, AD2) measured the water pressure every hour with a sample rate of 1 Hz for 1024 s. For the remaining time within the hour, water current profiles were captured every 60 s with an averaging interval of 55 s.

[11] Atmospheric pressure, wind speed and wind direction were measured at four locations (E1–E4) around the horn H3 closest to the Cape (Figure 1c). Each measurement station included a barometer sensor and a 2D sonic anemometer, with sample frequencies of 4 Hz.

4. Results and Discussion

[12] During the field survey, the beach experienced the passage of a low pressure system across central Europe with three days of moderate westerly winds (10 m/s) and mild (Hs < 0.8 m) and moderate (0.8 < Hs < 1.6 m) wave energy conditions. Measurements indicate a maximum westerly wind of 10 m/s measured at station E2 (Figure 1c), which is considered as a reference station during the experiment due to its proximity to the Cape. Comparisons with the remaining stations indicate some longshore and cross-shore variation in wind speed (0.5 m/s) due to the presence of the Cape, and in wind direction (10°) due to the beach alignment (Bramato et al., submitted manuscript, 2008). The analysis of the surface elevation outside the embayment (AD1-AW2-AD2; Figure 1c) demonstrates the wave height longshore distribution varies in function with the energy content of the forcing conditions (mild and moderate sea conditions), which may maintain or reinforce the beach morphology, respectively.

[13] Figure 4 presents the spectral density distribution of the atmospheric conditions (wind velocity and barometric pressure) registered at sensor E2, along with the corresponding spectral density distribution at the four water pressure sensors (AW1, AW2, AD1 and AD2). The spectral density distributions of the atmospheric conditions are taken from a continuous one hour time series. Due to the low frequency variation of the barometric pressure, its mean variation is removed through a parabolic fit, which is then (1) segmented into 12 intervals of 512 s, (2) each segmented series is then corrected by removing the mean variation with a parabolic fit and (3) adjusted with a cosine window. The presented spectral density distribution for each sensor is the averaged distribution over the 12 segments, providing a spectral analysis with a degree of freedom of 24.

Figure 4.

Spectral density distribution of (a) the wind velocity and (c) the barometric pressure registered at sensor E2, along with (e) the corresponding spectral density distribution at the four water pressure sensors AW1, AW2, AD1 and AD2 during (left) moderate energetic conditions and (right) mild energetic conditions. Vertical lines represent the 95% confidence interval.

[14] The same procedure is applied to the water pressure time series. However, the time series of the water pressure is limited to 1024 s, hence the data is segmented into four intervals of 512 s. The mean variation of the water pressure is corrected with a linear fit to remove the low frequency tidal variation. In this case the degree of freedom of the analysis is 8.

[15] Figure 4 presents two cases of low frequency wind-wave coupling under moderate (Figure 4, left, 23:00 - 10th March) and less energetic (Figure 4, right, 12:00 – 10th March) conditions, as predicted by Quevedo et al. [2008]. Figure 4 only displays a fraction of the frequency range, with the low frequency peaks (f < 0.04 Hz) representing 12% and 1.5% of the incoming wave energy (0.12 Hz < f < 0.24 Hz) under moderate and less energetic conditions, respectively. During the first case (Figure 4, left), the wind approached from the west with an average wind speed of 9 m/s. The four pressure sensors presented two energetic peak harmonic frequencies, f1 = 0.018 Hz and f2 = 0.024 Hz, which are also present in the wind velocity spectrum. Peak f1 is also observed in the barometric pressure and can be attributed to vortex shedding effects from Cape Sacratif. Applying S similarity to Cape Sacratif (cross-shore dimension O[100 m]), the forcing due to a wind speed of 9 m/s results in a vortex shedding frequency of 0.018 Hz with a spacing of 500 m, which matches well with the observed frequency f1. The resulting pressure field forces different modes of progressive edge waves with a period of 55 s and wavelengths ranging from 600 to 2400 m. By mode interaction [Guza and Inman, 1975; Holman and Bowen, 1982] these waves can generate horns inter-spaced at 1200 m and 760 m, which correlate well with the spacing of the cuspate features H3–H5 and H3–H4, respectively. The second peak, f2, also appears in the wind velocity spectra, but not in the barometric pressure. At this time, no physical explanation can be given for this, but it appears that there is some additional wave water interaction occurring at the beach. It is anticipated that the observed physical processes will be better understood after future field campaigns.

[16] Figure 4 (right) presents a second observation of wind-wave coupling under mild conditions where the wind was blowing from the west with an average speed of 7 m/s. In this case, a single peak in the water pressure spectrum is observed at horns H3 and H4 with a frequency, f3, of 0.014 Hz. Applying S similarity to this wind condition results in a vortex shedding frequency of 0.014 Hz, which again matches well with the field observations. This pressure field forces different mode of progressive edge waves with a period of 71 s and wavelengths ranging from 800 to 1800 m, that can generate horns inter-spaced at 1460 m, which correlates well with the spacing of the cuspate feature H5–H6. In both cases, the energy content observed at the sensor AW1 is always lower than those closer to the shore (AW2, AD1 and AD2) as the infragravity wave energy decays with increasing water depth. The maximum energy content is observed at the two horns, H3 and H4, suggesting that the infragravity waves are trapped within the embayment and reflected between the horns.

[17] Historical records of the atmospheric conditions for the region show that the westerly winds over Cape Sacratif frequently occur at Carchuna Beach, for wind speeds up to 10 m/s [Quevedo et al., 2008]. However, the peaks in the atmospheric and water pressure spectra coupling were not constantly observed throughout the week, but only when the wind forcing conditions matched the required parameters for the vortices to develop; in any case, although the wind generates the pressure field over the sea surface, the bathymetry may select only some of the possible infragravity frequencies.

5. Conclusions

[18] Results from an intensive one week field survey consisting of simultaneous atmospheric and hydrodynamic measurements performed at Carchuna beach (Granada, Spain) indicate the existence of atmospheric-hydrodynamic coupling in the nearshore region that act to reinforce the existent morphology [Quevedo et al., 2008]. During the field survey, the beach experienced three days of moderate westerly winds (10 m/s) and mild (Hs < 0.8 m) and moderate (0.8 < Hs < 1.6 m) wave energy conditions. Spectral analysis of the atmospheric and hydrodynamic conditions of two cases of low frequency wind-wave coupling under moderate and less energetic conditions confirms the existence of a coupling mechanism, believed to be due to vortex shedding of the wind around Cape Sacratif, which may affect the characteristic morphology of the beach. This paper presents an interesting approach to studying the nearshore dynamic and morphological behavior by including the interaction between wind and wave energies.

Acknowledgments

[19] We would like to thank the following people who were involved in the field survey: M. Cabrerizo, A. Lazcano, A. Moñino, D. Navidad and J. Sánchez. A. Baquerizo is also acknowledged for her support during the data analysis. Projects BORRASCAS CTM2005-06583, P05-RNM-968 and P06-RNM-1573 supported this research. Significant improvements to the original manuscript were suggested by an anonymous referee.

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