Beach cusps and inner surf zone processes: growth or destruction? A case study of Trafalgar Beach (Cádiz, Spain

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Beach cusps and inner surf zone processes: growth or destruction? A case study of Trafalgar Beach (Cádiz, Spain

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  Beach cusps and inner surf zone processes: growth or destruction? A case study of Trafalgar Beach (Cádiz, Spain) ROLAND GARNIER  1,2 , MIGUEL ORTEGA-SÁNCHEZ  3 , MIGUEL A. LOSADA  3 , ALBERT FALQUÉS  4  and NICHOLAS DODD  1 1 Environmental Fluid Mechanics Research Centre, Process and Environmental Division, Faculty of Engineering, University of Nottingham, Nottingham, UK. 2 Instituto de Hidráulica Ambiental (IH), Universidad de Cantabria, E.T.S. Ingenieros de Caminos, C. y P., Av. de los Castros, s/n. 39005 Santander, Spain. E-mail: roland.garnier@unican.es 3 Centro Andaluz de Medio Ambiente, Universidad de Granada, Granada, Spain. 4 Departament de Física Aplicada, Universitat Politècnica de Catalunya, Campus Nord - Mòdul B4, 08034 Barcelona, Spain. SUMMARY: Large beach cusps (LBC, wavelength of ~  30 m) are intertidal features that can alternately exist in the swash and in the inner surf zone due to tidal sea level changes. They have a larger cross-shore extent (up to 50 m) than traditional cusps. This extent has been explained by a shift of the swash zone during falling tide. The cusps immerse at rising tide and previous studies indicate that surf zone processes are exclusively destructive. Here, the behaviour of large beach cusps in the inner surf zone is investigated by using a 2DH morphological numerical model applied to Trafalgar Beach (Cádiz, Spain). The model results indicate that the inner surf zone processes do not always destroy the cusps but can in fact reinforce them by considering neither the swash processes nor the tidal changes. More generally, in conditions favouring the presence of the LBC the surf zone of a beach can be unstable, leading to the formation of transverse/oblique sand bars that can have characteristics similar to the LBC. Thus, in principle, the LBC could emerge not only due to swash zone morphodynamics but also due to surf zone morphodynamics or a combination of both. Keywords : beach cusps, surf zone, sand bars, instability, beach morphology, beach features, rip currents, wave processes on beaches.RESUMEN: Formas cuspidales de playas y procesos de la zona de rompientes interna: crecimiento o destruc-ción? Aplicación a la playa de Trafalgar (Cádiz, España).  – Las formas cuspidales de grandes dimensiones (LBC, longitudes de onda ~ 30 m) constituyen un sistema morfológico rítmico a lo largo de la playa que tiene una parte que se encuentra alternativamente en la zona de swash (flujo/reflujo) y en la zona de rompientes interna debido a los cambios del nivel del mar. Tienen una distancia de penetración de hasta 50 m, superior por tanto a la de las cúspides ordinarias. Esta elon-gación parece debido a la traslación de la zona de swash durante la marea descendente. En marea ascendente estas estructuras están sumergidas y los estudios previos consideran que los procesos de la zona de rompientes las destruyen. En este trabajo se analiza el comportamiento de estas formas en la zona de rompientes de la playa de Trafalgar (Cádiz) usando un modelo numérico morfológico 2DH. Los resultados muestran que, sin considerar ni los procesos de swash ni el cambio de marea, los procesos de la zona de rompientes no necesariamente destruyen LBC, sino que pueden reforzarlas. De forma más general, en condiciones favorables a la presencia de LBC, se pueden formar barras de arena con características similares a LBC debido a procesos de auto-organización en la zona de rompientes. Palabras clave : cúspides de playa, zona de rompientes, inestabilidad, morfología de playas, estructura de playas, corriente de retorno superficial, procesos del oleaje sobre las playas. S CIENTIA  M ARINA  74(3)September 2010, 539-553, Barcelona (Spain)ISSN: 0214-8358doi: 10.3989/scimar.2010.74n3539  540  • R. GARNIER et al. SCI. MAR., 74(3), September 2010, 539-553. ISSN 0214-8358 doi 10.3989/scimar.2010.74n3539 INTRODUCTIONBeach cusps are a longitudinal regular series of horns and embayments which characterize an undulat-ing shoreline. They have been listed with a large range of length scales: their wavelength λ c  (alongshore spac-ing between two consecutive horns) can range from centimetres to hundreds of metres. This is strongly related to their time scale, which is from minutes to days, respectively, and also to the wave period of the forcing conditions. The mechanisms at the srcin of their formation can also differ, and there is still a large uncertainty regarding this.The largest cusps are also called ‘megacusps’, ‘gi-ant cusps’ or ‘surf zone cusps’ ( λ c ~ 100 m). They are due to surf zone processes and commonly correspond to the shore attachment of transverse/oblique bars. These bars and the associated rip current circulation are very often related to an off-shore crescentic bar sys-tem (Inman and Guza, 1982; Wright and Short, 1984;  Short, 1999; Ortega-Sánchez et al. , 2003; Calvete  et al. , 2005; Castelle et al. , 2007; Garnier et al. , 2008).The smaller cusps ( λ c ~ 1-50 m) are considered standard beach cusps and are supposed to form by swash zone processes (‘swash cusps’). Currently, two different main theories explain their formation (Mas-selink et al. , 1997; Coco et al. , 1999; Almar et al. , 2008): (1) the standing sub-harmonic edge wave theory (Guza and Inman, 1975; Holland and Holman,  1996) and (2) the self-organization theory (Werner  and Fink, 1993; Masselink and Pattiaratchi, 1998; Coco et al. , 2000, 2003, 2004; Dodd et al. , 2008). The edge wave hypothesis can sometimes explain the initial formation of cusps for non-breaking waves, but not the further step of their evolution. Indeed, the presence of finite amplitude cusps theoretically inhibits the edge waves (Guza and Bowen, 1975), and some experimental studies show that cusps can exist in the absence of edge waves (Masselink  et al. , 2004). Moreover, although Ciriano et al.  (2005) observed the coexistence of cusps and edge waves, there was no evidence that edge waves were standing, which is a key requisite of the edge wave mechanism. In this theory the cusps grow as a reaction to a hydro-dynamical instability. The self-organization theory is probably now the most accepted and can explain the entire evolution of the cusps in agreement with the observations, from their formation and their growth by positive feedback between flow and morphology until the saturation of their growth by diffusion proc-esses. In a recent development in line with the self-organization approach, Dodd et al.  (2008) showed that cusps can grow by an apparent hydrodynamical positive feedback mechanism that is intimately linked to bore driven swash, and is enhanced by morphologi-cal feedback.The study of the rhythmic morphology at a sandy beach in Trafalgar (Spain) carried out by Ortega-Sánchez et al.  (2008) distinguishes the smaller cusps ( λ c <20 m) from the ‘large beach cusps’ (‘LBC’, λ c ~ 30 m), based on the fact that the former have a shorter protruding distance S c  (cross-shore extent of a cusp) than the latter. The classification was made using the threshold value of S c =5 m. The small cusps (S c <5 m) appear in the upper beachface and are formed at high tide by swash processes. On the other hand, the large cusps (S c >5 m) can have a protruding distance of up to S c =50 m. This can be explained by the cross-shore shift of the swash zone due to the variation of the tide level (the tidal range is between 1.2 and 3.8 m at the study site). Although the distinction between the small cusps, which are the most frequently observed, and the LBC had not been done before Ortega-Sánchez et al.  (2008), other studies already reported the LBC in tidal environ-ments (Holland, 1998; Coco et al. , 2004; Almar et al. , 2008). The LBC are distinguished from the small cusps as they do not appear exclusively on upper beach; they have a larger scale (wave length) and a larger protrud-ing distance. Moreover the LBC are notable because they sometimes present an oblique orientation with respect to the mean shoreline, and they sometimes migrate alongshore. These distinctions suggest that different mechanisms could be at the srcin of the for-mation of these cusps.Coco et al.  (2004) investigated the mechanisms be-hind the behaviour of cusps that are similar to the LBC observed at Trafalgar Beach. They find that the cusps grow during a falling tide because bays erode more than horns. They reproduce this behaviour as a result of self organization by using a numerical model based on the ballistic theory. Conversely their beach surveys indicate that the cusps wane during a rising tide. Two reasons are given. First, water particles infiltrate pref-erentially in embayments causing deposition. Second, the morphology is smoothed seaward of the swash front. They consider this effect, by including an extra diffusion term. Therefore, at the rising tide, when the previously formed cusps shift into the surf zone, they are damped. Their model results show that the main reason for the reduction of the cross-shore extent of cusps is the surf zone diffusivity rather than the swash processes.However, surf zone modelling studies which do not consider the swash zone processes (Ribas  et al. , 2003; Caballeria et al. , 2002; van Leeuwen et al. , 2006; Gar-nier et al. , 2006) show that not only can diffusion occur in the surf zone of a planar beach, but also instabilities can emerge from self-organization. In particular, the nonlinear 2DH study by Garnier et al.  (2006) reveals the emergence of transverse bars with similar charac-teristics to the large cusps at Trafalgar Beach. These bars are found to be an equilibrium state of the surf zone. One limitation of these surf zone models is the assumption of a rectilinear absorbing wall at the shore-line boundary. Thus, the horizontal shoreline evolu-tion is not taken into account. However, the bed level at the wall is allowed to move vertically and we can  BEACH CUSPS AND INNER SURF ZONE PROCESSES • 541 SCI. MAR., 74(3), September 2010, 539-553. ISSN 0214-8358 doi 10.3989/scimar.2010.74n3539 consider that a horizontal oscillation of the shoreline is induced by the deposition/erosion of sediment next to the wall generating a horn/embayment at the shoreline, respectively. This assumption has been considered to explain the formation of megacusps (Calvete et al. , 2005; Garnier et al. , 2008), which are well known surf zone features.Although Coco et al.  (2004) succeeded in repro-ducing the general behaviour of the large cusps, and therefore the fact that they were damped in the surf zone, a specific surf zone instability study of a cuspate beach deserves attention. Furthermore, some cusp characteristics, such as the oblique orientation and the alongshore migration, were not correctly reproduced with their model. Thus, the main goal of this work is to study the morphodynamic instability of the surf zone of Trafalgar Beach for wave conditions and initial topographies typically measured during the large cusp events but in highly idealized conditions so as to focus on the basic 2DH processes. For instance, the swash zone processes are excluded and the tide level varia-tions are not taken into account. This work will give insight into the possible growth of the LBC in the surf zone as an analogy with the megacusps. It will allow us to identify the morphological and hydrodynamical beach configuration that is favourable for this growth. Actually, a new and more general objective is here pur-sued: understanding the interaction between the swash and the surf zones through beach cusp behaviour.The article is organized as follows. First, the study site and the data used are presented. Then, the rhythmic morphologies and some beach cusps formation events are selected and described. After that, the numerical model and the results are described. Finally, a conclu-sion is given.STUDY SITETrafalgar Beach is located in a mesotidal and swell-dominated coastal environment along the southwest Spanish coast, in the Gulf of Cádiz (Fig. 1). It is an approximately 2-km-long sandy beach with a mean NNW-SSE alignment. The astronomical tide is se-midiurnal, with an average amplitude of 2 m and a tidal range between 0.9 m and 4 m. Waves are predominant-ly from the west and break on the beach within a nar-row breaking zone. A more complete description of the site is given by Ortega-Sánchez et al.  (2008). For the Fig . 1. – Location of the study site and detailed nearshore bathymetry of Trafalgar Beach surveyed in June 2006, with zoom on beach cusps.  542  • R. GARNIER et al. SCI. MAR., 74(3), September 2010, 539-553. ISSN 0214-8358 doi 10.3989/scimar.2010.74n3539 predominant significant wave height, H S =0.75 m, and the mean tidal range, T R =2 m, the relative tidal range is 2.7. Estimating the settling velocity for a medium grain size of d 50 =0.5 mm, and for a mean wave period of T=9 s, the beach-type parameter is W =1.2 (Wright and Short, 1984). This value is representative of a re-flective beach, characterized by low-energy and long-period (swell) waves (Masselink and Short, 1993).Nearshore bathymetry and beach topography meas-ured in 2006 showed that Trafalgar Beach has a width of 40-70 m, increasing towards Trafalgar Cape. It is composed of medium and coarse sand ranging from 0.35 to 1 mm. A plane beach morphology dominates the nearshore zone and no alongshore sand bars were found (Fig. 1). The beach frequently exhibits rhythmic features of different dimensions, with beach cusps being the most common ones (Fig. 1). It can also fre-quently be observed that the geometrical characteris-tics of the cusps vary alongshore, being different close to the cape and far from it. The average beach slope within the cuspate features ranges between 0.06 and 0.10 for the cusp embayments and between 0.10 and 0.18 for the cusp horns. The nearshore beach slope away from the cuspate features ranges between 0.016 near the Cape and 0.026 close to the northern end of the study area.DATA Video images In October 2003 a video-monitoring station based on the ARGUS technique (Aarninkhof and Holman, 1999; Holman and Stanley, 2007) was installed at the Trafalgar lighthouse, 50 m above mean sea level. The station includes 3 video cameras that collect an instan-taneous image (snapshot), a 10-minute time-averaged image (timex) and a variance image every 10 minutes. Hourly images from each day were themselves aver-aged to create a ‘daytimex’, a composite image that reveals the daily mean morphology (Fig. 2).Using the technique presented by Holland et al.  (1997), video images are georeferenced and morpho-logical features can be digitized to estimate their geo-metrical characteristics. The accuracy of this process is typically one pixel. In the present paper we will concentrate on midbeach, so one pixel corresponds to a ground accuracy of 0.25 and 1.4 m in the cross-shore and alongshore directions, respectively. Large beach cusps: general description Geometrical characteristics Ortega-Sánchez et al.  (2008) analysed 2 years of daily time exposure video images from the Argus station to explore the variability of the beachface morphology. Five different morphological states re-lated to the presence or absence of beach cusps and a berm were found: (1) large beach cusps, (2) short-protruding beach cusps, (3) low tide terraces, (4) plane beach berms and (5) plane beaches. The main ‘characteristic’ morphological feature of the large Fig . 2. – Examples of timex images from (a) camera 1 showing the part of the beach closest to Trafalgar Cape; (b) camera 2 looking to the middle of the beach, and (c) camera 3 visualizing the northern part of the beach. 26 January 2005. S b S c A c A b beach cuspssur zoneswas zonexzswash zonesurf zonebeach cusps Fig . 3. – Main beach cusp characteristics for a fixed tide. S c  and A c  are the protruding distance and the amplitude of the part of the cusps that is in the swash zone, i.e. these parameters are measured at Trafalgar Beach. S b  and A b  correspond to the surf zone part of the cusps, i.e., where cusps can be interpreted as bars (they are model results). Notice that S c  and A c  are measured at low tide, and S b  and A b  change with the tide level.  BEACH CUSPS AND INNER SURF ZONE PROCESSES • 543 SCI. MAR., 74(3), September 2010, 539-553. ISSN 0214-8358 doi 10.3989/scimar.2010.74n3539 beach cusps is the protruding distance S c  (Fig. 3). It is defined as the cross-shore span of a horn, so that, if the angle between the cusp horn and the coastline normal is β c , the 2D (horizontal) extent of a cusp is S c  /cos( β c ) (Fig. 4). S c  is always larger than 5 m, with some measurements showing values up to 50 m. Large beach cusps (LBC) correspond to the predominant beachface morphology and are present 60% of the time. LBC are located across the intertid-al zone and during high tide waves can break within the embayments. Thus, cusps seem to be interacting with both surf and swash processes. Several of their characteristics are reminiscent of surf zone rhyth-mic features that appear by self-organization (Ribas  et al. , 2003; Garnier et al. , 2006). The first of these are their length scale, i.e. their protruding distance, their wavelength λ c  (or spacing) and their amplitude Fig . 4. – (a) Plan view of the beach showing LBC morphology, 26 January 2005. (b) Cross-shore profiles, 8 May 2006. Fig . 5. – Snapshot of the cusps during a tide excursion, 7 January 2005. Left: timex images from camera 2. Right: Plan view after rectification.
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