Experimental simulation of sandy beaches under waves and tides: hydro-morphodynamic analysis

Transcription

1 Experimental simulation of sandy beaches under waves and tides: hydro-morphodynamic analysis 1791 Experimental simulation of sandy beaches under waves and tides: hydro-morphodynamic analysis Alaa Khoury, Armelle Jarno-Druaux and François Marin Laboratoire Ondes et Milieux complexes, UMR 6294 CNRS Université du Havre, BP 540, Le Havre cedex, France ABSTRACT Khoury, A., Jarno-Druaux, A., and Marin, F., Experimental simulation of sandy beaches under waves and tides: hydro-morphodynamic analysis Proceedings 12 th International Coastal Symposium (Plymouth, England), Journal of Coastal Research, Special Issue No. 65, pp , ISSN Numerous studies have been carried out on sandy beach morphology; however, the physical processes which govern beach morphodynamic are still not well understood, despite the significance of this subject in view of the direct applications for coastal erosion. The present work brings a contribution to the study of these processes from well controlled tests carried out in a 10-m-long and 0.49-m-wide wave flume with macro and mega-tidal regime simulations. The tests were carried out with very fine or fine sand of relative density s=2.65. The incident waves and the free surface in the shoaling zone were measured with resistive probes. The wave breaking height and the free surface in the swash zone were recorded with an optical method. The temporal evolution of bottom profiles was obtained using an acoustic method. Intertidal bars were generated; such bars were previously not observed in physical modeling to the authors knowledge. Present experimental results are compared with field observations. Formation processes of intertidal bars are analyzed; we show in particular the significant effect of the relative tide range, of waves asymmetry, and of subtidal bars on these processes. Small local variations of the beach profile in the surf zone exhibit significant outcomes on the runup. ADDITIONAL INDEX WORDS: Wave flume, Morphodynamics, Intertidal bar, runup. INTRODUCTION Sand beach profile dynamics has received extensive attention because of its direct application for coastal erosion, in particular in the context of climate changes, elevation of the sea level, and growing population density in the coastal zone. Very few laboratory studies deal with the case of waves and tides and even less of the macro-megatidal beaches such as encountered on the Normandy coast, France (Levoy et al., 2000).Tides are directly involved in the formation of intertidal bars. As stated by Masselink et al. (2006) in a review paper, tide plays a morphological role shifting the wave processes at high and low level and imposing different action durations according to the different processes. On the other hand, the tides do not play a significant role on the formation of the subtidal bar, which is controlled by wave processes. The subtidal bar is affected by deeper water processes - in the shoaling and breaking zones - than the intertidal bar. Intertidal bars are distinguished on the base of morphological criteria. Three types of bars are identified: slip-face bars, low amplitude ridges and sand waves (Masselink 2006). Intertidal bars have received less attention than subtidal bars in spite of their major role for beach stability during storm events. Slip-face bars, also referred to as swash bars (e.g. Greenwood and Davidson- Arnott, 1979, Carter 1988), are often fronted by one or more subtidal bars (Aagaard et al., 1998 a et b, Masselink et al., 2011). Two processes of formation are considered. According to Kroon (1994), a small ridge is formed due to the deposition of sediments DOI: /SI received 07 December 2012; accepted 06 March Coastal Education & Research Foundation 2013 in the low tide area after storm conditions and during mild conditions following the storm. It subsequently develops into an intertidal bar. Another scenario is proposed with an onshore migration of a breaker bar formed in the subtidal zone (Hayes & Boothroyd 1969, Davis et al., 1972). A few field studies deal with the morphodynamic feedback on bar build-up and destruction (Masselink et al., 2011). The swash zone, located at the interface between land and sea defines a region particularly sensitive where wave runup contributes to the erosion/accretion of the coastline (Holland et al., 1995). It is shown from field experiments that tides may strongly modulate swash oscillations on an intermediate barred beach under mild wave conditions (Guedes et al., 2011). In addition, swash hydrodynamics is dominated by incident wave frequencies at high tide whereas energy in the band of infragravity frequences increases at low tide due to increasing dissipation by breaking over the bar. Furthermore, Iribarren number calculated with the offshore parameters, used to scale the amplitude of incident swash oscillations (e.g., Miche 1951, Holman and Sallenger, 1985, Stockdon et al., 2006), is insufficient to predict accurately the runup for complex beach profiles subjected to tides (Stockdon et al., 2006, Guedes et al., 2011). During field studies, the identification of key processes is difficult due to the complex interactions between beach morphology, waves and tides in uncontrolled environmental conditions and laboratory investigations are still required to study selected processes. We study the morphodynamics of sandy beaches under waves and tides from well controlled tests carried out in a wave flume with mega- and macro-tidal regime simulations. The tides play a significant role in different

2 1792 Khoury, et al. processes. The first part of the paper consists in an exploratory study to identify tides actions. Then, we consider two aspects. We analyze the process of formation of an intertidal bar in high tiderange conditions and compare the bar formed with field data. The tides are also involved in the dynamics of swash zone. We focus on the high tide phase for a beach exhibiting an important erosion in the upper beach zone. The variations in the runup signal are analysed through the evolution of the free surface and beach morphology in the breaker and surf zones. EXPERIMENTAL SET-UP AND TEST CONDITIONS The experiments were carried out in a 10 m long, 0.5 m high and 0.49 m wide wave flume at LOMC laboratory, University of Le Havre (France). Based on the Froude similitude for the waves and tides generation, the length and temporal scales may be considered to be 1/100 and 1/10, respectively. Saleh Salem et al. (2011) have shown that the typical differences between the beach morphologies in reflective and intermediate regime (Masselink and Short, 1993) are well reproduced in this flume. The 5-m initial long beach profiles were entirely made of natural sand. Tests were carried out with very fine (D 50 =111 microns) or fine sand (D 50 =173 microns) of relative density s=2.65. Initial profiles were plane or barred. The temporal evolution of bottom profiles was obtained using an acoustic method. Seatek ultrasonic ranging system with a linear array of twelve transducers mounted on a movable carriage is employed to provide 3D bed profiles. The tests were performed in the intermediate regime according to the Masselink and Short (1993) classification based on the values of the dimensionless fall velocity and of the relative tidal range (RTR). The values of the Dean number Ω=H b /WsT where H b is the breaking wave height, Ws the sediment fall velocity, and T the wave period have been varied from 2 to 5 for present tests. The present tests conditions are given in Table 1 with the previous ones from Saleh Salem et al. (2011). The equilibrium profiles for Tests 1, 3, 5 and 7 are the initial profiles of Tests 2, 4, 6 and 8, respectively. We simulated complex beach profiles with subtidal bars. The duration of each test was sufficiently long to reach equilibrium profiles. The equilibrium state is defined using a criterion based on the velocity of bottom profile variation V f (Kamalinezhad, 2004; Saleh Salem et al., 2011). We consider that the equilibrium state is reached when the mean beach profile velocity tends towards a fixed low value (< 2 mm/hour). Regular waves were generated by an oscillating paddle. The incident waves were measured with two resistive probes and analyzed by the method of Goda (Goda et al., 1976). Six other probes allowed a spatiotemporal analysis of the free surface in the shoaling zone. The cross-shore analysis of the hydrodynamic characteristics of the wave (asymmetry, height, non-linearity,) is very important for the interpretation of the morphological results. The horizontal and vertical wave skewnesses (sk v and sk a ) measuring the asymmetry about horizontal and vertical axes were estimated from the third-order moment of the free surface elevation η(t) (Nielsen, 2006) and its temporal derivative a= η/ t (Hsu et al., 2006): 3 2 sk (1) v 3 / 2 a a sk a (2) 3/ 2 2 a a where <:> the brackets denote averaging. The free surface and bed level were video recorded in the breaker, surf and swash zones during a tidal cycle using a digital video camera situated aside the channel (Fig.1). The resolution is 0.5 mm/pixel. The length of the observation field is 400 mm. Numerous authors have tried to connect the type of breaking with the hydrodynamic characteristics and the local slope. Galvin (1968) used the numbers of Iribarren ζ 0 and ζ b respectively offshore and in the breaker zone to describe the various types of breaking. The parameter ζ 0 is also used for the run-up. ζ 0 and ζ b are given by: tan tan 0 (3) b (4) H L L 0 0 where tanβ is the beach slope and H 0 and L 0 are deep water wave height and wave length, respectively. For present tests, a precise estimation of the wave breaking heights was obtained from the videos. Figure 1. Image video of the surf and swash zones (Test 6). H b 0 3 Table 1. Test conditions ( Tests 1 to 4, Saleh Salem et al (2011) ; Tests 5 to 8, present tests) Test number H 0 (cm) d (cm) L 0 (m) D 50 (µm) T (s) Ω TR (cm) RTR Initial profile (B: 1 bar; P: plane) P B P B P B P B

3 Experimental simulation of sandy beaches under waves and tides: hydro-morphodynamic analysis 1793 Using a pump, the mean water level was changed to simulate a 12 hours tidal period (72 min at the flume scale) with a 6-m tidal range TR (Tests 1 to 4) and a 10-m tidal range (Tests 5 to 8). Fig. 2 shows a schematic description of the temporal variation of the mean water level measured with a resistive probe in the presence of the beach. ranges. An initial subtidal bar was present for both tests. The equilibrium profiles exhibit an intertidal bar for Test 8 (very fine sand, Fig. 4), not for Test 2 (fine sand, Fig. 5). Tests 2 and 4 have been carried out with different values of the Dean number but with the same low tidal range. Figure 5 shows that the increase of the Dean number for Test 4 compared to Test 2 does not lead to the formation of an intertidal bar. The tidal range appears to be a significant parameter for the generation of intertidal bars; the processes involved in the formation of intertidal bars are considered in the next section. Figure 2. Temporal variation of the mean water level. The dashed and continuous lines refer to a 6-m and 10-m tidal range simulation, respectively. E denotes the equilibrium profile before the tide and L and H the Low and High tide levels. The associated number indicates the number of reproduced tidal cycles. Figure 4. The beach profiles at the equilibrium state for Tests 7 and 8. QUALITATIVE OBSERVATIONS For this part of the study, we varied different hydrodynamic parameters (forcing, tidal range (TR), water level (d)), sedimentary parameters (grain size), and the initial profile to identify the effect of the tides on the beaches equilibrium morphology. An increase of the tidal range for a fixed value of the Dean number leads to a strong erosion of the upper part of the beach as shown on Fig. 3 for Tests 5 and 6, where the high position of the breaking zone at high tide for Test 6 is exhibited. Figure 5. Comparison between the equilibrium profiles obtained for Tests 2 and 4. Figure 3. The beach profiles at the equilibrium state for Tests 5 and 6. The small and the large arrows designate the positions of the breaking zone at the equilibrium state for Low Tide Level (L.T.L.) and High tide Level (H.T.L.), respectively. Test 2 and Test 8 have been carried out with the same wave conditions, but with different sediment sizes, and then with different values of the Dean number and with different tidal DISCUSSION Formation of an intertidal bar Let us study the formation mechanism of the intertidal bar observed for Test 8. The test conditions lead to an intermediate beach with a relative tidal range of 2.6 and a Dean number of 4.9. The initial beach profile is barred. The influence of the tides is rapid and significant morphological changes are observed on the beach profile since the first tidal cycle (Fig. 6). It results in an erosion of the subtidal bar on its offshore face (Fig.7 Δh L1-E curve - region from x=-90 mm to x=+430mm) with a decrease in the local slope from 0.13 to 0.09 in the breaking zone at low tide. Part of the sediments removed from the subtidal bar is transported onshore due to wave asymmetry in the surf zone, and deposited in the swash zone by swash processes around low tide level (Fig.7 Δh L1-E curve from x=2250 to x=2560 mm). At high tide, an erosion of the beach takes place in the breaking zone, and sediments are transported further up the beach in the surf zone

4 1794 Khoury, et al. (Fig.7 Δh H1-L1 curve from x=2260 to x=2880 mm). A small ridge is formed. It develops into an intertidal bar that grows and moves onshore during the successive further cycles of tide. After six tidal cycles the bar has reached its maximum size and did not move anymore (Fig. 8). The upper part of the beach is protected by the presence of the bar as shown in Fig. 4. processes both involved in the growth and onshore migration of the bar. Figure 8. Evolution of the migration speed of the intertidal bar during the tide simulation. V L and V H designate the velocities calculated between successive low tides and high tides, respectively. Figure 6. Temporal evolution of beach profile for Test 8. The instants E, L1, H1, L6, H6 and E6 are defined on Fig. 2. Hydrodynamics and beach morphology in the surf and swash zones Let us focus on the swash zone for the equilibrium state of Test 6 characterized by a non-marked subtidal bar causing little dissipation of the incident wave at high tide and an upper part of the beach severely eroded (Fig. 3). The relative wave height H/h across the crest of the bar does not exceed 0.4 and waves shoal till they break at a short distance from the shoreline. Wave runup R(t) is defined as the dynamic elevation of the vertical water level above still-water level due to wave action. It is commonly decomposed into a quasi-steady super elevation (setup) and a dynamic evolution of the water level about such super elevation (swash) (Guza and Thornton, 1982). Figure 7. Net change Δh of the beach level after one tidal cycle. The instants E, L1 and H1 are defined on Fig. 2. The bar builds up and moves during the entire tidal cycle. It grows and moves faster during the rising and high tides through surf processes than during the ebb and at low tides through swash processes (Fig. 8). The onshore migration rate of the bar is m per day at the channel scale, or 1.50 m per day at full scale. This value is comparable to the values measured in-situ (Owens and Frobel 1977, Kroon 1994, Aagaard et al., 1998 a). At the end of the sixth tidal cycle, the bar is pronounced with an elevation calculated between the trough and the crest equal to m (channel scale), or 2.50 m at full scale. It is characterized by a steep landward slope and a gentle seaward slope (3.5 ). The morphology and morphological response of the intertidal bar formed in the channel is similar to the slip-face bar type described from field experiments (Owens and Frobel 1977) in a review paper by Masselink et al., However, the process of intertidal bar formation described herein differs slightly from the one proposed by Kroon (1994). In particular, wave conditions generated in the channel are fixed and do not correspond to storm conditions. Furthermore, the slip-face bar is fronted by a subtidal bar which participates in the formation of the bar. In field study, the role of subtidal bars in the formation of intertidal bars has not been identified. It is also shown that the swash zone at low tide coincides with the surf zone at high tide. Consequently, the nearshore bar is alternately exposed to swash and surf zone Figure 9.Evolution of the runup for Test 6 during the high tide stage. The dotted line represents the still water level at high tide (h=280 mm), S : static setup, S ~ : dynamic setup, dark and light coloured diamonds refer to swash signal and dynamic setup, respectively. The runup elevation time series has been extracted from videos during the high tide when waves are the most energetic. The results are plotted on Figure 9 where we represent one second (25 points spaced on one wave period) of the high tide phase every thirty seconds. The static setup S has been calculated averaging the runup elevation time series on the total high tide phase. Fluctuations in the wave setup occur during the high tide defining a dynamic component of the wave setup S ~. This component is calculated for each wave cycle acquired. Although the equilibrium of the beach is reached at the tidal cycle scale after six cycles, substantial changes are observed in the runup signal during the 10

5 Experimental simulation of sandy beaches under waves and tides: hydro-morphodynamic analysis 1795 Table 2. Hydrodynamic and morphologic parameters in the breaker, surf and swash zones. Beginning of high tide Middle of high tide End of high tide offshore H b (m) / X b (m) / / / 3.69 Breaker zone Beach slope b H s (m) Beach slope Surf zone s sk v and sk a - surf zone, x=3.80 m 1.43 / / / 1.08 sk v and sk a - surf zone, x=3.90 m 0.79 / / / 1.27 Swash zone Beach slope sk v and sk a 0.01 / / / minutes of high tide phase at the channel scale. The dynamic setup oscillates between +3.5 mm and -3.5 mm and the swash also undergoes significant changes in amplitude. It can be noted that low level values of the dynamic setup are associated with high values of the amplitude of the swash and vice versa. tide. It first increases before decreasing. In order to understand the origin of the observed variations, we quantify the hydrodynamic and morphological changes occurring in the surf and swash zones. To this end, we calculate local slopes and the Iribarren numbers in the breaker, surf and swash zones at the beginning, middle and end of the high tide with characteristics of breaking waves (position and height). Values of the asymmetry coefficients sk v and sk a are also given in Table 2 in the surf and swash zones. This Table is completed by Figure 11, where the evolution of waves in the surf and swash zones is depicted with the beach level in the surf zone. Figure 10. Powerspectra of the swash signal during high tide for the beginning (BHT),middle (MHT) and end (EHT) of the high tide phase (log-log scale). The high tide phase has been segmented in three parts of 40 seconds at the beginning, middle and end of the phase. The energy associated with the swash signal is calculated for each part of the phase and powerspectra are presented in Figure 10. The major part of the energy in the swash spectra is contained at the incident frequency. The energy is not constant during the phase of high Figure 11. Evolution of the beach level and water level in the surf and swash zones during the high tide stage. The origin of the elevations is the level of the beach toe. The evolution of the beach morphology occurs mainly at the beginning of high tide. Overall, the adaptation of the beach profile causes a decrease of wave heights in the breaking, surf and swash zones. Characteristics of breaking change with an increase of the

6 1796 Khoury, et al. bed slope, a decrease in wave height and a slight offshore shift of the breaking point. After breaking, the wave propagates in the surf zone where it deforms and its energy is partly dissipated. The wave skewnesses vary significantly during the high tide (Table 2) and undergo rapid spatial variations between the two studied positions spaced by a short distance of only ten centimeters in the surf zone. There is a significant erosion caused by the breaking at x=3.810 m where x=0 corresponds to the toe of the beach at the beginning of the test. The wave is less asymmetric and the coefficient sk v slightly decreases with increasing values of the time. The vertical asymmetry of the wave increases rapidly when the wave approaches the shore and the typical sawtooth shape is found at x=3.930 m. The velocity skewness induces onshore transport (Hsu et al., 2004). This contribution to transport is balanced by the seaward undertow transport (Marino-Tapia et al., 2007). Then, the wave reaches the swash zone. The bed slope increases at the beginning of high tide causing an increased amplitude of the runup. The wave is horizontally symmetric during the high tide but vertically, the runup undergoes great variations. The wave vertical asymmetry varies from sk a =0.69 to sk a =-0.64 before reaching a very low value at the end of the high tide phase. During the same time, the beach profile reaches a morphological equilibrium. Iribarren numbers ζ b and ζ s calculated with the local slopes and wave heights in the breaker and surf zones evolve during the high tide due to local changes in the wave height and beach slope. These local changes in beach morphology and wave characteristics induce the observed significant changes in the characteristics of the runup during the high tide. CONCLUSION Beach cross-shore dynamics are studied from a physical modelling in a wave flume under waves and tides. We investigated the conditions for the formation of an intertidal bar. The offshore incident wave energy, the initial beach profile, and the relative tidal range act on the conditions of formation of the bar. We reproduced in our modelling the formation of an intertidal bar identified as a slip-face bar following the classification of Masselink et al., The bar is alternately exposed to swash zone processes at low tide and surf zone processes at high tide. The intertidal bar is fronted by a subtidal bar involved in its formation. A thorough study of the high tide phase shows a high sensitivity of the runup to small local variations of the beach in the breaking and surf zones. ACKNOWLEDGEMENT Financial support by the Haute Normandie region ( ELIT project) is gratefully acknowledged. LITERATURE CITED Aagaard, T., Nielsen, J., Greenwood, B., 1998a. Suspended sediment transport and nearshore bar formation on a shallow intermediate state beach. 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