Journal of Coastal Develpopment ISSN : 1410-5217 Volume 16, Num er 2,Fe ruary 2013 : 158-186 Acrredited : 83/Kep/Dikti/200, Original paper NEW EMPIRICAL FORMULAE OF UNDERTOW VELOCITY ON MIXED AND GRAVEL BEACHES Christos antoniadis External Research Fellow in Port Engineering in Civil Engineering Department of Democritus University of Thrace Xanthi 67100 Greece Received : February 3 2013; ,ccepted: February 27 2013 ABSTRACT This paper reports a series of 3-dimensional physical model tests to measure cross-shore current data, generated by oblique wave attack, along gravel and mixed beaches with a uniform slope and a trench. Coastal managers and coastal engineers are beginning to give attention to gravel and mixed beaches due to the fact that they are two of the most effective natural sea defences.There is a need, from a scientific and coastal management perspective to have a deeper understanding of how gravel and mixed beaches operate.The studies described in this paper aim to investigate the behaviour of the undertow velocity on mixed and gravel beaches. xisting formulae have been used to predict the experimental results and new equations for predicting the undertow velocity under these conditions are proposed. The new empirical formulae predict time- and depth-averaged undertow and are based on a nonlinear regression of a modification of the Grasmeijer#s and Ruessink#s model where the %ones where divided based on the related distance of the point of interest and the breaking point. Verification with large-scale experiments showed that the new formulae predicted well the undertow velocities on mixed and gravel beach with trench and uniform slope. Keywords: gravel mixed beach wave-induced currents trench wave brea.ing undertow *Correspondence: Phone: /30- 6070701011; Fax: /30- 2231062030; E-mail: cantoniadis704hotmail.com INTRODUCTION ,s the obli6ue waves brea. to the shoreline they are not constant over depth 7Coastal two mean currents are generated flowing Engineering Manual 20038. The main parallel 7long-shore currents8 and straight characteristic of the cross-shore current is the normal 7cross-shore currents8 to the coast. existence of the two-dimensional circulation in These two mean currents can be considered as the surf zone .nown as >undertow current? components of a continuum flow field from which flows in the seawards direction from the which the resulting wave-induced mean current shoreline. This current is directed offshore on structure is illustrated in Fig. 17Svendsen and the bottom balanced with the onshore flow of Lorenz 10108. These nearshore currents in water carried by the brea.ing waves. Closer to combination with the stirring action of the the water surface the resulting current is in the waves are important for the sediment transport onshore direction. The undertow current may and therefore are significant factors in be relatively strong being almost 1% to 10% of morphological changes. Conse6uently they the wave celerity 7 8 near the bottom. are of great importance for managers of coastal The undertow is the result of an imbalance areas coastal engineers and marine geologistics between the excess momentum flux induced by 7Visser 10018. the brea.ing wave the mass flux of the carrier Cross-shore currents are related to the wave and the surface roller concentrated on the mass compensation under brea.ing waves and surface layer between the wave crest and Journal of Coastal Develpopment ISSN : 1410-5217 Volume 16, Num er 2,Fe ruary 2013 : 158-186 Acrredited : 83/Kep/Dikti/200, trough and the hydrostatic excess pressure Table 1 and Table 28 was used to examine caused by the local mean water level gradient wave brea.ing formulae for obli6uely incident 7setup8 which becomes predominant below waves on mixed and gravel beaches wave trough level 7Ariand and Bamphuis 7,ntoniadis 20008. 10038. The undertow can be considered as an ATERIALS AND ETHODS explanation of bar formation 7in the surf-zone M M close to the wave brea.ing point8 observed under wide range of conditions on beach The xperiment profiles in the laboratory and in the field 7Ariand and Bamphuis 1003; Svendsen 1013a The experiments were carried out in the three- and Deigaardet al. 10018. dimensional wave basin located at Franzius- The first 6uantitative analysis of the Institute 7Marienwerder8 Dannover University. undertow was by Dyhr-Cielsen and Sorensen The experiments ran for nearly 70 days and 710708. Furthermore the undertow profile is were underta.en for a beach model which solved by Dally and Dean 710138 Svendsen consisted at first of gravel sediment and 71013a8 Dansen and Svendsen 710138 Stive secondly of mixed sediment. The beach model and Eind 710138 Svendsen et al. 710178 and with dimensions of 1m x 7m x 0.7m was set up Svendsen and Auhr Dansen 710118. in the middle of the wave basin. It was open to To extend our understanding within the the side from which the generated waves were approaching. The beach model was oriented in coastal environment a 3-dimensional physical such a way that waves generated by the wave model 7see paddle were always approaching it with an angle of 120 7Fig.28. Aeach bathymetry consisted of a uniform slope beach 7straight- line parallel contour8 and a trench 7curved contour8 with a width of 2m as shown in Fg.3. The location and the dimensions of the trench in the physical model would not have any significant impact in the profile changes of the beach with the uniform slope. Data Collection The experiment comprised of ten tests which were mainly focused on the wave current Fig. 2 measurements across the gravel and mixed beach. The measurements of the wave driven current were carried out with an ,DV. The measurements of currents started 30 minutes after the first wave was generated for both regular and random waves. These 30 minutes were sufficient to eliminate bed level changes during the measurements which could influence the currents. ,t that point an e6uilibrium state was reached in which no sediments were moving. Dowever for the mixed beach the sand was moved slightly after the 30 minutes period without any sufficient influence in the measurements. The currents Fig. 3 were measured in time at three cross-shore sections of the beach. The first was at the Journal of Coastal Develpopment ISSN : 1410-5217 Volume 16, Num er 2,Fe ruary 2013 : 158-186 Acrredited : 83/Kep/Dikti/200, curved beach section and the other two at the Test 2 where the highest wave conditions of the straight beach section for all three space experiment occurred. directions Vx Vy and Vz. These sections are Rip currents are usually confused with the shown as lines in Fig.3. Velocities Vx and Vy undertow. ,s the waves move to the shoreline were considered positive when heading towards produces setup. Aecause of the inclination of the positive direction of x and y axes 7Fig.38 the water level the setup water is essentially while the vertical velocity Vz was considered piled up against the shoreline in an unstable positive when heading upwards. The condition. If this unstable condition exists measurements had reached the maximum of - along a barred coast or along some of the 3.7m at y-direction due to the fact that the steeper coasts the setup produces seaward ,DV can wor. only at submerged sections. flowing currents that are rather narrow and that Despite that the number of current velocity create circulation cells within the surf zone. measurements that was ta.en was satisfactory. These narrow currents are called rip currents. Current velocity measurements were carried Ehen wind and waves push water towards out at various levels along the z direction. ,t the shore the previous bac.wash is often each level the current velocity measurements pushed sideways by the oncoming waves. This were ta.en over a period of 60 seconds. water streams along the shoreline until it finds Observations for regular waves started at the an exit bac. to the sea. The resulting rip current surface and deepened with a constant 2cm is usually narrow and located in a trench. In integral until the maximum point was reached. general while a common misconception is that The maximum point was the point at which the a rip occurring under the water instead of on ,DV could ta.e logical measurements usually top G an undertow G is strong enough to drag that was between 2 and 10cm above the bed people under the surface of the water; the level. The deepest point of measurement was current is actually strongest at the surface. In 32cm below water surface. some areas rip currents will persist during low- The same procedure was followed for to moderate- energy wave conditions and then random waves but with a 10cm integral. The during high-energy wave conditions the rips deepest point of measurement for random will lose their definition and undertow will be waves was 30cm below the water surface. This primary mode of seaward return of water from procedure allowed an estimate of the vertical unstable condition of setup. structure of the time-averaged velocity and a Though it has to be mentioned that at more accurate determination of the depth- some locations near the bed the reverse averaged current velocities. The depth- current is replaced by a shoreward current. This averaged current velocity V was determined as: behaviour of currents is carried out from Test 3 to Test 10 7especially with uniform slope >Lines 2 and Line 3?8. The shoreward direction of these currents also affected the sediment Data Analysis transport as the sediment showed to be slightly moved shoreward at the locations influenced by The cross-shore currents of each line and for each test that measured from the experiments these currents.