VELOCITY FIELD UNDER PROPAGATING WAVES


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1 VELOCITY FIELD UNDER PROPAGATING WAVES OVER A SUBMERGED HORIZONTAL PLATE AND INDUCED FORCES Arndt Hildebrandt and Torsten Schlurmann FranziusInstitute for Hydraulic, Waterways and Coastal Engineering, Leibniz Universität Hannover, Hannover Abstract: Under the key assumption of linearity, the mathematical solutions for progressive smallamplitude water waves provide the basis for applications to numerous problems. It enables to describe and quantify most phenomena that are related to engineering interests having a bearing on coastal and ocean design. However, some of those essential postulations are unfounded when dealing with water waves being significantly transformed due to interaction with structures. Complex effects like wave breaking, air entrainment or turbulence may become dominant and encourage applying nonlinear models for an appropriate simulation. Artificial reefs made of a horizontal submerged plate are typical structures with high wave interaction. In this paper we describe processes on the basis of physical tests in a wave flume, which support the validation of numerical models. I. INTRODUCTION Artificial reefs belong to the passive shore protection installations and they provide the preferred choice for natural areas of coastline. They gain more and more attention from public authorities and consulting engineers, because traditional solutions with breakwaters are perceived as troublesome due to the considerable height above the mean sea level acting as blocked obstructions. In most cases, the construction of massive breakwaters weakens or even stops the near shore currents and thus the circulation of water and oxygen between the open sea and protected areas. This leads to disturbed spawning grounds and plant growth. A special type of an artificial breakwater is build with a horizontal plate. The major advantages of a construction like this are the fully submerged structure and the porous profile for water circulation. Furthermore, the traffic of small boats is not limited by the structure. The wave damping effect by the submerged plate results in reduced wave heights with the generation of higher harmonic waves behind the artificial reef. The wave damping in offshore areas weakens the incoming sea state, which enables the design of less expensive active coastal protection strategies/ facilities. Generally, submerged breakwaters induce only a fractional wave breaking, due to the characteristic of the energy distribution under progressive waves. The main part of the energy is located in the upper water body right beneath the surface. The wave height is reduced to nearly 50% by a horizontal plate at a submerged location at 10% of the water depth [1]. For most cases the fractional wave breaking is completely sufficient and also intended for beach accumulation purposes by reduced waves carrying sand to the shoreline without producing scour behind the structure. In addition to other parameters the wave damping depends on the ratio of wavelength to the length of the horizontal plate. For this reason submerged breakwaters are also known and used as a filter because of different damping effects on wave forms. Figure 1. Submerged artificial reef along the southern shore of the Dominican Republic near Bayahibe ( II. EXPERIMENTAL SETUP The physical tests were carried out at the FranziusInstitute for Hydraulic, Waterways and Coastal Engineering in a 100m long wave flume with a width of 2.2m and constant water depth of 0.60m. Due to the limited capacity of the force gauges and for illumination purposes, the main cannel width was reduced to 0.505m by applying a training wall as illustrated in fig. 2. The training wall is 5m long and extends 2.56m in front of the plate and 1.64m behind the plate. The suspended horizontal plate is 0.80m 421
2 long and was supported by three vertical columns with force gauges at each head (fig. 3). The transparent measuring setup was positioned 26m behind the wave maker levelled with the window section of the wave flume. The training wall consists of a dark coating to achieve a high contrast with the seeding material for the Particle Image Velocimetry (PIV) method [2]. Four wave gauges were positioned along the wave flume with the following distances to the leading edge of the submerged plate: m (wave gauge 1) m (wave gauge 2) 00.00m (leading edge of horizontal plate) m (trailing edge of horizontal plate) m (wave gauge 3) m (wave gauge 4) The horizontal plate was fixed between the sidewalls for the PIVtests to prevent movements of the plate and to eliminate disturbing currents along the longitudinal side of the plate. The tests for the estimation of the vertical forces were performed with a free suspended plate. However, 2mm of space had to be adjusted between the sidewalls and the plate, to prevent the influence by friction and to minimize the influence by currents alongside the slots. Nine different waves with H = wave height and T = wave period were generated to measure the vertical forces (force) and to investigate the flow field with the PIV method as listed below: Figure 2. Crosssection of experimental setup H=5cm H=10cm H=15cm T=0.96s Force Force / PIV Force T=1.60s Force / PIV Force / PIV Force / PIV T=2.24s Force Force / PIV Force For all tests three relative submerged depths t/d (with t= submerged depth and d= water depth) were investigated with t/d = 0.1, 0.2 and 0.3 (fig. 4). Furthermore, all tests with a wave period T = 2.24s were sampled with 14.3Hz, for T = 1.6s with 20Hz, and for T = 0.96s with 33.3Hz, resulting in a fixed number of 32 samples per wave period. Note that fig. 5 is taken from additional tests by the author at the University of Wuppertal. A similar experimental setup was used with the same PIVcamera and a transparent wave flume. Figure 3. Sideview of submerged plate Figure 4. Relative submerged depths t/d = 6cm/60cm = 0.1, 0.2 and
3 III. VELOCITY FIELD AND VORTEX PATTERNS The PIVMethod was used for the investigation of the flow patterns at the trailing edge of the submerged plate, for this is the location of vortex shedding and wave breaking. PIV offers a nonintrusive method to measure the flow field simultaneously along the horizontal plate in a certain area. Two seeding materials of polyamide spheres were used for the tests with diameters smaller than 1mm and with diameters of 2mm. All movies were recorded with 500 frames per second and a maximal length of 16 seconds. The interrogation areas of the frames were correlated with MatPIV v developed by J. K. Sveen of the Department of Mathematics at Oslo University [3]. In the following, the observed vortex patterns and the resulting flow fields will be presented, together with investigation results of the varied parameters relative submerged depth (t/d), wave height (H), and wave period (T). Figure 6. Vortex pattern for relative submerging depth t/d=0.1, wave height H=5cm and wave period T=1.6s Figure 7. Vortex pattern for relative submerging depth t/d=0.3, wave height H=10cm and wave period T=1.6s Figure 5. Snapshot of the flow field before (a) and during (b) wave breaking for a wave period of 1.0s, wave height 4cm and relative submerged depth 0.2. All investigated wave heights and wave periods show an initial generation of a vortex pair shortly after the flow reversal of the wave. The vortex ( A, Fig. 7) develops during the reversing current at the trailing edge of the plate and gains intensity until the wave breaking sets in (Fig. 6, 7). The developing time of the vortex for all investigated waves is approximately 3040% of the wave period. Fig. 5a shows the velocity field for a wave period of 1.0s and 4cm wave height during the flow reversal under the wave trough. The formation of the vortex can be seen at the trailing edge of the plate. The current velocity for the vortex supply averages 15cm/s and becomes more intensive with values higher than 20cm/s directly before the wave breaking, which is visible by the upward pointing velocity arrows over the plate in fig. 5a. With increasing wave height H and submerging depth t, the vortex becomes more intense. This is seen in Fig. 6 with a generated vortex diameter of 5cm for H=5cm and t=6cm, while a vortex diameter of 12cm is found for H=10cm and t=18cm (Fig. 7). 423
4 For small values of submerging depth, t/d=0.1, the vortex is dragged to the surface, whereas a downward movement is observed for the relative depth t/d greater or equal to 0.2. The downward directed path of the vortex relates to the wave breaking near the trailing edge of the plate, which induces an impulsive force by the flow of the plunging water mass. Fig. 5b illustrates the flow field under the breaking wave and indicates jets with velocities exceeding 30cm/s. The plunging water mass encounters the relatively calm water body behind the plate and splits up in a major horizontal direction and a minor downwards directed part, which forms the motion of the vortex. The resulting current above the horizontal plate generates a new vortex pair at the edge, indicated with B in Fig. 7. The developing vortex is enforced by the following flow reversal of the wave trough, which sets in and leads to a circulating current under the plate ( C, Fig. 7). This vortex sheds with the initiation of the next vortex, which is the result of the circulating current, as described in the first place. The intensity of the vortex depends on the approaching wave height and the described vortex patterns are repeated. The relative submerged depth has significant influence on the position of wave breaking. It was found that the waves break in the middle of the plate for t/d values of 0.1 (Fig. 6) and for relative submerged depths of t/d = 0.3 the wave breaking takes place behind the trailing edge (Fig. 7). This has direct influence on the vortex pattern and thus affects the currents under the plate, which should be taken into account for sediment and scour estimations. REFERENCES [1] H. Kaldenhoff, K. U. Graw, Unkonventionelle Küstenschutzbauwerke ; Zeitschrift der Bergischen Universität  Wuppertal, S , 1994 [2] J. Grue, P. L.F. Liu, G. K. Pedersen, PIV and water waves, Advances in coastal and ocean engineering, World Scientific, 2004 [3] J. K. Sveen, An introduction to MatPIV v.1.6.1, Department of Mathematics, Mechanics and applied Mathematics, University of Oslo, 2004 IV. INDUCED FORCES The investigation of the maximum wave loads reveals that the upwards directed forces exceed the downward directed forces for most cases by a factor of 1.4 and for H=15cm, T=1.6s and t=12cm up to a factor of 2. Fig. 8 shows the wave loads for the three tested wave heights over the wave periods and points out that, as expected, increasing wave heights result in higher wave loads for up and downward forces. A similar trend is seen for increasing wave periods, however, the trend is reversed for periods of 2.23s at a relative submerged depth of 0.3. Further analysis and tests are in progress to get more detailed information about the linear and nonlinear coherences of increasing wave height and gaining load. Reduced maximum forces were observed for increasing submerging depth. This could result from the exponentially decreasing wave kinematics and therewith also decreasing dynamic pressure component for growing water depth. Numerical calculations are in progress to analyse the time resolved pressure distribution under and above the plate. The investigation of wave energy dissipation in coherence with the length of the plate and the pitch of the plate as well as nonlinear wave interaction is subject of further analysis and additional tests. The earlier mentioned formation of jets due to wave breaking and their influence on the modification of higher harmonics is part of future studies. 424
5 Figure 8. Maximum upward and downward directed forces for wave heights of 5, 10, and 15cm 425
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