The “Wave Bridge” for bypassing oceanic wave momentum

J. Ocean Eng. Mar. Energy (2015) 1:395–404 DOI 10.1007/s40722-015-0028-0 RESEARCH ARTICLE The “Wave Bridge” for bypassing oceanic wave momentum Sebastian Timmerberg1 · Thomas Börner1 · Mostafa Shakeri1 · Reza Ghorbani2 · Mohammad-Reza Alam1 Received: 1 October 2014 / Accepted: 4 May 2015 / Published online: 4 June 2015 © Springer International Publishing AG 2015 Abstract Here, we introduce and investigate the concept of the Wave Bridge that can bypass the momentum of oceanic waves about ocean objects. The Wave Bridge is composed of a wave energy absorber on the upstream side of an ocean object, and a wave maker on its downstream side. The wave absorber and the wave maker are mechanically connected in such a way that the wave energy absorbed on the upstream side is simultaneously used by the wave maker downstream of the ocean object to generate waves. The Wave Bridge therefore protects the ocean object from waves by transferring incident wave energy from the upstream to the downstream. Furthermore, since the wave absorbed upstream is the same as the one generated downstream, the corresponding horizontal forces are equal in magnitude and opposite in sign and hence cancel each other, resulting in a zero net horizontal force on the Wave Bridge and its supporting structure. Our experimental results show a wave protection efficiency of up to 97 % and a horizontal force protection efficiency of up to 80 %. We also investigate the effect of the finite height of the Wave Bridge and the resulting wave energy leakage B Mohammad-Reza Alam Sebastian Timmerberg Thomas Börner Mostafa Shakeri Reza Ghorbani 1 Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA 2 Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, HI 96822, USA underneath the plungers on the overall protection efficiency. The Wave Bridge and its variants may reduce the costs of offshore structures by reducing the wave loads, provide calm water in the midst of an energetic ocean for future offshore cities, and conserve energy of dynamic position systems by reducing the wave-induced disturbances of vessels. Keywords Experimental hydrodynamics · Wave load protection · Offshore structures · High-efficiency wave energy absorption · Wave maker 1 Introduction Oceanic waves carry both energy and momentum. A wave energy harvester placed upstream of an ocean object can absorb the incident wave energy, but not the horizontal momentum. As a result while waves disappear downstream of the harvester, the wave force is to be endured by the structure that the wave harvester is attached to. The higher the efficiency of the wave energy absorption, the lesser are waves downstream, however, higher horizontal net force are thus induced into the structure. Now, consider a wave maker installed downstream of the structure generating exactly the same amount of energy absorbed upstream by the harvester. The wave maker exerts a horizontal force on the supporting structure, but in the opposite direction of the force of the wave absorber. If the wave maker and wave absorber have the same shape and configuration, then the magnitude of the two horizontal forces, theoretically, must be exactly the same. If furthermore the wave absorber and the wave maker have correct relative phase, then the sum of the horizontal forces will be zero. Here, we present the Wave Bridge, a mechanical device consisting of two plungers which are directly connected to each other to create a protected area 123 396 J. Ocean Eng. Mar. Energy (2015) 1:395–404 with calm water in between the wave maker and the wave absorber. This is the main idea behind the Wave Bridge (cf. Fig. 1). The entire Wave Bridge including both plungers and their mechanical connection is hinged onto an ocean object. Since in the ideal case the net horizontal force on the hinged point is zero and the stress induced by wave forces only occurs in the mechanical connection, the Wave Bridge shields the ocean object from wave impact. In other words, waves are forced to bypass the ocean structure through the Wave Bridge, just as momentum bypasses intermediate spheres in the Newton’s cradle resulting in a zero net force on bypassed spheres. Specifically in our Wave Bridge design, we use wedgeshaped plunger-type wave energy harvester and wave maker that, if properly made for a specific ocean environment, can theoretically have an efficiency of unity (i.e., absorb the entire energy of incoming waves). In this case, the entire wave energy and wave momentum can be bypassed about the ocean structure. Thus, the protected ocean structure does not experience any waves or any wave-induced horizontal forces. A plunger-type wedge-shaped wave maker (and an equal wave absorber) is an asymmetric two-dimensional wedge-shaped float with one vertical side and one sloped side. As this plunger moves in the vertical direction, it generates waves on the sloped side, while not much waves will be excited on the flat side. These devices are typically surface piercing and their vertical extent may or may not reach the bottom. In this sense, they are almost the opposite of surge-type converters that are hinged at the bottom and, z λs x Transmitted Waves Incident Surface Wave Protected Area Fig. 1 Two-dimensional schematic presentation of the Wave Bridge. A wedge-shaped plunger absorbs incident wave energy upstream of the offshore structure and via a purely mechanical mechanism transfers it to the downstream of the structure by another wedge-shaped plunger that acts as a wave maker. As a result, waves bypass the offshore structure: the offshore structure does not experience wave action and the net horizontal force on the entire system is significantly reduced. The Wave Bridge may be connected to the offshore structure as shown or be independently supported. Note that since the net horizontal force on the Wave Bridge is small (ideally zero), only a small force is endured by the supporting structure 123 depending on their designs, may or may not reach the free surface. Plunger-type wedge-shaped wave makers and wave energy converters have been subjects of extensive studies since decades ago. A finite depth wedge in an infinite depth water was studied analytically and experimentally by Wang (1974). For the case of a finite depth water and for a wedge that has a flat vertical side on one side and a sloped surface on the other, Wu (1988) investigated the radiated waves to the right numerically using a boundary collocation method (BCM), where the no-flow boundary condition on the flat side of the plunger is assumed to extend to the seabed. For the case of a finite height plunger Wu (1991) used a boundary element method to determine radiated waves on both sides of the plunger. These numerical results agree well with our investigations (Ellix and Arumugam 1984; Patel and Ionnaou 1980; Henderson et al. 2006). Plunger-type wedge-shaped floaters have also been (...truncated)