A Surfboard for Riding the Wave

The report, A Surfboard for Riding the Wave, by the high level Knowledge Exchange expert group on research data called for a collaborative data infrastructure that will enable researchers and other stakeholders from education, society and business to use, re-use and exploit research data to the maximum benefit of science and society. The Knowledge Exchange partners have embraced this vision and commissioned a report that translates Riding the Wave into actions for the four partner countries and beyond. This paper builds on this report and presents an overview of the present situation with regard to research data in Denmark, Germany, the Netherlands and the United Kingdom and offers broad outlines for a possible action programme for the four countries in realising the envisaged collaborative data infrastructure. An action programme at the level of four countries will require the involvement of all stakeholders from the scientific community

Design, Construction and Testing of a Hydraulic Power Take-Off for Wave Energy Converters

This paper presents the construction, mathematical modeling and testing of a scaled universal hydraulic Power Take-Off (PTO) device for Wave Energy Converters (WECs). A specific prototype and test bench were designed and built to carry out the tests. The results obtained from these tests were used to adjust an in-house mathematical model. The PTO was initially designed to be coupled to a scaled wave energy capture device with a low speed and high torque oscillating motion and high power fluctuations. Any Energy Capture Device (ECD) that fulfils these requirements can be coupled to this PTO, provided that its scale is adequately defined depending on the rated power of the full scale prototype. The initial calibration included estimation of the pressure drops in the different components, the pressurization time of the oil inside the hydraulic cylinders and the volumetric efficiency of the complete circuit. Since the overall efficiency measured during the tests ranged from 0.69 to 0.8 and the dynamic performance of the PTO was satisfactory, the results are really promising and it is believed that this solution might prove effective in real devices.

Wave Sensor Technologies, St Petersburg, Florida, March 7-9, 2007: workshop proceedings

The Alliance for Coastal Technologies (ACT) convened a workshop on "Wave Sensor Technologies" in St. Petersburg, Florida on March 7-9, 2007, hosted by the University of South Florida (USF) College of Marine Science, an ACT partner institution. The primary objectives of this workshop were to: 1) define the present state of wave measurement technologies, 2) identify the major impediments to their advancement, and 3) make strategic recommendations for future development and on the necessary steps to integrate wave measurement sensors into operational coastal ocean observing systems. The participants were from various sectors, including research scientists, technology developers and industry providers, and technology users, such as operational coastal managers and coastal decision makers. Waves consistently are ranked as a critical variable for numerous coastal issues, from maritime transportation to beach erosion to habitat restoration. For the purposes of this workshop, the participants focused on measuring "wind waves" (i.e., waves on the water surface, generated by the wind, restored by gravity and existing between approximately 3 and 30-second periods), although it was recognized that a wide range of both forced and free waves exist on and in the oceans. Also, whereas the workshop put emphasis on the nearshore coastal component of wave measurements, the participants also stressed the importance of open ocean surface waves measurement. Wave sensor technologies that are presently available for both environments include bottom-mounted pressure gauges, surface following buoys, wave staffs, acoustic Doppler current profilers, and shore-based remote sensing radar instruments. One of the recurring themes of workshop discussions was the dichotomous nature of wave data users. The two separate groups, open ocean wave data users and the nearshore/coastal wave data users, have different requirements. Generally, the user requirements increase both in spatial/temporal resolution and precision as one moves closer to shore. Most ocean going mariners are adequately satisfied with measurements of wave period and height and a wave general direction. However, most coastal and nearshore users require at least the first five Fourier parameters ("First 5"): wave energy and the first four directional Fourier coefficients. Furthermore, wave research scientists would like sensors capable of providing measurements beyond the first four Fourier coefficients. It was debated whether or not high precision wave observations in one location can take the place of a less precise measurement at a different location. This could be accomplished by advancing wave models and using wave models to extend data to nearby areas. However, the consensus was that models are no substitution for in situ wave data.[PDF contains 26 pages]

Effects of volumetric allocation on heave response of semisubmersible in deep sea

The configuration of semisubmersibles consisting of pontoons and columns and their corresponding heave motion response in incident progressive waves are examined. The purpose of the present study is to provide a theoretical approach to estimating the effects of volumetric allocation on natural period and response amplitude operator (RAO) in heave motion. We conclude that the amplitude of heave motion response can be considerably suppressed by appropriately adjusting volumetric allocation so that the natural heave period keeps away from the range of wave energy. The theoretical formulae are found in good agreement with the corresponding computational results by WAMIT.

Invariants, Lie-Bäcklund operators and Bäcklund transformations

This thesis is mainly concerned with the application of groups of transformations to differential equations and in particular with the connection between the group structure of a given equation and the existence of exact solutions and conservation laws. In this respect the Lie-Bäcklund groups of tangent transformations, particular cases of which are the Lie tangent and the Lie point groups, are extensively used.

In Chapter I we first review the classical results of Lie, Bäcklund and Bianchi as well as the more recent ones due mainly to Ovsjannikov. We then concentrate on the Lie-Bäcklund groups (or more precisely on the corresponding Lie-Bäcklund operators), as introduced by Ibragimov and Anderson, and prove some lemmas about them which are useful for the following chapters. Finally we introduce the concept of a conditionally admissible operator (as opposed to an admissible one) and show how this can be used to generate exact solutions.

In Chapter II we establish the group nature of all separable solutions and conserved quantities in classical mechanics by analyzing the group structure of the Hamilton-Jacobi equation. It is shown that consideration of only Lie point groups is insufficient. For this purpose a special type of Lie-Bäcklund groups, those equivalent to Lie tangent groups, is used. It is also shown how these generalized groups induce Lie point groups on Hamilton's equations. The generalization of the above results to any first order equation, where the dependent variable does not appear explicitly, is obvious. In the second part of this chapter we investigate admissible operators (or equivalently constants of motion) of the Hamilton-Jacobi equation with polynornial dependence on the momenta. The form of the most general constant of motion linear, quadratic and cubic in the momenta is explicitly found. Emphasis is given to the quadratic case, where the particular case of a fixed (say zero) energy state is also considered; it is shown that in the latter case additional symmetries may appear. Finally, some potentials of physical interest admitting higher symmetries are considered. These include potentials due to two centers and limiting cases thereof. The most general two-center potential admitting a quadratic constant of motion is obtained, as well as the corresponding invariant. Also some new cubic invariants are found.

In Chapter III we first establish the group nature of all separable solutions of any linear, homogeneous equation. We then concentrate on the Schrodinger equation and look for an algorithm which generates a quantum invariant from a classical one. The problem of an isomorphism between functions in classical observables and quantum observables is studied concretely and constructively. For functions at most quadratic in the momenta an isomorphism is possible which agrees with Weyl' s transform and which takes invariants into invariants. It is not possible to extend the isomorphism indefinitely. The requirement that an invariant goes into an invariant may necessitate variants of Weyl' s transform. This is illustrated for the case of cubic invariants. Finally, the case of a specific value of energy is considered; in this case Weyl's transform does not yield an isomorphism even for the quadratic case. However, for this case a correspondence mapping a classical invariant to a quantum orie is explicitly found.

Chapters IV and V are concerned with the general group structure of evolution equations. In Chapter IV we establish a one to one correspondence between admissible Lie-Bäcklund operators of evolution equations (derivable from a variational principle) and conservation laws of these equations. This correspondence takes the form of a simple algorithm.

In Chapter V we first establish the group nature of all Bäcklund transformations (BT) by proving that any solution generated by a BT is invariant under the action of some conditionally admissible operator. We then use an algorithm based on invariance criteria to rederive many known BT and to derive some new ones. Finally, we propose a generalization of BT which, among other advantages, clarifies the connection between the wave-train solution and a BT in the sense that, a BT may be thought of as a variation of parameters of some. special case of the wave-train solution (usually the solitary wave one). Some open problems are indicated.

Most of the material of Chapters II and III is contained in [I], [II], [III] and [IV] and the first part of Chapter V in [V].

The stability of traveling wave solutions of parabolic equations

A method for determining by inspection the stability or instability of any solution u(t,x) = ɸ(x-ct) of any smooth equation of the form u_t = f(u_(xx),u_x,u where ∂/∂a f(a,b,c) > 0 for all arguments a,b,c, is developed. The connection between the mean wavespeed of solutions u(t,x) and their initial conditions u(0,x) is also explored. The mean wavespeed results and some of the stability results are then extended to include equations which contain integrals and also to include some special systems of equations. The results are applied to several physical examples.

Some problems of edge waves and standing waves on beaches

Some problems of edge waves and standing waves on beaches are examined.

The nonlinear interaction of a wave normally incident on a sloping beach with a subharmonic edge wave is studied. A two-timing expansion is used in the full nonlinear theory to obtain the modulation equations which describe the evolution of the waves. It is shown how large amplitude edge waves are produced; and the results of the theory are compared with some recent laboratory experiments.

Traveling edge waves are considered in two situations. First, the full linear theory is examined to find the finite depth effect on the edge waves produced by a moving pressure disturbance. In the second situation, a Stokes' expansion is used to discuss the nonlinear effects in shallow water edge waves traveling over a bottom of arbitrary shape. The results are compared with the ones of the full theory for a uniformly sloping bottom.

The finite amplitude effects for waves incident on a sloping beach, with perfect reflection, are considered. A Stokes' expansion is used in the full nonlinear theory to find the corrections to the dispersion relation for the cases of normal and oblique incidence.

Finally, an abstract formulation of the linear water waves problem is given in terms of a self adjoint but nonlocal operator. The appropriate spectral representations are developed for two particular cases.