It is well known that second order effects may in many cases be important for the nonlinear hydrodynamic problems arising in ocean engineering. Despite considerable efforts having been made in the past in calculating second order unsteady forces, similar studies are rare for the actual second order velocity potential itself, which is important for the understanding of wave kinematics. A mathematical model has been developed for the calculation of the second order sum frequency diffraction potential for fixed bodies in waves. It is believed that a first step towards the solution of the second order problem is the accurate evaluation of the first order quantities. By the use of Green's second identity, the first order problem can be cast into the form of a Fredholm integral equation and then solved by the Boundary Element Method. Some new developments based on this technique have been undertaken in this work, and as a result, there is a major improvement in the accuracy of the first order analysis. For the second order problem, the solution procedures are similar to those used for the first order problem except that special techniques have been developed to calculate efficiently the additional free surface integral which decays slowly to infinity in a highly oscillatory manner. In addition, an effective method has also been implemented to calculate the second derivative term in the free surface integral. From the numerical results presented, a number of interesting findings are illustrated. A closed form expression for a vertical circular cylinder has also been developed which not only furnishes a valuable check on the general numerical model but also provides some physical explanation for the second order phenomena. Moreover, it has been used to investigate some theoretical problems which (in the past) have caused confusion and error in the second order analysis. They are mainly associated with the troublesome nonhomogeneity presented in the free surface boundary condition.

Thesis (Ph. D.)--Oregon State University, 2009. / Printout. Includes bibliographical references. Also available on the World Wide Web.

Many wave energy convertors are designed to use either vertical (heave) or horizontal (surge) movements of waves. But the frequency response of small heaving buoys and oscillating water column devices shows that they are too stiff and so their resonance is at too short a period. A device moving in the horizontal (surge) direction has less restoring spring and so its resonance is at too long a period. It follows that a device that moved at some intermediate slope angle could have an intermediate value of hydrodynamic stiffness and so be resonant at a variable and desirable part of the wave spectrum. There have been two series of model tests in this work. The first used a simple free-floating model with no power take-off apparatus and with constraint achieved by means of a large inertia plate lying in the slope plane. The second used a rig that constrained the slope movement of the buoy head by means of hydrostatic bearings running on a guide rod set to the chosen slope angle. An external power take-off system was used to simulate a linear damper for absorbing the incident wave energy and control the motion of the model. This thesis firstly studies the potential of varying the slope angle as a way of tuning the natural period of the device to suit useful wave periods. Secondly, it studies the experimental and theoretical power capture ability of models with different slope angles in regular waves in the frequency domain. The hydrodynamic coefficients of the model were determined both experimentally and numerically based on linear hydrodynamic concepts. The power absorption of the models was calculated using the experimental data of the hydrodynamic coefficients and also measured directly. Some control of power take-off was also investigated. Some irregular wave tests were carried out for the 45 degrees slope angle case. The results show that it is feasible to alter the slope angle of the device as a way of tuning its natural period. However, in further studies of the power capture ability for different slope angles, the device shows a very wide bandwidth and high efficiency performance when it is set to 45 degrees slope angle. This suggests that to constrain the device to a 45 degrees slope angle is suitable for most of the sea states.