An exponential growth in the offshore industry has resulted in a corresponding increase in demand for quick, accurate, and implementable designs. With the increase in size of the structure relative to the wave amplitude, analysis should be performed using the diffraction theory. The steady wave drift force on a submerged body is a second-order quantity. With a potential flow assumption, the force arises from the diffraction and radiation of the waves from the interaction with the body. For a fixed body in waves the steady force is contributed from the wave diffraction effect alone. Numerical solutions for are generally needed for the computation of the steady drift force on submerged structures. In this study the steady wave drift forces on several fixed bodies of basic shapes are derived in closed form. The thesis addresses the steady drift forces on the following basic structures: a box, a vertical circular cylinder, a submerged horizontal cylinder, a bottom-seated horizontal half cylinder, a bottom-seated hemisphere, a submerged sphere, and an ellipsoid. The results developed demonstrate the importance of various independent non-dimensional parameters. To achieve speed and accuracy of the analytical/numerical solutions for the second order forces on the basic bodies with symmetry has been presented. Mathematical formulation of the boundary value problem and its second order solution have been described using the different coordinates depending on the symmetry and nature of the object. Charts and formulas have been developed to provide solution for the second order wave forces on different basic structures like cylinder, sphere and ellipsoids. This study is helpful for a first pass estimate of the steady drift force where the translational and rotational contributions are neglected. The illustrative examples provide a sense of the accuracy and an approach to bound the results of complex geometries by approximating them as simpler geometries.

Using the method of matched asymptotic expansions the reflection and transmission coefficients are calculated for scattering of oblique water waves by a vertical barrier. Here an assumption is made that the barrier is small compared to the wavelength and the depth of water. A number of sloshing problems are considered. The eigenfrequencies are calculated when a body is placed in a rectangular tank. Here the bodies considered are a vertical surface-piercing or bottom-mounted barrier, and circular and elliptic cylinders. When the body is a vertical barrier, the eigenfunction expansion method is applied. When the body is either a circular or elliptic cylinder, and the motion is two-dimensional, the boundary element method is applied to calculate the eigenfrequencies. For comparison, two approximations, "a wide-spacing", and "a small-body" are used for a vertical barrier and circular cylinder. In the wide-spacing approximation, the assumption is made that the wavelength is small compared with the distance between the body and walls. The small-body approximation means that a typical dimension of the body is much larger than the cross-sectional length scale of the fluid motion. For an elliptic cylinder, the method of matched asymptotic expansions is used and compared with the result of the boundary- element method. Also a higher-order solution is obtained using the method of matched asymptotic expansions, and it is compared with the exact solution for a surface-piercing barrier. Again the assumption is made that the length scale of the motion is much larger than a typical body dimension. Finally, the drift force on multiple bodies is considered the ratio of horizontal drift force in the direction of wave advance on two cylinders to that on an isolated cylinder is calculated. The method of matched asymptotic expansions is used under the assumption that the wavelength is much greater than the cylinder spacing.