ABSTRACT

Theoretical and experimental results for gravity wave interaction with a hemispherical object resting on the ocean floor are presented. The hydrodynamic problem of wave interaction with large submerged objects such as submerged oil storage tanks is approached by means of diffraction theory. Numerical results for horizontal and vertical force coefficients and corresponding phase shift angles are presented. These results are compared with results, obtained from a simpler approach to show where the effects due to the proximity of the free surface and the relative size of the object become significant. Also, corresponding experimental results are presented for comparison with the theory.

INTRODUCTION

In recent years ever increasing attention is being given to the exploitation of natural resources in the coastal waters of the oceans. Such exploitation is predicated at least partly on the ability to design and build large scale structures offshore. For this purpose, it is necessary to have a better understanding of the forces induced by surface gravity waves on structures such as large submerged oil storage tanks. This paper contributes towards such understanding by taking a basic approach to the problem of wave interaction with a large hemispherical tank. Although the shape considered is somewhat idealized, it is representative of practical shapes and the results provide some insight and understanding into the fundamental problem.

Wave forces acting on such objects as piles 1, submerged pipe lines2, or other shapes such as small spheres 3, have been the subject of investigation for nearly two decades. A common feature of all of these studies is the condition that the object size is small compared to the length of the incident wave. This condition, which prevails in most practical applications, simplifies the general problem of wave/structure interaction in that it allows the assumption that the presence of the object has no effect on the incident wave. Accordingly it may be assumed that the flow field existing at the center of the object extends to infinity and the force can be represented as the sum of two components, drag and inertia. The component due to dragis proportional to the product of a drag coefficient, Cd, and the square of the velocity. The component due to inertia, on the other hand, is proportional to the product of the inertia coefficient, (1+Cm), where Cm is the added-mass coefficient, and the local fluid acceleration. The, expression for wave force which involves these two terms was originally applied by Morison, Johnson and O'Brien1 in the study of wave forces on piles and; consequently, has come to be known as the "Morison equation".

However, as the size of the object in relation to the wave length increases, the simplifying assumptions upon which the Morison equation is based are eventually violated and this simple relationship no longer yields valid results.

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