Drift Forces on a Freely-Floating Sphere in Water of Finite Depth(I) -Momentum Theorem Method-

유한수심(有限水深)의 해상(海上)에서 규칙파(規則波)에 놓인 구(球)에 작용(作用)하는 표류력(漂流力)(I) -운동량(運動量) 이론(理論) 방법(方法)-

The drift force acting on a freely-floating sphere in water of finite depth is studied within the framework of a linear potential theory. A velocity potential describing fluid motion is determined by distribution pulsating sources and dipoles on the immersed surface of the sphere. Upon knowing values of the potential, hydrodynamic forces are evaluated by integrating pressures over the immersed surface of the sphere. The motion response of the sphere in water of finite depth is obtained by solving the equation of motion. From these results, the drift force on the sphere is evaluated by the momentum theorem, in which a far-field velocity potential is utilized in forms of Kochin function. The drift force coefficient Cdr of a fixed sphere increases monotononically with non-dimensional wave frequency ${\sigma}a$. On the other hand, in freely-floating case, the Cdr has a peak value at ${\sigma}a$ of heave resonance. The magnitude of the drift force coefficient Cdr in the case of finite depth is different form that for deep water, but the general tendency seems to be similar in both cases. It is to note that Cdr is greater than 1.0 when non-dimensional water depth d/a is 1.5 in the case of freely-floating sphere.