Abstract
The mathematical formulation of the linearized potential theory for a slowly translating body undergoing oscillations in infinitely deep water is derived based on a perturbation series in terms of forward speed. It is shown that the hydrodynamic force on the oscillating body can be obtained from the solution of the velocity potential without forward speed, if second-order terms in forward speed are neglected. An example of a submerged circular cylinder is discussed. The numerical results are compared with the general solution of the linearized potential theory by a coupled finite-element method (Wu & Eatock Taylor 1987) which is not restricted to low forward speeds. Very good agreement is found. The nonlinear effect of the steady potential on the hydrodynamic forces is also discussed and is illustrated for a floating semicircular cylinder.
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