ASYMPTOTIC ANALYSIS OF WAVE RESISTANCE OF A SUBMERGED BODY MOVING WITH AN OSCILLATING VELOCITY

An asymptotic study is made of potential and free-surface elevation du e to forward motion of a submerged body with an oscillating velocity. The latter is supposed to be a short period. As the nondimensional per iod epsilon much less than 1, the singular perturbation technique is a pplied. Using two-term expansion for the potential, the principal term s of asymptotics for instant and mean values of wave resistance are ob tained. The mean value (up to a term O(epsilon)) is the sum of two add ends, the first of which is the wave resistance of the same body movin g at the mean speed. The second addend is proportional to the dispersi on of velocity with the coefficient depending on the form of the body. This coefficient vanishes if the body is symmetric with respect to th e mid-section. Numerical examples for the two-dimensional problem show that there exist cylinders with the following property: the absolute value of wave resistance decreases when passing from motion at the mea n speed to motion with oscillating velocity.