THE PERIODIC HEAVING MOTION OF A HALF-IMMERSED SPHERE: THE ANALYTIC FORM OF THE VELOCITY POTENTIAL LONG-WAVE ASYMPTOTICS OF THE VIRTUAL-MASS COEFFICIENT
VICTORIA UNIV OF MANCHESTER (UNITED KINGDOM)
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The analytic form of the velocity potential of a heaving hemisphere is studied. The potential is expanded in terms of a wave source and of wave free potentials, and the coefficients in the expansion are studied 1 when the dimensionless wave number Ka is small, and 2 when Ka is arbitrary. A typical result is that the virtual mass coefficient is the real part of n Ka i A1Ka A1Ka n Ka - i A2Ka A2Ka, where the functions AKa are entire functions of Ka, real for real Ka. The argument depends on the expansion of a surface source in powers of Kr and n Kr, given here for the first time. A similar theory, not given here, can be developed for two-dimensional moving cylinders. It is believed that investigations of this kind will be helpful in studying the damped motion of freely floating bodies on still water.
- Fluid Mechanics