THE PERIODIC HEAVING MOTION OF A HALF-IMMERSED SPHERE: THE ANALYTIC FORM OF THE VELOCITY POTENTIAL LONG-WAVE ASYMPTOTICS OF THE VIRTUAL-MASS COEFFICIENT
Abstract
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 ) A1*(Ka) A1**(Ka)/( n Ka - i )A2*(Ka) A2**(Ka), where the functions A(Ka) 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1962
- Accession Number
- AD0408465
Entities
People
- F. Ursell
Organizations
- University of Victoria