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Wave drift damping of floating bodies in slow yaw motion

Published online by Cambridge University Press:  26 April 2006

John Grue  and
Enok Palm
John Grue
Affiliation:
Mechanics Division, Department of Mathematics, University of Oslo, Norway
Enok Palm
Affiliation:
Mechanics Division, Department of Mathematics, University of Oslo, Norway
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Abstract

Wave diffraction, wave forces and wave drift damping due to a floating body performing a slow rotation about the vertical axis (yaw) is considered. The rotation angle of the body may be arbitrary. The angular velocity is assumed small compared to the wave frequency, however. The problem is formulated in the frame of reference following the slow rotation of the body, accounting for non-Newtonian forces. By applying the method of multiple timescales, the fluid flow is determined consistently to leading order in the slow angular velocity and to second order in the wave amplitude. Mathematical solution of the problem is obtained by means of integral equations that are applicable to geometries of arbitrary shape. The wave loads are found by applying conservation of linear and angular momentum. The wave drift damping is expressed by the far-field amplitudes of the wave field and the dipole moments of the time-averaged second-order potential. Numerical results are presented for a ship and a vertical cylinder describing a circular path in the horizontal plane. The results show that the wave drift damping due to a slow yaw motion of a floating body is one order of magnitude larger than the time-averaged forces and moment when there is no rotation. Wave drift damping due to slow rotation and slow translation are found to be of equal importance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 319 , 25 July 1996 , pp. 323 - 352
Copyright
© 1996 Cambridge University Press

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