Unsteady three-dimensional sources in deep water with an elastic cover and their applications

• Published in: Journal of Fluid Mechanics
• Main Author: Sturova, Izolda V.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 2013
• Subjects: Laplace; Ice Sheet
• Online Access: http://dx.doi.org/10.1017/jfm.2013.303; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112013003030

Abstract The velocity potential is derived for a transient source of arbitrary strength undergoing arbitrary three-dimensional motion. The initially quiescent fluid of infinite depth is assumed to be inviscid, incompressible and homogeneous. The upper surface of the fluid is covered by a thin layer of elastic material of uniform density with lateral stress. The linearized initial boundary-value problem is formulated within the framework of the potential-flow theory, and the Laplace transform technique is employed to obtain the solution. The potential of a time-harmonic source with forward speed is obtained as a particular case. The far-field wave motion at long time is determined via the method of stationary phase. The problems of radiation (surge, sway and heave) of the flexural–gravity waves by a submerged sphere advancing at constant forward speed are investigated. The method of multipole expansions is used. Numerical results are obtained for the wave-making resistance and lift, added-mass and damping coefficients. The effects of an ice sheet and broken ice on the hydrodynamic loads are discussed in detail.