Three-dimensional interaction between uniform current and a submerged horizontal cylinder in an ice-covered channel

Abstract

The problem of interaction of a uniform current with a submerged horizontal circular cylinder in an ice-covered channel is considered. The fluid flow is described by linearized velocity potential theory and the ice sheet is treated as a thin elastic plate. The potential due to a source or the Green function satisfying all boundary conditions apart from that on the body surface is first derived. This can be used to derive the boundary integral equation for a body of arbitrary shape. It can also be used to obtain the solution due to multipoles by differentiating the Green function with its position directly. For a transverse circular cylinder, through distributing multipoles along its centre line, the velocity potential can be written in an infinite series with unknown coefficients, which can be determined from the impermeable condition on a body surface. A major feature here is that different from the free surface problem, or a channel without the ice sheet cover, this problem is fully three-dimensional because of the constraints along the intersection of the ice sheet with the channel wall. It has been also confirmed that there is an infinite number of critical speeds. Whenever the current speed passes a critical value, the force on the body and wave pattern change rapidly, and two more wave components are generated at the far-field. Extensive results are provided for hydroelastic waves and hydrodynamic forces when the ice sheet is under different edge conditions, and the insight of their physical features is discussed.