RESEARCH PAPER Hydrodynamic Forces on a Submerged Horizontal Circular Cylinder in Water with an Ice Cover Nityananda Thakur 1 • Dilip Das 2 Received: 2 February 2016 / Accepted: 8 June 2016 Ó Shiraz University 2016 Abstract Using the multipoles method, we formulate the problems of hydrodynamic forces on a submerged circular cylinder in water with an ice cover, the ice cover being modelled as an elastic plate of very small thickness. This leads to an infinite system of linear equations which are solved numerically by standard techniques. The vertical and horizontal forces on the circular cylinder are obtained and depicted graphically against the wave number for various values of flexural rigidity of the ice cover to show the effect of the presence of ice cover on these quantities. When the flexural rigidity is taken to be zero, the results coincide with the vertical and horizontal forces on the circular cylinder for the cases of water with a free surface. Keywords Water wave scattering  Submerged circular cylinder  Ice cover  Vertical and horizontal forces 1 Introduction The solution of the scattering and radiation problem for a submerged and floating bodies, in infinite or finite depth water, has been explored for decades for various shapes of bodies. The problem of water wave scattering by a hori- zontal circular cylinder fully submerged in deep water having a free surface was investigated long back by Dean (1948) and Ursell (1950). Garrett (1971) solved the scat- tering problem by determining the vertical force, horizontal force and torque for a circular dock in water of finite depth. Black (1975) looked at the wave forces on bodies which are vertically axisymmetric using an integral equation formulation in water of finite depth. Evans and Linton (1989) used the multipole method to solve the two-di- mensional problems of radiation and scattering of water waves by a submerged horizontal circular cylinder in finite depth water as part of a need to determine accurately the natural frequencies of oscillation of a highly buoyant tethered cylinder. Linton (1991) investigated the problems of radiation (both heave and sway) and scattering of water waves by a sphere submerged in finite depth water using the same method. Also, one of the attractive features of multipole expansion methods for this type of problem is that the evaluation of hydrodynamic forces on a submerged circular cylinder in infinite depth water is investigated (cf. Linton and McIver 2001). It is observed that the amplitudes of the vertical and horizontal forces are identical, but they are 90° out of phase. All the above works are related to an ocean with a free surface. Recently, there has been considerable interest in the investigation of ice–wave interaction problems due to an increase in scientific activities in the polar regions. The ice cover is modelled as a thin ice sheet, of which still a smaller part is immersed in water and is composed of materials having elastic properties. Already, quite a num- ber of researchers have considered various types of water wave problems in ocean with an ice cover modelled as a thin elastic plate [cf. Fox and Squire (1994), Meylan and Squire (1994), Balmforth and Craster (1999), Chakrabarti (2000), Chung and Fox (2002), Evans and Porter (2003), Linton and Chung (2003), Mandal and Basu (2004), Das and Mandal (2006, 2007, 2008a, b, 2010), Das and Thakur & Dilip Das dilipdas99@gmail.com; dasdilip9@gmail.com 1 Department of Mathematics, Surendranath Evening College, 24/2 M. G. Road, Kolkata 700009, India 2 Department of Mathematics, Shibpur Dhinbundhoo Institution (College), 412/1 G. T. Road, Howrah 711102, India 123 Iran. J. Sci. Technol. Trans. Sci. DOI 10.1007/s40995-016-0044-5