ABSTRACT

Motion of a slender solid in a fluid under an ice sheet is considered. A snow cover is arranged on the ice sheet. It is supposed that fluid is ideal and incompressible. The ice cover is modelled by a thin elastic plate. Two types of snow cover (dry and flooded) are considered. Dry snow is modeled by a thin viscoelastic isotropic plate with small Young's modulus. Flooded snow is modeled by viscous layer. Influence of snow cover on a stress-strained state of an ice cover from moving of an underwater body is analyzed. It is theoretically obtained that snow cover leads to decrease of height of a flexural-gravity wave. The stresses in an ice cover significantly decrease in comparison with a clear ice cover without snow.

INTRODUCTION

It is known that moving of an underwater body in liquid near the surface covered with an ice cover causes flexural gravity waves in ice- water system (Kheisin, 1969). This phenomenon was investigated experimentally on models of submarines (Kozin and Onischuk, 1994; Kozin and Zemlyak, 2012). The early theoretical studies were conducted by Kheisin (1969) for steady motion of a vortex under a layer of broken ice. Bukatov and Zharkov (1995) and Kozin and Pogorelova (2008) considered a steady motion of a point source of mass in liquid under a floating elastic plate. Pogorelova (2011) investigated nonstationary driving of a source under a floating plate. The motion of a submarine under a non-breakable plate was modeled experimentally and was investigated theoretically (Pogorelova et al, 2012). Theoretical and experimental data are in good agreement.

In natural conditions the ice cover is usually covered with snow. Snow cover can introduce amendments in pictures of deflections of an ice cover when subject to a vessel moving underneath the ice cover. Mechanical characteristics of snow cover are investigated long ago. There are many works devoted to this subject (Gray and Male, 1981; Mellor, 1977; Voitkovskiy, 1977). It is known (Prinsenberg et al, 2011) that the average thickness of snow cover on ice cover is equal to about 50 cm in the Arctic regions. The functional dependences of an elastic modulus and Poisson's ratio of dry snow from porosity and density are given in (Golubev and Frolov, 1998). The results of acoustic measurements of mechanical characteristics of snow cover near the weather station in Barentsburg (Spitsbergen) are given in (Epifanov, 2014).

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