# Waves on a compressed floating ice plate caused by motion of a dipole in water

Stepanyants, Yury ORCID: https://orcid.org/0000-0003-4546-0310 and Sturova, Izolda V. (2020) Waves on a compressed floating ice plate caused by motion of a dipole in water. Journal of Fluid Mechanics, 907:A7. A7-1. ISSN 0022-1120

## Abstract

In the linear approximation, we study wave motions of a compressed elastic ice sheet caused by the motion of a two-dimensional dipole in the water beneath the sheet. The fluid flow is described by the potential theory, while the ice sheet is modelled through a thin elastic plate floating on the water surface. The solution for the vertical displacement of the ice sheet is derived for a transient dipole undergoing arbitrary two-dimensional motion. Three cases are considered in detail when the dipole moves horizontally with a uniform speed at some depth or horizontally oscillates, or moves and oscillates. The formulae for the plate displacement are derived for the fluid of finite depth, but then analysed in detail for the infinitely deep case. We show that the character of the solutions is different in the different domains of the parameter plane and classify the possible cases. Then we calculate the wave patterns on the plate for the different regimes of dipole motion and typical values of plate parameters. The studied problem can be considered as the simplified model of motion of a circular cylinder in a water under an ice cover. In the last section we compare the characteristics of wave motions onsetting in the far-field zone of the flow around a circular cylinder and its dipole approximation and show that the difference in the wave characteristics and force loads for these two cases is small and quickly vanishes when the ice plate thickness increases. In conclusion, we present estimates of amplitudes and wavelengths of wave perturbations for the real oceanic conditions.

Item Type: Article (Commonwealth Reporting Category C) Yes Live Archive Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 -) Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 -) 26 Nov 2020 04:18 15 Feb 2021 23:34 ice sheets, ocean processes, elastic waves 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics04 Earth Sciences > 0405 Oceanography > 040503 Physical Oceanography01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490109 Theoretical and applied mechanics51 PHYSICAL SCIENCES > 5103 Classical physics > 510399 Classical physics not elsewhere classified E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical SciencesE Expanding Knowledge > 97 Expanding Knowledge > 970104 Expanding Knowledge in the Earth Sciences 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280120 Expanding knowledge in the physical sciences https://doi.org/10.1017/jfm.2020.764 http://eprints.usq.edu.au/id/eprint/40167