2015/12/02 by Nikolay Kuznetsov, Kuznetsov, Nikolay, Oleg V. Motygin +3
Computer Science · Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #35Q35 #76B15 #Advanced Mathematical Modeling in Engineering #Arctic and Antarctic ice dynamics #Elasticity and Wave Propagation #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35Q35 #msc:76B15 #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1512.01252
13 pages, 4 figures. arXiv admin note: text overlap with arXiv:1503.02194
arxiv created 2015/12/02 · openalex publication_date 2015/12/02 · arxiv updated 2015/12/07 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
A mechanical system consisting of water covered by brash ice and a body freely floating near equilibrium is considered. The water occupies a half-space into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes of the coupled motion which is assumed to be of small amplitude. The corresponding linear setting for time-harmonic oscillations reduces to a spectral problem whose parameter is the frequency. A constant that characterises the brash ice divides the set of frequencies into two subsets and the results obtained for each of these subsets are essentially different. For frequencies belonging to a finite interval adjacent to zero, the total energy of motion is finite and the equipartition of energy holds for the whole system. For every frequency from this interval, a family of motionless bodies trapping waves is constructed by virtue of the semi-inverse procedure. For sufficiently large frequencies outside of this interval, all solutions of finite energy are trivial.