Solution of the Problem of Submerged Body Oscillations in a Frozen Channel with Linearly Varying Ice Thickness
УДК 534.1:532.3:517.9
Abstract
The paper considers the problem of hydroelastic waves generated by a submerged body undergoing vertical translational oscillations in a rectangular frozen channel of finite depth and width. The ice is modeled as a thin viscoelastic plate with its thickness varying linearly across the channel. The edges of the plate are frozen to the channel walls. The deflection of the ice cover is described within the framework of linear elasticity theory. The case of the symmetric thickness variation of the ice cover with respect to the channel's central line is studied. The liquid beneath the plate is inviscid and incompressible. The fluid flow induced by the plate deflection is potential. The oscillating submerged body is modeled as a three-dimensional dipole, which generates flow and pressure corresponding to a rigid sphere when oscillating in an unbounded fluid. The radius of the sphere is related to the dipole's velocity and its intensity. The dipole velocity varies periodically, resulting in changes in its intensity, while maintaining the body's shape unchanged. The velocity potential of the dipole placed in a rectangular channel with rigid walls is obtained using the method of image reflections.
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Squire V., Hosking R., Kerr A., Langhorne P Moving Loads on Ice Plates. Kluwer Academic Publishers. 1996. 230 p. DOI: 10.1007/978-94-009-1649-4
Korobkin A.A., Khabakhpasheva T.I., Papin A.A. Waves Propagating Along a Channel with Ice Cover // European Journal of Mechanics B-fluids. 2014. Vol. 47. P. 166-175. DOI: 10.1016/j. euromechflu.2014.01.007
Kheysin Y. Moving Load on an Elastic Plate Which Floats on the Surface of an Ideal Fluid // Izvestiya Akademii Nauk SSSR. Otdelenie Tekhnicheskih Nauk. Mekhanika i Mashinostroenie. 1963. Vol. 1. P. 178-180.
Ren K., Wu G.X., Li Z.F. Hydroelastic Waves Propagating in an Ice-Covered Channel // Journal of Fluid Mechanics. 2020. Vol. 886. A18. DOI: 10.1017/jfm.2019.1042
Batyaev E.A., Khabakhpasheva T.I. Hydroelastic Waves in a Channel Covered with a Free Ice Sheet // Journal of Fluid Dynamics. 2015. Vol. 50. No 6. P. 775-788. DOI: 10.1134/ S0015462815060071
Daly S.F. Wave Propagation in Ice-Covered Channels. // Journal Hydraul. 1993. Vol. 119. No 8. P. 895-910. DOI: 10.1061/(ASCE)0733-9429(1993)119:8(895)
Stepanyants Y.A., Sturova I.V Waves on a Compressed Floating Ice Caused by Motion of a Dipole in Water // Journal of Fluid Mechanics. 2020. Vol. 907. A7. DOI: 10.1017/jfm.2020.764
Козин В.М., Чижиумов С.Д., Земляк В.Л. Исследование влияния ледовых условий на эффективность резонансного способа разрушения ледяного покрова, реализуемого подводными судами // Прикладная механика и техническая физика. 2010. Т. 51. № 3. С. 118-125.
Wu G.X. Radiation and Diffraction by a Submerged Sphere Advancing in Water Waves of Finite Depth // Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. 1995. Vol. 448. No 1932. P. 29-54. DOI: 10.1098/rspa.1995.0002
Shishmarev K.A., Zavyalova K.N., Batyaev E.A., Khabakhpasheva T.I. Hydroelastic Waves in a Frozen Channel with Non-Uniform Thickness of Ice // Water. 2022. Vol. 14. No 3: 281. DOI: 10.3390/w14030281
Sturova I.V., Tkacheva L.A. Wave Motion in a Fluid Under an Inhomogeneous Ice Cover // Journal of Physics: Conference Series. 2017. Vol. 894. No 1: 012092. DOI: 10.1088/17426596/894/1/012092
Savin A.A., Savin A.S. Waves Generated on an Ice Cover by a Source Pulsating in Fluid // Journal of Fluid Dynamics. 2013. Vol. 48. No 3. P 303-309. DOI: 10.1134/S0015462813030034
Shishmarev K.A, Khabakhpasheva T.I., Korobkin A.A. Ice Response to an Underwater Body Moving in a Frozen Channel // Applied Ocean Research. 2019. Vol. 91. No 1. Р. 101877. DOI: 10.1016/j.apor.2019.101877
Tkacheva L. A. Oscillations of a Body Submerged in Fluid beneath an Ice Cover in the Neighborhood of a Vertical Wall // Journal of Fluid Dynamics. 2021. Vol. 56. No 1. P 50-65. DOI: 10.1134/S0015462821010146
Das D., Mandal B.N. Water Wave Radiation by a Sphere Submerged in Water with an Ice-Cover // Archive of Applied Mechanics. 2008. Vol. 78. P. 649-661. DOI: 10.1007/s00419-007-0186-1
Thorne R.C. Multipole Expansions in the Theory of Surface Waves // Mathematical Proceedings of the Cambridge Philosophical Society. 1953. Vol. 49. P. 707-716. DOI: 10.1017/ S0305004100028905
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