Force impact of a flow of an infinitely deep liquid on a source under ice cover

   A characteristic natural factor of the polar regions of the World Ocean and freezing sea areas is the presence of ice cover. The floating ice cover, which determines the dynamic interaction between the ocean and the atmosphere, affects the dynamics of not only the sea surface, but also subsurface waters, while both the ice cover and the entire mass of liquid beneath it participate in the general vertical movement. It is assumed that the ice cover is continuous, that is, its horizontal scales exceed the lengths of the excited waves and, under fairly natural conditions, is modeled by a thin elastic plate, the deformations of which are small and the plate is physically linear. The problem of calculating the force impact of a flow of an infinitely deep homogeneous liquid on a localized source under the ice cover is solved. The problem is solved for the two-dimensional case. Integral representation of the solution for wave drag and lift is obtained, which arise due to the presence of an ice cover and act on the source. The results of calculations of the force action acting on a localized source, simulating a blunt semi-infinite body of finite width, and a dipole, simulating a cylinder, are presented for various values of the oncoming flow velocity and their immersion depth. Numerical calculations show that as the depth of the source immersion increases, the force effect of the fluid flow, which occurs due to the presence of an ice cover, decreases. The dependences of the wave resistance and lift force on the velocity of the incoming fluid flow demonstrate a qualitatively different behavior. The obtained results with different values of the physical parameters included in them make it possible to evaluate the characteristics of ice cover disturbances and its impact on various sources of natural and anthropogenic disturbances observed in real marine conditions.

1. Surface and internal waves in Arctic seas. St. Petersburg, Gidrometeoizdat, 2002. 360 p. (in Russian)

2. Mei C.C., Stiassnie M., Yue D.K.-P. Theory and applications of ocean surface waves. Advanced Series of Ocean Engineering. Vol. 42. London, World Scientific Publishing, 2018. 1240 p. doi: 10.1142/10212

3. Velarde M.G., Tarakanov R. Yu., Marchenko A.V. (Eds.). The ocean in motion. Springer Oceanography. Springer International Publishing AG, 2018. 625 p. doi:10.1007/978-3-319-71934-4

4. Morozov E.G. Oceanic internal tides: observations, analysis and modeling. Cham, Springer, 2018. 304 p. doi: 10.1007/978-3-319-73159-9

5. Marchenko A.V., Morozov E.G., Muzylev S.V., Shestov A.S. Interaction of short internal waves with the ice cover in an Arctic fjord. Oceanology. 2010, 50(1), 18–27. doi: 10.1134/S0001437010010029

6. Zyryanov V.N. Under-ice seiches. Water Resources. 2011, 38(3), 261–274 doi: 10.1134/S0097807811020163

7. Zolotukhin A.B., Gudmestad O.T., Ermakov A.I. Fundamentals of offshore fields development and offshore structures construction in the Arctic. Moscow, GUP Izdatelstvo Neft I Gaz RGU nefti I gaza im.I.M.Gubkina, 2000. 770 p. (in Russian).

8. Sidnjaev N.I. Theoretical studies of hydrodynamics in an underwater explosion of a point source. Inzenerny Zurnal: Nauka i Innovastii 2013, 2, URL: https://engjournal.ru/catalog/appmath/hidden/614.html (Accessed 09. 03. 2023) (in Russian).

9. Bukatov A.E. Waves in the sea with floating ice. Sevastopol, FGBUN MGI. 2017. 360 p. (in Russian).

10. Nesterov S.V., Shamajev A.S., Shamajev S.I. Methods, procedures and means of aerospace radio tomography of nearsurface regions of the Earth. Moscow, Nauchnij Mir, 1996. 272 p. (in Russian).

11. Bulatov V.V., Vladimirov Yu.V. Wave dynamics of stratified mediums. Moscow, Nauka Publishers, 2012. 584 p.

12. Svirkunov P.N., Kalashnik M.V. Phase patterns of dispersive waves from moving localized sources. Physics-Uspekhi. 2014, 57(1), 80–91. doi: 10.3367/UFNe.0184.201401d.0089

13. Il’ichev A.T. Solitary waves in hydrodynamic models. Moscow, Fizmatlit, 2003. 256 p. (in Russian).

14. Il’ichev A.T. Effective wavelength of envelope waves on the water surface beneath an ice sheet: small amplitudes and moderate depths. Theoretical and Mathematical Physics. 2021, 208, 1182–1200. doi: 10.1134/S0040577921090026

15. Savin A.S., Savin A.A. Three-dimensional problem of disturbing a ice cover by a dipole moving in fluid. Fluid Dynamics. 2015, 50(5), 613–620. doi: 10.1134/S0015462815050026

16. Sturova I.V. Motion of a load over an ice sheet with non-uniform compression. Fluid Dynamics. 2021, 56(4), 503–512. doi: 10.1134/S0015462821040121

17. Dinvay E., Kalisch H., Parau E.I. Fully dispersive models for moving loads on ice sheets. Journal of Fluid Mechanics. 2019, 876, 122–149. doi: 10.1017/jfm.2019.530

18. Sturova I.V. Radiation of waves by a cylinder submerged in water with ice floe or polynya. Journal of Fluid Mechanics. 2015, 784, 373–395. doi: 10.1017/jfm.2015.582

19. Loytsyansky L.G. Fluid and gas mechanics. Moscow, Fizmatlit. 1987. 784 p. (in Russian).

20. Sretensky L.N. Theory of fluid wave motions. Moscow, Nauka. 1977. 815 p. (in Russian).

21. Lavrentjev M.A., Shabat B.V. Methods of the theory of complex variable functions. Moscow, Fizmatlit, 1987. 688 p. (in Russian).