Nonlinear oscillations of the interface of two liquids at the angular oscillations of the tank
The development of rocket and space technology in recent years has led to the widespread use of various cryogenic liquids. To increase the shelf life of cryo-products on board spacecraft or in tankers of future space filling stations, it is proposed to create a certain stock of cryo-product, which is simultaneously in a two-phase or three-phase state and forms layers of liquid. The paper considers the problem in a nonlinear formulation about the oscillations of the interface of a two-layer liquid in an arbitrary axisymmetric cavity of a solid body performing angular oscillations around a horizontal axis. For the considered class of cavities with an arbitrary bottom and a lid, the nonlinear problem is reduced to the sequential solution of linear boundary value problems. Nonlinear differential equations describing the oscillations of the interface between two liquids in the vicinity of the main resonance are obtained. In the case of a circular cylindrical cavity with flat bottoms, solutions of boundary value problems in the form of cylindrical functions were used to calculate linear and nonlinear hydrodynamic coefficients depending on the depth and density of the upper liquid.
 Sretensky L.N. Teoriya volnovykh dvizheniy zhidkosti [Theory of wave motions of liquid]. Moscow, Nauka Publ., 1977, 815 p.
 Landau L.D., Lifshits E.M. Teoreticheskaya fizika. T. VI: Gidrodinamika [Theoretical physics.Vol. VI: Hydrodynamics]. Moscow, Nauka Publ., 1986, 735 p.
 Selezov I.T., Avramenko O.V., Naradovy V.V. Dinamicheskie sistemy — Dynamical Systems, 2011, vol. 1 (29), no. 1, pp. 53–68.
 Bukreev V.I., Sturova I.V., Chebotnikov A.V. Izv. RAN. Mekhanika zhidkosti i gaza — Fluid Dynamics, 2014, no. 3, pp. 110–118.
 Kozlov N.V., Shuvalova D.A. Sovremennye problemy nauki i obrazovaniya — Modern Problems of Science and Education. Surgery, 2014, no. 6. Available at: http://www.science-education.ru/ru/article/view?id=16669 (accessed March 3, 2021).
 Gaziev E.L. Modelirovanie sobstvennykh kolebaniy sistemy «idealnaya kapillyarnaia zhidkost-barotropny gaz» v tsilindricheskom konteynere [Modeling of natural oscillations of the system “ideal capillary liquid-barotropic gas” in a cylindrical container]. Book of Abstracts of Crimean International Mathematics Conference (CIMC-2003). Simferopol, KNTs NANU Publ., 2013, vol. 3, pp. 51–52.
 Kalinichenko V.A. Effect of an upper layer of viscous liquid on breaking surface gravity waves. Journal of Physics: Conference Series, 2019, 1301, paper no. 012017.
 Pozhalostin A.A., Goncharov D.A. Inzhenerny zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2013, iss. 12 (24). DOI: 10.18698/2308-6033-2013-12-1147
 Chashechkin Yu.D., Baydulov V.G., Bardakov R.N., Vasilev A.Yu., Gorodtsov V.A., Kistovich A.V., Stepanova E.V., Chaplina T.O. Modelirovanie techeniy stratifitsirovannykh i vrashchayuschikhsya zhidkostey [Modeling of flows of stratified and rotating fluids]. Moscow, Nauka Publ., 2010, 349 p. ISBN: 978-5-02-037459-1
 Kalinichenko V.A. Regularization of barotropic gravity waves in a two-layer fluid. Fluid Dynamics, 2019, vol. 54, no. 6, pp. 761–773.
 Win Ko Ko, Temnov A.N. Nauka i obrazovanie. MGTU im. N.E. Baumana — Science & Education, Bauman Moscow State Technical University, 2016, no. 10, pp. 85–101. DOI: 10.7463/1016.0847158
 Win Ko Ko, Temnov A.N. Experimental and theoretical studies of oscillations of stratified fluid. IOP Conference Series: Materials Science and Engineering, 2018, no. 468, paper no. 012031.
 Win Ko Ko, Temnov A.N. Research of amplitude-frequency characteristics of nonlinear oscillations of the interface of two-layered liquid. International Journal of Mechanical and Mechatronics Engineering, 2020, vol. 14, no. 1, pp. 7–13.
 Lukovskiy I.A. Vvedenie v nelineynuyu dinamiku tverdogo tela s polostyami, soderzhaschimi zhidkost [Introduction to nonlinear dynamics of a rigid body with cavities containing a liquid]. Kiev, Nauk. Dumka Publ., 1990, 296 p. ISBN: 5-12-001308-2
 Narimanov G.S., Dokuchaev L.V., Lukovskiy I.A. Nelineynaya dinamika letatelnogo apparata s zhidkostyu [Nonlinear dynamics of an aircraft with a liquid]. Moscow, Mashinostroenie Publ., 1977, 208 p.
 Mikishev G.N, Rabinovich B.I. Dinamika tvrdogo tela s polostyami, chastichno zapolnennymi zhidkost [Dynamics of a rigid body with cavities partially filled with liquid]. Moscow, Mashinostroenie Publ., 1968, 532 p.
 Zhukovskiy N.E. O dvizhenii tverdogo tela, imeyushchego polosti, napolnennye odnorodnoy kapelnoy zhidkostyu [On the motion of a rigid body with cavities filled with a homogeneous dropping liquid]. Moscow, Gostekhizdat. Publ., 1948, 143 p.
 Limarchenko O.S. Nelineynye zadachi dinamiki zhidkosti v rezervuarakh netsilindricheskoy formy [Nonlinear problems of fluid dynamics in non-cylindrical reservoirs]. Kiev, Adverta Publ., 2017, 130 p.
 Liska R. Nonhydrostatic two-layer models of incompressible flow. Computer Math. Applic., 1995, vol. 29, no. 9, pp. 25–37.
 Choi W., Camassa R. Fully nonlinear internal waves in a two-fluid system. J. Fluid Mech., 1999, no. 396, pp. 1–36.
 Barannyk L.L., Papageorgiou D.T. Fully nonlinear gravity-capillary solitary waves in a two-fluid system of finite depth. Journal of Engineering Mathematics, 2002, vol. 42, pp. 321–339.
 Rocca M. La, Sciortino G., Adduce C., Boniforti M.A. Experimental and theoretical investigation on the sloshing of a two-liquid system with free surface. Physics of Fluid, 2005, no. 17, paper no. 062101.
 Rocca M. La, Sciortino G., Adduce C., Boniforti M.A. Interfacial gravity waves in a two-fluid system. Fluid Dynamics Research, 2002, no. 30, pp. 31–66.
 Camassa R., Hurley M.W., McLaughlin R.M., Passaggia P.-Y., Thomson C.F.C. Experimental investigation of nonlinear internal waves in deep water with miscible fluids. Journal of Ocean Engineering and Marine Energy, 2018, vol. 4, pp. 243–257.
 Win Ko Ko, Temnov A.N. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika — Tomsk State University Journal of Mathematics and Mechanics, 2021, no. 69. DOI: 10.17223/19988621/69/8
 Win Ko Ko, Temnov A.N. Effects of oscillations of a two-layer liquid in an axisymmetric vessel. AIP Conference Proceedings, 2021, no. 2318, paper no. 020004. https://doi.org/10.1063/5.0035840