Abstract
The stability of a moving cylinder in a circulation flow of an ideal incompressible fluid with constant vorticity inside a stationary outer cylinder is investigated using Lagrangian mechanics methods. The Lagrange function in the form of a series expansion by a small displacement of the cylinder and the stability condition in the nonlinear approximation are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kop’ev, V.F. and Chernyshev, S.A., Instability of an oscillating cylinder in a circulation flow of ideal fluid, Fluid Dyn., 2000, vol. 35, no. 6, pp. 858–871.
Miles, J.W., On the generation of surface waves by shear flow. Part 2, J. Fluid Mech., 1959, vol. 6, no. 4, pp. 568–582.
Kop’ev, V.F. and Chernyshev, S.A., Vortex ring oscillations, the development of turbulence in vortex rings and generation of sound, Phys. Usp., 2000, vol. 43, no. 7, pp. 663–690.
Kopiev, V.F., Chernyshev, S.A., and Yudin, M.A., Instability of a cylinder in the circulation flow of incompressible ideal fluid, J. Appl. Math. Mech., 2017, vol. 81, no. 2, pp. 148–156.
Drazin, P.G. and Reid, W.H., Hydrodynamic Stability, 2nd ed., Cambridge: Univ. Press, 2004.
Chernyavskii, V.M. and Shtemler, Yu.M., Stability of couette flow between free cylinders with allowance for self-gravitation, Fluid Dyn., 1991, vol. 26, no. 5, pp. 729–737.
Vladimirov, V.A. and Ilin, K.I., On the arnold stability of a solid in a plane steady flow of an ideal incompressible fluid, Theor. Comput. Fluid Dyn., 1998, vol. 10, pp. 425–437.
Vladimirov, V.A. and Ilin, K.I., On the stability of the dynamical system ‘rigid body + inviscid fluid’, J. Fluid Mech., 1999, vol. 386, pp. 43–75.
Thomson, W. and Tait, P., Treatise on Natural Philsophy, Oxford: Univ. Press, 1867, vol. 1.
Kirchhoff, G., Mechanik, Leipzig: B.G. Teubner, 1897.
Thomson, W., On the motion of rigid solids circulating irrotationally through perforations in them or a fixed solid, Philos. Mag., vol. 45: Proc. R. Soc. Edinburgh, 1872, vol. 7, pp. 668–682.
Zhukovskii, N.E., Motion of the solid with cavities filled with homogeneous dropping liquid, in Izbrannye sochineniya (Selected Works), Moscow, Leningrad: Gostekhizdat, 1948, vol. 1, pp. 31–152.
Okhotsimskii, D.E., To the motion of solid with cavities partly filled with liquid, Prikl. Mat. Mekh., 1956, vol. 20, no. 1, pp. 3–20.
Moiseev, N.N. and Rumyantsev, V.V., Dinamika tela s polostyami, soderzhashchimi zhidkost’ (Dynamics for Solid with Liquid Filled Cavities), Moscow: Nauka, 1965.
Lamb, H., Hydrodynamics, Cambridge: Univ. Press, 1912.
Petrov, A.G., Hamiltonian principle and some dynamical problems on ideal liquid, Prikl. Mat. Mekh., 1983, vol. 47, no. 1, pp. 48–55.
Goncharov, V.P. and Pavlov, V.I., Gamil’tonovaya vikhrevaya i volnovaya dinamika (Hamiltonian Vortex and Wave Dynamics), Moscow: GEOS, 2008.
Kapitsa, P.L., Rapidly rotating rotor under friction: stability and whirling speed transition, Zh. Tekh. Fiz., 1939, vol. 9, no. 2, pp. 124–146.
Zhuravlev, V.F., Osnovy teoreticheskoi mekhaniki (Foundations of Theoretical Mechanics), Moscow: Fizmatlit, 2001.
Petrov, A.G., Analiticheskaya gidrodinamika (Analytical Hydrodynamics), Moscow: Fizmatlit, 2009.
Gantmakher, F.R., Lektsii po analiticheskoi mekhanike (Lectures on Analytical Mechanics), Moscow: Nauka, 1966.
Funding
This research was supported by Russian Science Foundation (project no. 19-19-00373).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Russian Text © The Author(s), 2019, published in Prikladnaya Matematika i Mekhanika, 2019, Vol. 83, No. 3, pp. 393–402.
Rights and permissions
About this article
Cite this article
Petrov, A.G., Yudin, M.A. On Cylinder Dynamics in Bounded Ideal Fluid Flow with Constant Vorticity. Fluid Dyn 54, 898–906 (2019). https://doi.org/10.1134/S0015462819070127
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462819070127