Abstract
An analytical model describing the motion of vortex rings in an incompressible fluid is constructed. The model is valid both for homogeneous and inhomogeneous vortices buoyant in the gravity field, as well as for combined vortices. The expansion angle of a buoyant vortex is found from the characteristic parameters that define the flow rather than specified on the basis of experiments. Significant differences in the expansion angles of homogeneous and buoyant vortex rings are explained. The calculation results for the proposed model are compared with the results of laboratory experiments and data on the rise of the cloud produced by an atomic explosion.
Similar content being viewed by others
References
H. Lamb, Hydrodynamics (Dover, New York, 1945).
L. E. Fraenkel, “On Steady Vortex Rings of Small Cross-Section in an Ideal Fluid,” Proc. Roy. Soc. London, Ser. A 316(1524), 29–62 (1970).
P. G. Saffman, “The Velocity of Viscous Vortex Rings,” Stud. Appl. Math. 49(4), 371–380 (1970).
A. T. Onufriev, “Theory of the Motion of a Vortex Ring Under Gravity. Rise of the Cloud from a Nuclear Explosion,” Prikl. Mekh. Tekh. Fiz. 8(2), 3–15 (1967) [J. Appl. Mech. Tech. Phys. 8 (2), 1–7 (1967)].
V. F. Tarasov, “On the Motion of a Buoyant Vortex Ring,” in Dynamics of Continuous Media, No. 23 (Inst. of Hydrodynamics, Sib. Branch, USSR Acad. of Sci., Novosibirsk, 1975), pp. 210–218.
B. R. Morton, G. I. Taylor, and J. S. Turner, “Turbulent Gravitational Convection from Maintained and Instantaneous Sources,” Proc. Roy. Soc. London, Ser. A 234(1196), 1–23 (1956).
C. P. Wang, “Motion of an Isolated Buoyant Thermal,” Phys. Fluids 14(8), 1643–1647 (1971).
T. Maxworthy, “Turbulent Vortex Rings,” J. Fluid Mech. 64(2), 227–241 (1974).
Yu. S. Rusakov, “Dynamics of the Vertical Movement of a Turbulent Vortex Ring,” Izv. Ross. Akad. Nauk, Fiz. Atmos. Okeana 37(6), 750–760 (2001).
B. A. Lugovtsov, A. A. Lugovtsov, and V. F. Tarasov, “On the Motion of Turbulent Vortex Ring,” in Dynamics of Continuous Media, No. 3 (Inst. of Hydrodynamics, Sib. Branch, USSR Acad. of Sci., Novosibirsk, 1969), pp. 50–60.
Yu. A. Gostintsev, Yu. S. Matveev, V. E. Nebogatov, and A. F. Solodovnik, “On the Physical Modeling of Turbulent Thermals,” Prikl. Mekh. Tekh. Fiz. 27(6), 53–57 (1986) [J. Appl. Mech. Tech. Phys. 27 (6), 836–839 (1986)].
D. G. Akhmetov, Vortex Rings Vortex Rings (Izd. Geo, Novosibirsk, 2007; Springer, Berlin, 2009).
V. A. Vladimirov, “Vortical Momentum of Flows of an Incompressible Fluid,” Prikl. Mekh. Tekh. Fiz. 18(6), 72–77 (1977) [J. Appl. Mech. Tech. Phys. 18 (6), 791–794 (1986)].
B. I. Zaslavskii and I. M. Sotnikov, “Experimental Study of Buoyant Vortex Rings,” Prikl. Mekh. Tekh. Fiz. 24(1), 20–26 (1983) [J. Appl. Mech. Tech. Phys. 24 (1), 16–21 (1983)].
The Effect of Nuclear Weapons, Ed. by S. Glasstone (U.S. Department of Defense and U.S. Atomic Energy Commission, 1962; Voenizdat, Moscow, 1965).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.V. Nikulin.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 55, No. 4, pp. 11–18, July–August, 2014
Rights and permissions
About this article
Cite this article
Nikulin, V.V. Analytical model of motion of turbulent vortex rings in an incompressible fluid. J Appl Mech Tech Phy 55, 558–564 (2014). https://doi.org/10.1134/S0021894414040026
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894414040026