Abstract
Within the framework of the magnetohydrodynamic approach, a system of equations is derived for nonlinear evolution of long-wave axisymmetric perturbations on a conducting fluid jet with surface electric current, located along the axis of a conducting solid cylinder in a longitudinal magnetic field. The fluid is assumed to be inviscid, incompressible, and ideally conducting, like the cylinder walls. It is shown that, if the longitudinal field is uniform and the axial flow is shear-free, this system can be either hyperbolic or elliptic-hyperbolic, depending on problem parameters. The boundaries of hyperbolicity and ellipticity regions in the space of solutions are determined. In the hyperbolicity region, equations of characteristics and conditions on them are obtained. The problem of the decay of velocity discontinuity on the jet is considered. Conditions are found for the existence of a continuous self-similar solution in the hyperbolicity region, corresponding to collision of jets.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford (1961).
A. S. Gupta, “On the capillary instability of a jet carrying an axial current with or without a longitudinal magnetic field,” Proc. Roy. Soc. London, Ser. A, 278, No. 1373, 214-227 (1964).
Yu. M. Gel’fgat, S. V. Ol’shanskii, and G. A. Yavnaist, “Investigation of destruction of a liquid-metal jet under the action of axial current,” Magn. Gidrodin., No. 2, 59-54 (1973).
Yu. G. Gubarev and V. V. Nikulin, “Linear long-wave instability of one class of steady jet ows of an ideal uid in the field of its own electric field,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 2, 64-75 (2001).
J. J. Stoker, Water Waves, Interscience Publishers, New York (1957).
L. V. Ovsyannikov, “Two-layer ‘shallow-water’ model,” J. Appl. Mech. Tech. Phys., 20, No. 2, 127-135 (1979).
L. V. Ovsyannikov, “Justification of the shallow-water theory,” in: Dynamics of Continuous Media (collected scientific papers) [in Russian], No. 15, Novosibirsk (1973), pp. 104-125.
L. V. Ovsyannikov, “Justification of the shallow-water theory,” in: Proc. All-Union Conf. on Equations withPartial Derivatives Devoted to the 75th Anniversary of Academician I. G. Petrovskii [in Russian], Izd. Mosk.Univ., Moscow (1978), pp. 185-188.
L. D. Landau and E. M. Lifshits, Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media [in Russian],Nauka, Moscow (1982).
V. E. Zakharov, “Benney equations and quasiclassical approximation in the inverse problem method,” Funkts.Anal. Prilozh., 14, No. 2, 15-24 (1980).
L. V. Ovsyannikov, Lectures in Fundamentals of Gas Dynamics [in Russian], Nauka, Moscow (1981).
V. Yu. Liapidevskii, “Problem of discontinuity decay for two-layer ‘shallow-water’ equations,” in: Dynamics ofContinuous Media (collected scientific papers) [in Russian], No. 50, Novosibirsk (1981), pp. 85-97.
Yu. E. Adam’yan, A. N. Berezkin, V. M. Vasilevskii, et al., “Inuence of the axial superstrong magnetic field on the process of plasma expansion and heating upon an electric explosion of a wire,” in: Megagauss andMegaampere Pulse Technology and Applications, Proc. VII Int. Conf. on Generation of Megagauss MagneticFields and Related Experiments (Sarov, August 5-10, 1996), Vol. 2, Inst. of Experimental Physics, Sarov (1997),pp. 752-763.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nikulin, V.V. Model of Nonlinear Evolution of Long-Wave Perturbations on an Ideally Conducting Jet with Current in a Longitudinal Magnetic Field. Collision of Magnetized Jets. Journal of Applied Mechanics and Technical Physics 44, 305–311 (2003). https://doi.org/10.1023/A:1023402920396
Issue Date:
DOI: https://doi.org/10.1023/A:1023402920396