Abstract:
The problem of the linear stability of steady-state axisymmetric shear jet flows of a perfectly conducting inviscid incompressible fluid with a free surface in an azimuthal magnetic field is studied. The necessary and sufficient condition for the stability of these flows against small axisymmetric long-wave perturbations of special form is obtained by the direct Lyapunov method. It is shown that if this stability condition is not satisfied, the steady-state flows considered are unstable to arbitrary small axisymmetric long-wave perturbations. A priori exponential estimates are obtained for the growth of small perturbations. Examples are given of the steady-state flows and small perturbations imposed on them which evolve in time according to the estimates obtained.
Keywords:
jet shear flows, long-wave approximation, stability, direct Lyapunov method.
Citation:
Yu. G. Gubarev, “Stability of steady-state shear jet flows of an ideal fluid with a free boundary in an azimuthal magnetic field against small long-wave perturbations”, Prikl. Mekh. Tekh. Fiz., 45:2 (2004), 111–123; J. Appl. Mech. Tech. Phys., 45:2 (2004), 239–248
\Bibitem{Gub04}
\by Yu.~G.~Gubarev
\paper Stability of steady-state shear jet flows of an ideal fluid with a free boundary in an azimuthal magnetic field against small long-wave perturbations
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2004
\vol 45
\issue 2
\pages 111--123
\mathnet{http://mi.mathnet.ru/pmtf2363}
\elib{https://elibrary.ru/item.asp?id=17249161}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2004
\vol 45
\issue 2
\pages 239--248
\crossref{https://doi.org/10.1023/B:JAMT.0000017587.78416.b8}
Linking options:
https://www.mathnet.ru/eng/pmtf2363
https://www.mathnet.ru/eng/pmtf/v45/i2/p111
This publication is cited in the following 2 articles:
Yuriy G. Gubarev, AIP Conference Proceedings, 2027, 2018, 030025
Yu. G. Gubarev, “Linear stability criterion for steady screw magnetohydrodynamic flows of ideal fluid”, Thermophys. Aeromech., 16:3 (2009), 407
Citation in format AMSBIB
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