| Abstract: | The problem of the linear stability of a single particular class of helical steady-state flows of an ideal incompressible
infinitely-conducting fluid in a magnetic field is studied. A necessary and sufficient condition of stability of this class
of flows with respect to perturbations of the same symmetry type is obtained by the direct Lyapunov method 1, 2]. A priori
two-sided exponential estimates of the perturbation growth are derived, the corresponding exponents being calculated using
the steady flow parameters and the initial data for the perturbations. A class of the most rapidly growing perturbations is
identified and an exact formula for determining their growth rate is obtained. An example of steady-state flows and initial
perturbations whose linear stage of development with time can be described by means of the estimates obtained is constructed.
Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 150–156, January–February,
1999.
The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-01771). |
