MHD Instability in cylindric Taylor-Couette flow
msra(2001)
摘要
The linear marginal instability of an axisymmetric MHD Taylor-Couette flow of
infinite vertical extension is considered. For flows with a resting outer
cylinder there is a well-known characteristic Reynolds number even without
magnetic field but for sufficiently weak magnetic fields there are solutions
with smaller Reynolds numbers so that a characteristic minimum exists. The
minimum only exists, however, for not too small magnetic Prandtl numbers. For
small magnetic Prandtl numbers one only finds the typical magnetic suppression
of the instability.
We are here particularly interested in the case where the outer cylinder
rotates so fast that the Rayleigh criterion for hydrodynamic stability is
fulfilled. We find that for given magnetic Prandtl number now always a magnetic
field amplitude exists where the characteristic Reynolds number is minimal.
These critical values are computed for different magnetic Prandtl numbers. In
all cases the Reynolds numbers are running with 1/Pm so that for the small
magnetic Prandtl numbers of sodium (10^-5) or gallium (10^-6) the critical
Reynolds numbers exceed values of 10^6 or 10^, resp.
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关键词
critical value,reynolds number,magnetic field,hydrodynamic stability
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