A linear stability analysis has been implemented for hydromagnetic
dissipative Couette
flow, a viscous electrically conducting fluid between rotating concentric
cylinders in the
presence of a uniform axial magnetic field. The small-gap equations with
respect to
non-axisymmetric disturbances are derived and solved by a direct numerical
procedure.
Both types of boundary conditions, conducting and non-conducting walls,
are
considered. A parametric study covering wide ranges of μ, the ratio
of angular velocity
of the outer cylinder to that of inner cylinder, and Q, the Hartmann
number which
represents the strength of axial magnetic field, is conducted. Results
show that the
stability characteristics depend on the conductivity of the cylinders.
For the case of
non-conducting walls, it is found that the critical disturbance is a non-axisymmetric
mode as the value of μ is sufficiently negative and the domain
of Q where non-axisymmetric
instability modes prevail is limited. Similar results are obtained for
conducting walls at low Hartmann number. In addition, the transition of
the onset of
instability from non-axisymmetric modes to axisymmetric modes for the case
μ=−1
with increasing strength of magnetic field are discussed in detail. For
high values of the
Hartmann number, the critical disturbance is always the axisymmetric stationary
mode
for non-conducting walls but not for conducting walls. For
−1[les ]μ<1, it is demonstrated that non-axisymmetric instability
modes prevail in a wide range of Q for
conducting walls and axisymmetric oscillatory modes may, in fact, become
more
critical than both of the non-axisymmetric and axisymmetric stationary
modes at
higher values of the Hartmann number.
THE STABILITY OF NON-DISSIPATIVE COUETTE FLOW IN THE PRESENCE OF AN AXIAL MAGNETIC FIELD
