On the transition of transient growth mechanism in Taylor–Dean flow

We investigate optimal perturbation and its transient growth characteristics in Taylor–Dean flow theoretically. The parameter [Formula: see text], accounting for the ratio of average pumping velocity induced by azimuthal pressure gradient to rotating velocity by rotating cylinders, is varied from −5 to 5. The results show that for the rigid rotation case, the energy growth of optimal perturbation is increased with increasing magnitude of azimuthal pressure gradient. Further, both the main and secondary peak of the amplitude of azimuthal velocity are seen to be shifted towards the outer cylinder for wide gap case, and both are shifted oppositely towards the inner cylinder for narrow gap case. Viewing the time evolution of the energies in the three velocity components for wide gap case, anti-lift-up mechanism replaces lift-up mechanism as the dominant mechanism for energy growth, when [Formula: see text] changes from −5 to 5. While for narrow gap case, lift-up mechanism is always responsible for transient growth of axisymmetric perturbation, no matter how strong azimuthal pressure gradient is considered.

Stability of Compressible Hollow Jet Pervaded by a Transverse Varying Magnetic Field

The magnetohydrodynamic stability of an ordinary compressible hollow cylinder pervaded by a transverse varying magnetic field, under the influence of capillary, inertia, and Lorentz force, has been developed. The problem is modelized. The basic equations formulated, solved, and, upon applying appropriate boundary conditions, the singular solutions are excluded. The eigenvalue relation has been derived and discussed. The capillary force has destabilizing influence only for long wavelengths in the axisymmetric perturbation but it is stabilizing in the rest and also so in the nonaxisymmetric perturbations. The compressibility increases the stable domains and simultaneously decreases those of instability. The electromagnetic force has different effects due to the axial uniform field and varying transverse one. The axial field is stabilizing for all wavelengths in all kinds of perturbations. The transverse field is stabilizing or not according to restrictions. Here, the high compressibility increases rapidly the magnetodynamic stable domains and leads to shrinking those of instability.

Capillary Electrodynamic Stability of Self-Gravitational Fluid Cylinder With Varying Electric Field

The instability of a self-gravitating fluid cylinder surrounded by a self-gravitating tenuous medium pervaded by transverse varying electric field is discussed under the combined effect of the capillary, self-gravitating, and electric forces. This has been done for all axisymmetric and nonaxisymmetric modes of perturbation. The problem is formulated and solved with excluding the singular solutions, and the stability criterion is derived. Several published works are obtained as limiting cases from the present general case and investigated, and moreover the results are interpreted physically. The model is stable due to the stabilizing effect of the transverse electric field in all modes of perturbation. The destabilizing effect of the capillary and self-gravitating forces is found in small domain in the axisymmetric perturbation. However, the stabilizing effects of the capillary and self-gravitating forces in large axisymmetric domains and in all nonaxisymmetric domains modify and improve the instability of the present model.

The nonlinear evolution of magnetic instabilities in a rapidly rotating annulus

A numerical investigation of the stability of an axisymmetric magnetic field is discussed. The magnetic field permeates a finitely conducting fluid contained within a rapidly rotating cylindrical annulus. The fluid is incompressible and viscid. The evolution of a non-axisymmetric perturbation to the axisymmetric magnetic field is governed by the momentum and induction equations which are integrated using a spectral timestep method. We follow the growth of the perturbation to finite amplitude and find that the character of the solution is dominated by the most unstable axially dependent mode found from the linear theory.

Magnetohydrodynamic stability of a streaming gas jet

The MHD stability of a gas jet surrounded by a streaming radially finite liquid cylinder (with solid cylindrical edge) is studied. The system is acted upon by capillary, electromagnetic and inertial liquid forces. The eigenvalue relation is established to all kinds of perturbations. The streaming has a strong destabilizing influence that is independent of all problem parameters. The capillary force is destabilizing only for small axisymmetric modes and stable for the rest. The electromagnetic force is strongly stabilizing whatever the intensities of the magnetic field. If the influence of the latter is sufficiently strong, the influence of the streaming can be completely suppressed. It is found that for an axisymmetric perturbation the domain of instability is the same whatever the value of the liquid radial distance.

Pulsational Instability of Accretion Disks around Compact Objects

Linear analysis shows that radial oscillations in accretion disks around compact object are overstable to axisymmetric perturbation under a variety of conditions. Furthermore, numerical simulations confirm that the radial oscillations induce quasi-periodic modulations of the disk luminosity. The disk oscillation model may be responsible for quasi-periodic oscillations (QPOs) observed in low mass X-ray binaries (LMXBs), cataclysmic variables (CVs), and other compact objects.