Taylor–Couette flow in the presence of a magnetic field is a problem belonging to classical hydromagnetics and deserves to be more widely studied than it has been to date. In the nonlinear regime the literature is scarce. We develop a formulation suitable for solution of the full three dimensional nonlinear hydromagnetic equations in cylindrical geometry, which is motived by the formulation for...

We consider the stability of a configuration consisting of a vertical magnetic field in a planar flow on elliptical streamlines in ideal hydromagnetics. In the absence of a magnetic field the elliptical flow is universally unstable (the “elliptical instability”). We find this universal instability persists in the presence of magnetic fields of arbitrary strength, although the growthrate decreas...

The effect of the magnetic skew on the Parker instability is investigated by means of the linear stability analysis for a gravitationally stratified gas layer permeated by a horizontal magnetic field. When the magnetic field is skewed (i.e., the field line direction is a function of the height), the wavelength of the most unstable mode is λ ∼ 10H where H is the pressure scale height. The growth...

Recent work on Alfvenic turbulence by Goldreich & Sridhar (1995; GS) suggests that the energy cascades almost entirely perpendicular to the local magnetic field. As a result, the cyclotron resonance is unimportant in dissipating the turbulent energy. Motivated by the GS cascade, we calculate the linear collisionless dissipation of Alfven waves with frequencies much less than the proton cyclotro...

Gravitational collapse of the cylindrical elongated cloud is studied by numerical magnetohydrodynamical simulations. In the infinitely long cloud in hydrostatic configuration, small perturbations grow by the gravitational instability. The most unstable mode indicated by a linear perturbation theory grows selectively even from a white noise. The growth rate agrees with that calculated by the lin...

In this, the second of a series of three papers, we continue a detailed description of ZEUS-2D, a numerical code for the simulation of uid dynamical ows in astrophysics including a self-consistent treatment of the e ects of magnetic elds and radiation transfer. In this paper, we give a detailed description of the magnetohydrodynamical (MHD) algorithms in ZEUS-2D. The recently developed constrai...