  High-resolution X-ray observations have revealed cavities and `cold fronts'
with sharp edges in temperature, density, and metallicity within galaxy
clusters. Their presence poses a puzzle since these features are not expected
to be hydrodynamically stable, or to remain sharp in the presence of diffusion.
However, a moving core or bubble in even a very weakly magnetized plasma
necessarily sweeps up enough magnetic field to build up a dynamically important
sheath around the object; the layer's strength is set by a competition between
`plowing up' of field and field lines slipping around the core. We show that a
two-dimensional approach to the problem is quite generally not possible. In
three dimensions, we show with analytic arguments and in numerical experiments,
that this magnetic layer modifies the dynamics of a plunging core, greatly
modifies the effects of hydrodynamic instabilities on the core, modifies the
geometry of stripped material, and even slows the fall of the core through
magnetic tension. We derive an expression for the maximum magnetic field
strength, the thickness of the layer, and the opening angle of the magnetic
wake. The morphology of the magnetic draping layer implies the suppression of
thermal conduction across the layer, thus conserving strong temperature
gradients over the contact surface. The intermittent amplification of the
magnetic field as well as the injection of MHD turbulence in the wake of the
core is identified to be due to vorticity generation within the magnetic
draping layer. These results have important consequences for understanding the
physical properties and the complex gasdynamical processes of the intra-cluster
medium, and apply quite generally to motions through other magnetized
environments, e.g., the ISM.
