  Elliptical galaxies moving through the intra-cluster medium (ICM) are
progressively stripped of their gaseous atmospheres. X-ray observations reveal
the structure of galactic tails, wakes, and the interface between the galactic
gas and the ICM. This fine-structure depends on dynamic conditions (galaxy
potential, initial gas contents, orbit in the host cluster), orbital stage
(early infall, pre-/post-pericenter passage), as well as on the still
ill-constrained ICM plasma properties (thermal conductivity, viscosity,
magnetic field structure). Paper I describes flow patterns and stages of
inviscid gas stripping. Here we study the effect of a Spitzer-like temperature
dependent viscosity corresponding to Reynolds numbers, Re, of 50 to 5000 with
respect to the ICM flow around the remnant atmosphere. Global flow patterns are
independent of viscosity in this Reynolds number range. Viscosity influences
two aspects: In inviscid stripping, Kelvin-Helmholtz instabilities (KHIs) at
the sides of the remnant atmosphere lead to observable horns or wings.
Increasing viscosity suppresses KHIs of increasing length scale, and thus
observable horns and wings. Furthermore, in inviscid stripping, stripped
galactic gas can mix with the ambient ICM in the galaxy's wake. This mixing is
suppressed increasingly with increasing viscosity, such that viscously stripped
galaxies have long X-ray bright, cool wakes. We provide mock X-ray images for
different stripping stages and conditions. While these qualitative results are
generic, we tailor our simulations to the Virgo galaxy M89 (NGC 4552), where
Re~ 50 corresponds to a viscosity of 10% of the Spitzer level. Paper III
compares new deep Chandra and archival XMM-Newton data to our simulations.
