  We investigate the damping of neutron star r-modes due to the presence of a
viscous boundary (Ekman) layer at the interface between the crust and the core.
Our study is motivated by the possibility that the gravitational-wave driven
instability of the inertial r-modes may become active in rapidly spinning
neutron stars, eg. in low-mass X-ray binaries, and the fact that a viscous
Ekman layer at the core-crust interface provides an efficient damping mechanism
for these oscillations. We review various approaches to the problem and carry
out an analytic calculation of the effects due to the Ekman layer for a rigid
crust. Our analytic estimates support previous numerical results, and provide
further insight into the intricacies of the problem. We add to previous work by
discussing the effect that compressibility and composition stratification have
on the boundary layer damping. We show that, while stratification is
unimportant for the r-mode problem, composition suppresses the damping rate by
about a factor of two (depending on the detailed equation of state).
