R-modes in the ocean of a magnetic neutron star

We study the dynamics of r-modes in the ocean of a magnetic neutron star. We modeled the star’s ocean with a spherical rotating thin shell and assumed that the magnetic field symmetry axis is not aligned to the shell’s spin axis. In the magnetohydrodynamic approximation, we calculate the frequency of $\mathrm{\ell }=m$ r-modes in the shell of an incompressible fluid. Different r-modes with $\mathrm{\ell }$ and $\mathrm{\ell }\pm 2$ are coupled by the {\it inclined} magnetic field. Kinematical secular effects for the motion of a fluid element in the shell undergoing $\mathrm{\ell }=m=2$ r-mode are studied. The magnetic corrected drift velocity of a given fluid element undergoing the $\mathrm{\ell }=m$ r-mode oscillations is obtained. The magnetic field increases the magnitude of the fluid drift produced by the r-mode drift velocity, the high-$\mathrm{\ell }$ modes in the ocean fluid will damp faster than the low-$\mathrm{\ell }$ ones.