  Spin-orbit misalignments have been detected in exoplanetary systems and
binary star systems. Tidal interactions may have played an important role in
the evolution of the spin-orbit angle. In this study, we investigate the tidal
interactions in spin-orbit misaligned systems. In particular, we focus on the
tidal response of a rotating fluid body to the obliquity tide, which may be
important for the evolution of the spin-orbit angle but hardly affects the
orbital evolution. The obliquity tide also provides a torque for the mutual
precession of the spin and orbital axes around the total angular momentum
vector, which has not yet been considered in previous studies on the tidal
interactions. In this paper, we first formulate a set of linearized equations
describing the tidal response in spin-orbit misaligned systems, taking into
account the precessional motion. Numerical solutions in a homogeneous fluid and
in a polytrope of index 1 show that dissipative inertial waves can be excited
on top of precession by the obliquity tide in the presence of a rigid core. The
tidal quality factor associated with the obliquity tide $Q'_{210}$ can be
several orders of magnitude smaller than those associated with other tidal
components if their frequencies fall outside the frequency range of inertial
waves. Therefore, it is possible that the spin-orbit misalignment undergoes
much more rapid decay than the orbital decay in hot Jupiter systems owing to
the enhanced dissipation of the obliquity tide.
