  Elliptical instability is due to a parametric resonance of two inertial modes
in a fluid velocity field with elliptical streamlines. This flow is a simple
model of the motion in a tidally deformed, rotating body. Elliptical
instability typically leads to three-dimensional turbulence. The associated
turbulent dissipation together with the dissipation of the large scale mode may
be important for the synchronization process in stellar and planetary binary
systems. In order to determine the influence of the compressibility on the
stability limits of tidal flows in stars or planets, we calculate the growth
rates of perturbations in flows with elliptical streamlines within ellipsoidal
boundaries of small ellipticity. In addition, the influence of the orbiting
frequency of the tidal perturber $\Omega_P$ and the viscosity of the fluid are
taken into account.
