Theory on Tidally Forced Planetary Waves in the Tachocline of Solar-like Stars

We present a new shallow-water formulation of forced magnetohydrodynamic Ross-
by waves originating in the tachocline of solar-like stars. As a novelty to former descriptions,
we add an external tidal potential to the equations and further include a linear damping law,
allowing us to study wave motions driven by arbitrary tidal forces. The model is applied to the
specific case of our sun, where we consider the action of the tidally dominant planet Jupiter.
We present an explicit analytic solution to this problem, which we finally use to estimate
characteristic responding wave amplitudes.