## Online material

### Appendix A: Dynamical equations for tidal flows in convective envelopes

The solutions of the system of dynamical equations for the envelope written in the co-rotating frame are separated into a non-wavelike part (with subscripts _{nw}), which corresponds to the immediate hydrostatic adjustment to the external tidal potential (*U*), and a wavelike part (with subscript _{w}) driven by the action of the Coriolis acceleration on the non-wavelike part, (A.1)

where ** s** is the displacement,

*e*_{z}the unit vector along the rotation axis,

*h*the specific enthalpy, and Φ is the self-gravitational potential of A. Primed variables denote an Eulerian perturbation in relation to the unperturbed state with unprimed variables. We note that

*U*being of the first order in tidal amplitude, it appears in perturbation equations. Finally,

*W*≡

*W*

_{nw}+

*W*

_{w}=

*h*′ + Φ′ +

*U*, while is the acceleration driving the wavelike part of the solution.

*© ESO, 2015*