EDP Sciences
Free access
Volume 580, August 2015
Article Number L3
Number of page(s) 5
Section Letters
DOI http://dx.doi.org/10.1051/0004-6361/201526472
Published online 23 July 2015

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, ez 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, WWnw + Ww = h′ + Φ′ + U, while is the acceleration driving the wavelike part of the solution.

© ESO, 2015