10.6084/m9.figshare.12643928.v1 Jérémie Vidal Jérémie Vidal David Cébron David Cébron SuppMat_Vidal_revised.pdf from Acoustic and inertial modes in planetary-like rotating ellipsoids The Royal Society 2020 rotating flows compressibility inertial modes triaxial ellipsoid planets 2020-07-11 16:30:35 Journal contribution https://rs.figshare.com/articles/journal_contribution/SuppMat_Vidal_revised_pdf_from_Acoustic_and_inertial_modes_in_planetary-like_rotating_ellipsoids/12643928 Finding hydrostatic solutions in ellipsoids is a challenging task. An idealised reference state has been introduced in the main text, which admits simple polynomial expressions in the Cartesian coordinates. We outline a method to obtain more realistic background models, which are compatible with the polynomial algorithm.