Gyroscopic polynomials

Gyroscopic alignment of a fluid occurs when flow structures align with the rotation axis. This often gives rise to highly spatially anisotropic columnar that in combination complex domain boundaries pose challenges for efficient numerical discretizations and computations. We define gyroscopic polynomials be three-dimensional expressed coordinate system conforms rotational alignment. remap original radius-dependent onto right cylindrical or annular create computational this system. find volume element coordinates leads naturally hierarchy orthonormal bases. build bases out Jacobi vertical generalized radial. Because these explicitly conform found rapidly rotating systems represent fields relatively small number modes. develop operator structure one-dimensional semi-classical orthogonal as building block differential operators full domains. The generate sparse linear discretization acting on enables simulation strong