  Approximate empirical models of thermal convection can allow us to identify
the essential properties of the flow in simplified form, and to produce
empirical estimates using only a few parameters. Such "low-dimensional"
empirical models can be constructed systematically by writing numerical or
experimental measurements as superpositions of a set of appropriate basis
modes, a process known as Galerkin projection. For three-dimensional convection
in a cylinder, those basis modes should be vector-valued, mutually orthogonal,
and defined in cylindrical coordinates. Here we construct such a basis set and
demonstrate that it has these desired properties and boundary conditions when
the exact constraint of incompressibility is relaxed. We show its use for
representing sample simulation data and point out its potential for
low-dimensional convection models.
