The suitability of some second moment closures is discussed herein. A general frame of strongly realisable models is exhibited, and the ability of so-called "slow" terms to provide return-to-isotropy is examined. Hyperbolicity of first order differential systems is then investigated. When focusing on a simple so-called Gaussian closure, the solution of the Riemann problem associated to the generalised convection system is detailed, which confirms that realisability still holds when non regular solutions are involved. A priori suitable numerical consequences are then discussed. These results should be related to recent work pertaining to the numerical modelling of compressible flows using second order closures.