  We consider a two-dimensional model of double-diffusive convection and its
time discretisation using a second-order scheme which treat the nonlinear term
explicitly (backward differentiation formula with a one-leg method). Uniform
bounds on the solutions of both the continuous and discrete models are derived
(under a timestep restriction for the discrete model), proving the existence of
attractors and invariant measures supported on them. As a consequence, the
convergence of the attractors and long time statistical properties of the
discrete model to those of the continuous one in the limit of vanishing
timestep can be obtained following established methods.
