An assessment of implicit-explicit time integrators for the pseudo-spectral approximation of Boussinesq thermal convection in an annulus

•Investigation of 26 IMEX schemes for Boussinesq convection in cylindrical annulus.•11 regimes studied, from laminar to turbulent.•Order 2 multistep and multistage schemes show expected order of convergence.•IMEX-RK schemes of order larger than 2 display occasional order reduction.•13 IMEX-RK schemes outperform popular CNAB2 scheme in advection-dominated limit.