A numerical solution of the linear Rayleigh-Bénard convection equations with the B- and C-grid formulations

Abstract

The numerical solutions of the linear Rayleigh-Bénard convection equations using the Arakawa B- and C-grid formulations are compared with the analytic solution. The results show that the C-grid simulates better the growth rates of unstable modes. A convective parameterization is required when the horizontal grid size is larger than the horizontal scale of the most unstable mode, the latter being of the same order as the depth scale of the unstable stratification. Non-hydrostatic effects become important when the horizontal grid size is smaller than the scale of the unstable stratification.