An evaluation of Eulerian and semi-Lagrangian advection schemes in simulations of rotating, stratified flows in the laboratory. Part I: Axisymmetric flow

A series of numerical simulations of steady, thermally stratified flow of a Boussinesq, incompressible fluid in a rotating, cylindrical fluid annulus were carried out over ranges of spatial resolution, grid stretch, and rotat ion rate. A range of different numerical advection schemes were used for th e representation of heat transport, including a conventional conservative s econd-order Eulerian scheme and three different variants of a semi-Lagrangi an scheme used either for temperature advection alone, or for both thermal and momentum advection. The resulting simulations were compared both with e ach other, and with high precision measurements of velocity, temperature. a nd total heat transport in the laboratory. The performance of the semi-Lagr angian scheme was found to be quite strongly sensitive to the spatial inter polation algorithm. A basic tensor cubic scheme generally produced good sim ulations of steady 2D and 3D flows, although the somewhat more accurate ten sor quintic scheme (which is, however. also significantly more expensive) a ppeared to offer some detectable improvements in accuracy and performance i n some cases. A split cubic scheme (which is computationally cheaper but fo rmally less accurate) gave generally poor results in practice and is not re commended. In all cases considered, both the fully Eulerian and most forms of the semi-Lagrangian schemes gave good quantitative agreement with the la boratory measurements when extrapolated to very high resolution. Some signi ficant systematic errors in the simulated heat transport and zonal momentum were found with all schemes, however, when run at moderate (though by no m eans very low) resolution. The semi-Lagrangian Schemes had a tendency to ov erestimate heat transport relative to the laboratory measurements compared with the Eulerian schemes, but the latter tended to overestimate zonal mome ntum relative to the laboratory flows compared with the fully semi-Lagrangi an simulations.