Flow over a backward-facing step, a numerical study comparing a zand a σ-coordinate model

Abstract

Homogeneous, nonrotating flow over a backward-facing rounded step is simulated using the 2D vertical version of two general circulation models, a z-coordinate model—the Massachusetts Institute of Technology general circulation model (MITgcm)— and a σ-coordinate model—the Bergen Ocean Model (BOM). The backward-facing step is a well-known testcase since it is geometrically simple but still embodies important flow characteristics such as separation point, reattachment length, and recirculation of the flow. The study compares the core of the two models and uses constant eddy viscosities and diffusivities. The Reynolds numbers ranges from 2·102 to 2·106. The results correspond with previously published results having a relatively stationary separation point and a fluctuating reattachment length due to downslope propagating eddies released from the reattachment zone for Reynolds numbers higher than or equal to 2 · 104. For Reynolds number within the laminar regime, the flow is stationary. The discrepancies between the models increase by enhancing Reynolds numbers. The σ-coordinate model experiences a reduction in eddy sizes with increasing resolution and Reynolds numbers in correspondence with published experiments, while the size of the eddies are independent of the Reynolds number using theMITgcm. Due tomixing generated by the staircase topography, the z-coordinate model gives a better convergence of the separation point and reattachment length compared with the BOM; however, this conclusion might change with the inclusion of a relevant turbulence scheme.