Revisiting the Bulk Relation for Heat Flux in the Free Convection Limit

We modify the velocity applied to the bulk relation for surface heat flux using turbulent kinetic energy, such that the effect of horizontal flow induced by unresolved free convection is incorporated. Numerical experiments with a large-eddy simulation (LES) and a single-column model (SCM) are examined for an ideal convective boundary layer. The surface fluxes obtained from both models are compared to investigate the effect of the velocity correction. It is confirmed that the surface heat flux calculated with the velocity correction is relatively consistent between the LES and SCM, even for a free convection case. Furthermore, the proposed method provides an evaluation of the surface heat flux that is insensitive to the model resolution, unlike the conventional method.