Buoyant Ekman Layer

Abstract

The solution of a steady‐state, baroclinic boundary layer over a two‐dimensional terrain in an $f$ plane is obtained. The boundary‐layer thickness is found to be dependent on both the stability ${\mathrm{S\hspace{0.17em}=\hspace{0.17em}\alpha }}_m{\mathrm{g[(T}}_m{\mathrm{/H)\hspace{0.17em}+\hspace{0.17em}(g/c}}_p{\text{)]\hspace{0.17em}(4Ω}}^2{\mathrm{L)}}^{\text{−1}}$ and the terrain slope. For a given terrain slope $\alpha$ and Prandtl number $\mathrm{\sigma \hspace{0.17em}=\hspace{0.17em}\nu /k}$ , a critical value of the stability parameter $S$ is found to exist and be equal to ${\mathrm{-(\alpha }}^2{\mathrm{\sigma )}}^{\text{−1}}$ , beyond which the $\text{O(1)}$ boundary layer disappears completely. Except for neutral stability, the solution conserves up‐slope (or down‐slope) mass transport when the free‐stream thermal wind is parallel to the ridges, reflecting the fact that the boundary layer is “leak free.” When the free stream possesses a small cross‐ridge component, the Ekman suction is necessarily nonzero even under nonneutral conditions, so that the influx from the interior may be accommodated.