Stable Boundary Layers with Subsidence: Scaling and Similarity of the Steady State

The stable boundary layer (SBL) subjected to large-scale subsidence is studied through large-eddy simulations (LESs) with fixed surface temperature and a linear subsidence velocity profile. These boundary layers reach a steady state, where thermal equilibrium is established by a balance between surface cooling and subsidence-induced heating. We identify three governing dimensionless groups by scaling the governing equations with the geostrophic wind and Coriolis frequency, and systematically investigate the impact of these external parameters on global flow properties and mean profiles in the steady state. The SBL depth, low-level jet, and the magnitude of the turbulent momentum flux are reduced when the dimensionless subsidence rate or Buoyancy number increases, while surface heat flux is enhanced. The normalized mean profiles of potential temperature and heat flux are predominantly controlled by the subsidence number, whereas they converge for simulations with different buoyancy and surface Rossby numbers. Within the surface layer, dimensionless velocity and potential temperature gradients in the steady SBL with subsidence show acceptable agreement to Monin–Obukhov similarity theory, whereas the data suggests improved similarity when a recently proposed mixed scaling parameter is used. We furthermore develop empirical correlations for the stability parameter \(h_\theta /L_O\) $h_{\theta }/L_O$ and a thermal shape factor, and propose a new unidirectional geostrophic drag law, to form a closed set of equations that estimates relevant flow properties from external parameters. The estimation errors compared to the LES data are less than 5% for friction velocity and surface heat flux, and at most 10% for the SBL depth \(h_\theta \) $h_{\theta }$ .