A Model Study of the Stably Stratified Planetary Boundary Layer

Abstract

A second-order turbulence model is used to study the stable boundary layer (SBL). Over a horizontal surface, a constant surface cooling rate drives the SBL to a steady state within a few hours. Parameterizations are developed for eddy diffusivities, the kinetic energy dissipation rate and the geostrophic drag law in this idealized case. Over a sloped surface, a constant cooling rate produces a quasi-steady-state SBL in which some flow properties continue to vary but h(|f|/u*L)½ becomes constant; however, this constant is a function of the wind direction relative to the slope and the baroclinity, as measured by the cooling rate times the slope. Calculated eddy diffusivity profiles in the baroclinic (sloping terrain) case compare well with recent data from Antarctica. If a surface energy budget is used rather than a constant cooling rate, the SBL does not reach a steady state even over a horizontal surface; the nondimensional height slowly decays. We conclude that equilibrium models of the SBL are likely to be much less applicable to the real world than are their counterparts for the convective boundary layer.