A k-ɛ Turbulence Model for the Stable Atmosphere

A realizable k-ɛ turbulence model of incompressible fluid is extended for the stable atmosphere after taking account of the buoyancy damping of gravity waves. The new model is consistent with the Monin-Obukhov similarity theory on the stable atmospheric boundary layer (ABL) over a horizontally uniform surface. The model is incorporated into an ABL model to simulate mean flow against observations. Its ABL-model output is compared with the Leipzig dataset, showing the turbulence model works well for a stable ABL. Specifically, the ABL model properly replicates 1) the mixing length, turbulent viscosity, and mean wind; 2) a significant decrease of the mixing length with height in the upper ABL and thus a reasonable altitude of the ABL top; and 3) a sensitivity of the mixing length and turbulent viscosity to atmospheric stability.