Direct simulation of the stably stratified turbulent Ekman layer

The three-dimensional time-dependent turbulent flow in the stably stratified Ekman layer over a smooth surface is computed numerically by directly solving the Navier–Stokes equations, using the Boussinesq approximation to account for buoyancy effects. All relevant scales of motion are included in the simulation so that no turbulence model is needed. The Ekman layer is an idealization of the Earth's boundary layer and provides information concerning atmospheric turbulence models. We find that, when non-dimensionalized according to Nieuwstadt's local scaling scheme, some of the simulation data agree very well with atmospheric measurements. The results also suggest that Brost & Wyngaard's ‘constant Froude number’ and Hunt's ‘shearing length’ stable layer models for the dissipation rate of turbulent kinetic energy are both valid, when Reynolds number effects are accounted for. Simple gradient closures for the temperature variance and heat flux demonstrate the same variation with Richardson number as in Mason & Derbyshire's large-eddy simulation (LES) study, implying both that the models are relatively insensitive to Reynolds number and that local scaling should work well when applied to the stable atmospheric layer. In general we find good agreement between the direct numerical simulation (DNS) results reported here and Mason & Derbyshire's LES results.