Explicit algebraic turbulence models and their application to the atmospheric boundary layer

Turbulent flows with buoyancy effects occur in many situations, both in industry and in the atmosphere. It is challenging to correctly model such flows, especially in the case of stably stratified turbulence, where vertical motions are damped by buoyancy forces. For this purpose, we have derived a so-called explicit algebraic model for the Reynolds stresses and turbulent heat flux that gives accurate predictions in flows with buoyancy effects. Although inspired by turbulence models from engineering, the main aim of our work is to improve the parametrization of turbulence in the atmospheric boundary layer(ABL).

Explicit algebraic models are a class of parametrizations that, on the one hand, are more advanced than standard flux-gradient relationships,while on the other hand being significantly easier to handle numerically than higher-order models, which require the solution of Reynolds stress transport equations. In our derivation, we have extended the ideas previously developed by Wallin & Johansson(2000) and Wikström et al. (2013), with a special focus on stable stratification. Careful considerations of the algebra lead to a consistent formulation of the Reynolds stresses and turbulent heat flux,which is more general and robust than previous models of a similar kind. The model is shown to give good results compared to direct numerical simulations of engineering test cases, such as turbulent channel flow.

The next step is to test the performance of the model in an atmospheric context. For this purpose, we make use of the test cases provided by the GABLS(GEWEX Atmospheric Boundary Layer Study) intercomparison project for single-column models. In the first of these test cases(GABLS-1, Cuxart et al. 2006), a stable atmospheric boundary layer develops through a constant surface cooling rate. The model is able to give good predictions of this case compared to LES and shows significant improvements compared to most other models tested in the GABLS project. The second test case simulates a full diurnal cycle (Svensson et al ., 2011) and will test the model's ability to handle both stable and convective conditions. Preliminary studies of this case have proven to be satisfactory. A more thorough comparison with other models will follow, as well as a study of the GABLS-4 case in which very stable conditions are considered.

References

Cuxart et al. (2006) "Single-column model intercomparison for a stably stratified atmospheric boundary layer.", Bound.-Layer Meteorol., 118, 272-303.

Lazeroms, W.M.J., Brethouwer, G., Wallin, S. & Johansson, A.V. (2013) "An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows." Accepted Accepted for publication in J. Fluid Mech.

Svensson et al. (2011) "Evaluation of the diurnal cycle in the atmospheric boundary layer over land as represented by a variety of single-column models: the second GABLS experiment." Bound.-Layer Meteorol., 140, 177-206.

Wallin, S. & Johansson, A.V. (2000) "An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows." J. Fluid Mech. 403, 89-132

Wikström, P.M., Wallin, S. & Johansson, A.V. (2000) "Derivation and investigation of a new explicit algebraic model for the passive scalar flux." Phys. Fluids, 12, 688-702.