The turbulent kinetic energy budget for shallow cumulus convection

Turbulence Kinetic Energy (TKE) budgets derived from large-eddy simulations of the cumulus-capped boundary layer are analysed using recently developed similarity ideas. The budgets for the main part of the cumulus layer and the overlying inversion and the cloud-base transition zone are considered separately. The terms in the budget can be scaled using the similarity theory developed by Grant and Brown (1999). Below the inversion, TKE is produced by buoyancy, with the transport of TKE representing a loss of TKE. In the inversion layer, the transport of TKE from the underlying cloud layer is the dominant production term, although negatively buoyant downdraughts are present in the upper part of the inversion and contribute to the production of TKE. The terms in the TKE budget in the transition zone between the subcloud and cloud layers scale with mixed-layer scales, but for the buoyancy production term there is a region in which both mixed-layer and cloud-layer scalings are valid. Using the mass-flux approximation in conjunction with the scaling results, it is shown that it is possible to obtain a parametrization of the cumulus mass-flux profile.