Third-order moment closure through a mass-flux approach

The parameterization of the third moments, the flux of the heat flux and th e flux of the potential temperature variance, is considered. It is shown th at present parameterizations of these moments using the mass-flux approach with a 'top-hat' profile assumption lead to a significant underestimation, resulting in an inaccurate representation of second moments in the convecti ve boundary layer. It is also shown that the underestimation is a result of the 'top-hat' profile assumption in which the sub-plume contributions to t he total fluxes are ignored. By including these contributions a new paramet erization is proposed, which satisfies the physical requirements of symmetr y and realizability, and gives results that are in fair agreement with the large-eddy simulation data.