Abstract
We describe one-dimensional (1D) simulations of the countergradient zone of mean potential temperature \(\overline{\theta}\) observed in the convective boundary layer (CBL). The method takes into account the third-order moments (TOMs) in a turbulent scheme of relatively low order, using the turbulent kinetic energy equation but without prognostic equations for other second-order moments. The countergradient term is formally linked to the third-order moments \(\overline{w^{\prime 2}\theta'}\) and \(\overline{w'\theta^{\prime 2}}\), and a simple parameterization of these TOMs is proposed. It is validated for several cases of a dry CBL, using large-eddy simulations that have been realized from the MESO-NH model. The analysis of the simulations shows that TOMs are responsible for the inversion of the sign of \(\partial \overline{\theta}\,/\,\partial z\) in the higher part of the CBL, and budget analysis shows that the main terms responsible for turbulent fluxes and variances are now well reproduced.
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