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Two-layer bulk models of the cloudy boundary layer are investigated, focusing on the consistency issues between common assumptions on the turbulent mixing and the thermodynamic profiles. Simplifications of the vertical structure of the conserved variables are shown to lead to inconsistent steady states: first, linear profiles in the cloud layer are incompatible with the common parameterizations of the turbulent mixing. Second, this approximation is inconsistent with simple models of andoi:10.1175/jas3427.1 fatcat:6vgdileijbf4tdeyzc3id4lvyu