Anisotropic turbulence is ubiquitous in atmospheric and oceanic boundary layers due to differences in energy injection mechanisms. Unlike mechanical production that injects energy in the streamwise velocity component, buoyancy affects only the vertical velocity component. This anisotropy in energy sources, quantified by the flux Richardson numberRi(f), is compensated by a "return to isotropy" (RTI) tendency of turbulent flows. Describing RTI in Reynolds-averaged models and across scales continues to be a challenge in stratified turbulent flows. Using phenomenological models for spectral energy transfers, the necessary conditions for which the widely-used Rotta model captures RTI across variousRi(f)and eddy sizes are discussed for the first time. This work unravels adjustments to the Rotta constant, withRi(f)and scale, necessary to obtain consistency between RTI models and the measured properties of the atmospheric surface layer for planar-homogeneous and stationary flows in the absence of subsidence. A range ofRi(f)and eddy sizes where the usage of a conventional Rotta model is prohibited is also found. Those adjustments lay the groundwork for new closure schemes.