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 number Ri 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 various Ri f and eddy sizes is discussed for the first time. This work unravels adjustments to the Rotta constant, with Ri 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 of Ri 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.

Plain Language Summary

In the atmosphere and in oceans, turbulence dominates much of the exchanges of momentum, heat, water vapor, and scalars such as carbon dioxide, ozone, or methane. Representing turbulence in numerical models of the Earth and climate system remains a first‐order problem, requiring the development of simplified approaches to describe the energetics of the flow. One such representation is based on the universal tendency of all turbulent flows to attain an isotropic state, where kinetic energy is equi‐partitioned among its three velocity components, labelled `return‐to‐isotropy'. However, the presence of buoyancy forces and mechanical generation of turbulence causes the flow to be anisotropic at a wide range of eddy sizes. To what degree this additional layer of complexity invalidates the use of existing models based on the aforementioned universal attainment of an isotropic state is explored here. Common representation of such phenomenon within existing climate‐ and meso‐scale models are shown to be satisfactory only for a restricted range of density stratification. The analysis unfolds conditions where adjustments to existing representations are required and others where their use is prohibited. Novel physical processes are also unfolded, providing guidance towards improved turbulence representation in a plethora of models.