Revisiting Bolgiano-Obukhov scaling for stably stratified turbulence

According to the celebrated Bolgiano-Obukhov phenomenology for moderately stably stratified turbulence, the energy spectrum in the inertial range shows a dual scaling; the kinetic energy follows (i) $\sim k^{-11/5}$ for $k k_B$, where $k_B$ is Bolgiano wavenumber. The $k^{-5/3}$ scaling akin to passive scalar turbulence is a direct consequence of the assumption that buoyancy is insignificant for $k>k_B$. We revisit this assumption, and using constancy of kinetic and potential energy fluxes and simple theoretical analysis, we demonstrate an absence of the $ k^{-5/3}$ spectrum. This is because the velocity field at small scales is too weak to establish a constant kinetic energy flux as in passive scalar turbulence. Our findings may have important implications in the modelling of stably stratified turbulence.