Revisiting Bolgiano–Obukhov scaling for moderately stably stratified turbulence

Abstract

According to the celebrated Bolgiano–Obukhov (Bolgiano, J. Geophys. Res., vol. 64 (12), 1959, pp. 2226–2229; Obukhov, Dokl. Akad. Nauk SSSR, vol. 125, 1959, p. 1246) phenomenology for moderately stably stratified turbulence, the energy spectrum in the inertial range shows a dual scaling: the kinetic energy follows (i) ∼k−11/5 for k<kB, and (ii) ∼k−5/3 for k>kB, where kB is the 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>kB. We revisit this assumption, and using the constancy of kinetic and potential energy fluxes and simple theoretical analysis, we find that the k−5/3 spectrum is absent. This is because the velocity field at small scales is too weak to establish a constant kinetic energy flux as in passive scalar turbulence. A quantitative condition for the existence of the second regime is also derived in the paper.