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Revisiting Bolgiano–Obukhov scaling for moderately stably stratified turbulence

  • Shadab Alam (a1), Anirban Guha (a1) (a2) and Mahendra K. Verma (a3)

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)  ${\sim}k^{-11/5}$ for $k<k_{B}$ , and (ii)  ${\sim}k^{-5/3}$ for $k>k_{B}$ , where $k_{B}$ 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 $k>k_{B}$ . 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.

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Corresponding author

Email address for correspondence: anirbanguha.ubc@gmail.com

References

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Revisiting Bolgiano–Obukhov scaling for moderately stably stratified turbulence

  • Shadab Alam (a1), Anirban Guha (a1) (a2) and Mahendra K. Verma (a3)

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