Kolmogorov argument for the scaling of the energy spectrum in a stratified fluid

• A Kolmogorov argument for global energy balance for turbulence in a stratified fluid is presented.
• It is seen that for unstable stratification an unambiguous argument cannot be set up.
• For stable stratification there is clear Kolmogorov scenario but the flux is a combination of kinetic and thermal fluxes.
• A pure Bolgiano–Obukhov scaling is seen only for wave-numbers greater than a critical wave-number.
• The critical wave-number decreases as the Richardson number increases.

In this work we show that the global energy balance part of the Kolmogorov argument for the kinetic energy spectrum in a homogeneous fluid repeated for the stratified fluid will inevitably exhibit a small deviation from perfect scaling. It is shown that an unambiguous scaling with an exponent of 11/5 can be observed only if the fluid is stably stratified in agreement with the original suggestion of Bolgiano. We find that even if the kinetic energy flux shows the predicted fall-off with wave-vector and the thermal energy (entropy) flux is constant, the kinetic energy spectrum will show a small deviation from perfect scaling.