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

Abstract

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.