Universal crossover from Kolmogorov to Bolgiano-Obukhov scaling in turbulence in a stably stratified fluid

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The energy spectrum E(k) of the turbulent kinetic energy at a given Richardson number Ri (a measure of stratification) is expected to be Kolmogorov-like (k−5/3) for Ri≪1 and Bolgiano-Obukhov like (k−11/5) for Ri≫1. This transition has rarely been seen. Using the Heisenberg – Chandrasekhar formulation of turbulence, we show that the transition is actually determined by the combination Ri4/3k and not by Ri alone. The transition can be described by a universal curve in the E(k) vs k plane.