Criteria for the asymptotic turbulence in rapidly rotating convection*

Turbulent rotating convection is the primary source of heat and momentum transfers in planetary and stellar flows. Key control parameters–the viscosity and the thermal diffusivity–in the flows are extremely small. As a result, theories often assume the existence of an asymptotic diffusivity-free heat scaling in the rapidly rotating convection, where the heat flux is independent of viscosity and thermal diffusivity. It is believed that when this heat scaling is achieved, the whole system becomes asymptotic or fully turbulent. Here, by performing extensive direct numerical simulations, we show that despite that the heat scaling behaves asymptotic, the kinetic energy dissipation rate can still be viscosity dependent, indicating the whole system is not fully asymptotic yet. A straightforward revision that bridges such a gap is presented based on the exact relations that link the dissipation rates with the heat transfer. Besides the heat scaling, an asymptotic Reynolds number scaling and a convective length scaling can be derived as well. The extrapolation of the results to more extreme parameters is only possible when all the three scalings are satisfied and when the flow is fully turbulent. Most importantly, realizing the asymptotic heat scaling itself does not necessarily signal the onset of the asymptotic or fully turbulent state in rapidly rotating convection.