Understanding the different scaling behavior in various shell models proposed for turbulent thermal convection

Different scaling behavior has been reported in various shell models proposed for turbulent thermal convection. In this paper, we show that buoyancy is not always relevant to the statistical properties of these shell models even though there is an explicit coupling between velocity and temperature in the equations of motion. When buoyancy is relevant (irrelevant) to the statistical properties, the scaling behavior is Bolgiano-Obukhov (Kolmogorov) plus intermittency corrections. We show that the intermittency corrections of temperature could be solely attributed to fluctuations in the entropy transfer rate when buoyancy is relevant but due to fluctuations in both energy and entropy transfer rates when buoyancy is irrelevant. This difference can be used as a criterion to distinguish whether temperature is behaving as an active or a passive scalar.