Scaling behavior of velocity and temperature in a shell model for thermal convective turbulence

Based on the conservation of total energy and entropy under conditions of nonviscosity and forcing-free, a shell model is developed to simulate the thermal convective turbulence. A fluxlike coupling mode is supposed to ensure that the total exchanging energy (EE) between the velocity and temperature is conserved when omitting the buoyancy, external forcing, and viscous effects. We call this EE conservation. Under such assumptions, the relative scaling exponents of structure functions with order p are almost parameter independent and consistent with a multiplicative cascade model presented by She and Leveque [Phys. Rev. Lett. 72, 336 (1994)]. Moreover, the energy spectra with different controlling parameters can be collapsed into a single curve by Kolmogorov scaling. Otherwise, the model behaviors may be parameter dependent.