Dynamical aspect of entropy transfer in free convection turbulence

Abstract

From a dynamical perspective, entropy transfer processes are investigated in two-dimensional free convection turbulence in comparison with an entropy cascade picture based on the coupled dynamics of the T vorticity $\mathit{\ensuremath{\chi}}\ensuremath{\equiv}({\ensuremath{\partial}}_{y}T,\ensuremath{-}{\ensuremath{\partial}}_{x}T)$ and the velocity gradient tensor. Typical entropy transfer processes are observed in direct numerical simulations. For these processes, two characteristic times, the transfer time and the staying time are determined: the former time obeys a Bolgiano-Obukhov (BO) time scaling corresponding to the eddy turnover time in energy cascade. It is suggested that this typical transfer process is not an elementary process of cascade but a dynamical manifestation of intermittency. To examine the meaning of the characteristic times of the typical entropy transfer process, a shell model is constructed based on the entropy cascade picture. By this model, it is shown numerically that typical entropy transfer processes are regarded as the fluctuations satisfying a dynamical similarity. This similarity proved by perturbation analysis requires naturally that the transfer time should obey the BO time scaling.