  It is known that turbulent energy is rapidly transferred in the direction of
the rotation axis in a rotating system, in comparison with the non-rotating
case. In this study, this phenomenon is investigated as a problem of energy
diffusion expressed by the Reynolds averaged Navier-Stokes (RANS) model. The
conventional gradient-diffusion approximation for the turbulent energy flux
cannot account for the enhanced energy transport observed in rotating
inhomogeneous turbulence. In order to adequately describe the phenomenon, we
propose a new model for the energy flux due to the pressure associated with the
rotational motion of a fluid. The model of the energy flux is expressed to be
proportional to the turbulent helicity. This property is closely related to the
group velocity of inertial waves in a rapidly rotating fluid. The validity of
the model is assessed using a direct numerical simulation (DNS) of
inhomogeneous turbulence under rotation. It is shown that most of the turbulent
energy transport enhanced by the system rotation is attributed to the pressure
diffusion term. The spatial distribution of the energy flux due to the pressure
related to the system rotation is similar to that of the turbulent helicity
with negative coefficient. Hence, the new model which is proportional to the
turbulent helicity is able to qualitatively account for the enhanced energy
flux due to the system rotation. Finally, the helical Rossby number is proposed
in order to estimate the relative importance of the energy flux enhanced by the
turbulent helicity and the rotation, in comparison to the conventional
gradient-diffusion approximation.
