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It is known that turbulent energy is rapidly transferred in the direction ofthe rotation axis in a rotating system, in comparison with the non-rotatingcase. In this study, this phenomenon is investigated as a problem of energydiffusion expressed by the Reynolds averaged Navier-Stokes (RANS) model. Theconventional gradient-diffusion approximation for the turbulent energy fluxcannot account for the enhanced energy transport observed in rotatinginhomogeneous turbulence. In order to adequately describe the phenomenon, wepropose a new model for the energy flux due to the pressure associated with therotational motion of a fluid. The model of the energy flux is expressed to beproportional to the turbulent helicity. This property is closely related to thegroup velocity of inertial waves in a rapidly rotating fluid. The validity ofthe model is assessed using a direct numerical simulation (DNS) ofinhomogeneous turbulence under rotation. It is shown that most of the turbulentenergy transport enhanced by the system rotation is attributed to the pressurediffusion term. The spatial distribution of the energy flux due to the pressurerelated to the system rotation is similar to that of the turbulent helicitywith negative coefficient. Hence, the new model which is proportional to theturbulent helicity is able to qualitatively account for the enhanced energyflux due to the system rotation. Finally, the helical Rossby number is proposedin order to estimate the relative importance of the energy flux enhanced by theturbulent helicity and the rotation, in comparison to the conventionalgradient-diffusion approximation.

Energy transport due to pressure diffusion enhanced by helicity and system rotation in inhomogeneous turbulence