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Energy transport due to pressure diffusion enhanced by helicity and system rotation in inhomogeneous turbulence
Phys. Rev. Fluids 3, 124601 – Published 3 December, 2018
DOI: https://doi.org/10.1103/PhysRevFluids.3.124601
Abstract
It is known that turbulent energy is rapidly transferred in the direction of the rotation axis in a rotating system, in comparison with the nonrotating 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 experiments, inhomogeneity of turbulence is modeled with an oscillating grid, leading to the turbulent energy falling off away from the grid. 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, which is the statistically averaged value of the inner product of the velocity and vorticity fluctuations. 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 of inhomogeneous turbulence under rotation where the flow configuration is similar to the oscillating-gird turbulence. 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 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.
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