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Recent numerical simulations showed that the mean flow is generated in inhomogeneous turbulence of an incompressible fluid accompanied with helicity and system rotation. In order to investigate the mechanism of this phenomenon, we carry out a numerical simulation of inhomogeneous turbulence in a rotating system. In the simulation, an external force is applied to inject inhomogeneous turbulent helicity and the rotation axis is taken to be perpendicular to the inhomogeneous direction. No mean velocity is set in the initial condition of the simulation. The simulation results show that only in the case with both the helical forcing and the system rotation, the mean flow directed to the rotation axis is generated and sustained. We investigate the physical origin of this flow-generation phenomenon by considering the budget of the Reynolds-stress transport equation. It is found that the pressure diffusion term has a large contribution in the Reynolds stress equation and supports the generated mean flow. It is shown that a model expression for the pressure diffusion can be expressed by the turbulent helicity gradient coupled with the angular velocity of the system rotation. This implies that inhomogeneous helicity can play a significant role for the generation of the large-scale velocity distribution in incompressible turbulent flows.

Mechanism of mean flow generation in rotating turbulence through inhomogeneous helicity