Helicity fluctuations and turbulent energy production in rotating and non-rotating pipes

In this paper finite-difference second-order accurate direct simulations have been used to investigate how the helicity density fluctuations change when a turbulent pipe rotates about its axis. In this case the rotation axis is parallel to the near wall vortical structures which play a fundamental role on the wall friction and turbulence production. The helicity density is the trace of the tensor γij′=〈vi′ωj′〉 whose elements form the components of v′×ω′. When the momentum equations are written in rotational form the turbulence energy production term splits into two parts, one related to the convection of the large scales and the other related to the energy cascade to the small scales. From data of direct simulations the changes of the turbulent production term profile with the rotation have been explained by the pdf of the v′×ω′ components. The links between the changes on the pdf of the v′×ω′ and the modifications of the vortical structures have been also investigated. The joint pdf of the dissipation with the helicity density has shown that the dissipation is highly correlated with regions of very low helicity density in the non-rotating pipe. When the pipe rotates the helicity density increases and the dissipation decreases. Since a drag reduction is one of the results of the background rotation, in this paper, it has been speculated that the alignment between velocity and vorticity could be a common feature in drag reducing flows.