We study the dynamics  of  long  flexible fibres in turbulent channel flow up to shear Reynolds number Re=1200. We perform DNS in a Euler-Lagrange framework, using a GPU-accelerated flow solver. We account for fluid inertia effects on the forces and torques experienced by the fibres, which may significantly alter their orientation dynamics as they drift away from the Jeffery orbits and strengthen the influence of local stretching. By comparing the drift time (order of a few periods of rotation) with the typical time of the flow velocity fluctuations, we focus on the conditions under which fluid inertia becomes important given the inter-mittent nature of the flow.