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Turbulence in a network of rigid fibers

The effect of a network of fixed rigid fibers on fluid flow is investigated by means of three-dimensional direct numerical simulations using an immersed boundary method for the fluid-structure coupling. Different flows are considered (i.e., cellular, parallel and homogeneous isotropic turbulent flow) in order to identify the modification of the classic energy budget occurring within canopies or fibrous media, as well as particle-laden flows. First, we investigate the stabilizing effect of the network on the Arnold-Beltrami-Childress (ABC) cellular flow, showing that, the steady configuration obtained for a sufficiently large fiber concentration mimics the single-phase stable solution at a lower Reynolds number. Focusing on the large-scale dynamics, the effect of the drag exerted by the network on the flow can be effectively modelled by means of a Darcy's friction term. For the latter, we propose a phenomenological expression that is corroborated when extending our analysis to the Kolmogorov parallel flow and homogeneous isotropic turbulence. Furthermore, we examine the overall energy distribution across the various scales of motion, highlighting the presence of small-scale activity with a peak in the energy spectra occurring at the wavenumber corresponding to the network spacing.