Dynamics of the velocity fluctuations in sedimenting suspensions of rigid fibres

We use direct numerical simulations to investigate fluid–solid interactions in suspensions of rigid fibres settling under gravity in a quiescent fluid. The solid-to-fluid density ratio is $\mathcal{O}(100)$ , while the Galileo number ( $ \textit{Ga}$ ) and fibre concentration ( $n\ell_{\kern-1.5pt f}^3$ ) are varied over the ranges $ \textit{Ga} \in [180, 900]$ and $n\ell_{\kern-1.5pt f}^3 \in [0.36, 23.15]$ ; $\ell_{\kern-1.5pt f}$ denotes the fibre length and $n$ the number density. At high $ \textit{Ga}$ and/or low $n\ell_{\kern-1.5pt f}^3$ , fibres cluster into gravity-aligned streamers with elevated concentrations and enhanced settling velocities, disrupting the flow homogeneity. As $ \textit{Ga}$ increases and/or $n\ell_{\kern-1.5pt f}^3$ decreases, the fluid-phase kinetic energy rises and the energy spectrum broadens, reflecting enhanced small-scale activity. The flow anisotropy is assessed by decomposing the energy spectrum into components aligned with and transverse to gravity. Vertical fluctuations are primarily driven by fluid–solid interactions, while transverse ones are maintained by pressure–strain effects that promote isotropy. With increasing $ \textit{Ga}$ , nonlinear interactions become more prominent, producing a net forward energy cascade toward smaller scales, punctuated by localised backscatter events. Analysis of the local velocity gradient tensor reveals distinct flow topologies: at low $ \textit{Ga}$ , the flow is dominated by axisymmetric compression and two-dimensional straining; at high $ \textit{Ga}$ , regions of high fibre concentration are governed by two-dimensional strain, while voids are associated with axisymmetric extension. The fluid motion is predominantly extensional rather than rotational.