Rotational and translational dispersion of fibres in isotropic turbulent flows

Abstract

The rotational and translational motions of fibres in fully developed isotropic turbulence are simulated for a range of turbulence Reynolds numbers. Equations for fibre motion based on the leading-order slender-body theory relate the fibre's translational and rotational velocities to zeroth and first moments of the fluid velocity along the fibre length. The translational and rotational motions of fibres with lengths that exceed the size of the smallest eddies are attenuated by the filtering associated with these spatial averages. The translational diffusivity of the fibres can be predicted using a simple theory that neglects any coupling between fibre orientation and the local direction of the fluid velocity. However, the coupling of fibre orientation with the axes of extension and rotation is found to greatly reduce the amplitude of the rotary motions and the rotational dispersion coefficient. The rotary dispersion coefficient is found to be on the order of the inverse integral time scale. However, its variation with Reynolds number suggests that the rotary dispersion is influenced by all the scales of turbulence over the limited range of Reynolds numbers explored in our simulations.