Investigating the origins of fluctuation forces on plates immersed in turbulent flows

A net force can arise on objects which lie in systems with complex energy partitions, even if the system is on average stationary. These forces are usually called fluctuation forces, as they arise due to the objects modifying the character of the fluctuations within the system. We continue the investigation of Spandan \emph{et al.}, \textit{Sci. Adv., 6(14), eaba0461} (2020), who found an attractive fluctuation force between two parallel square plates in homogeneous isotropic turbulence (HIT). We conduct simulations which systematically vary the plate size and Reynolds number. At $Re_\lambda=100$ small plates show a monotonic force dependence, with a maximum force for the smallest plate separations, while medium and large plates show a non-monotonic behaviour of the force with maximum attractive force at intermediate separations. We find that energy-related statistics cannot explain the dependence on plate separation of the force, but that statistics related to vorticity do show qualitative variations around the plate separation corresponding to the maximum force. This suggests that the role of plates in affecting intense vorticity structures is critical to the behaviour of the force. By decreasing $Re_\lambda$, we show that removing vortex stretching decreases the attractive force, but does not completely eliminate it, and find that the local maximum at intermediate distances becomes a local minimum. This confirms that the attractive force is related to vorticity, while suggesting that a second mechanism is present -- supporting the proposal for a two-fold origin from earlier work: the plates both restrict the presence of energy structures in the slit and pack intense vortical structures which stretch each other causing the pressure to drop.