Swimming freely near the ground leads to flow-mediated equilibrium altitudes

Abstract

Experiments and computations are presented for a foil pitching about its leading edge near a planar, solid boundary. The foil is examined when it is constrained in space and when it is unconstrained or freely swimming in the cross-stream direction. It was found that the foil has stable equilibrium altitudes: the time-averaged lift is zero at certain altitudes and acts to return the foil to these equilibria. These stable equilibrium altitudes exist for both constrained and freely swimming foils and are independent of the initial conditions of the foil. In all cases, the equilibrium altitudes move farther from the ground when the Strouhal number is increased or the reduced frequency is decreased. Potential flow simulations predict the equilibrium altitudes to within 3 %–11 %, indicating that the equilibrium altitudes are primarily due to inviscid mechanisms. In fact, it is determined that stable equilibrium altitudes arise from an interplay among three time-averaged forces: a negative jet deflection circulatory force, a positive quasistatic circulatory force and a negative added mass force. At equilibrium, the foil exhibits a deflected wake and experiences a thrust enhancement of 4 %–17 % with no penalty in efficiency as compared to a pitching foil far from the ground. These newfound lateral stability characteristics suggest that unsteady ground effect may play a role in the control strategies of near-boundary fish and fish-inspired robots.

Thrust generation during steady swimming and acceleration from rest in anguilliform swimmers

“…A similar conclusion was examined in the validation study of Lucas et al (2017). Recent work has shown that ground effects are not limited to accelerating swimming but are present in steady swimming as well (Kurt et al, 2019), suggesting that the presence of ground effects should not bias comparisons between the two swimming modes. Furthermore, using only sequences in which the animal remained in the laser sheet minimized possible ground effect discrepancies between sequences and treatments by ensuring that animals were filmed at the same height above the bottom (∼0.1 body lengths, bl; see below) for all sequences.…”

On the Fluid Dynamical Effects of Synchronization in Side-by-Side Swimmers

“…On the other hand, zooming into the problem of a single swimmer, despite the successes of Lighthill's theory to describe the mechanics of fish swimming [9], the ubiquitous problems of the interaction between a swimmer and its environment are out of its reach. This environment can be a wall, a substrate (a significant number of works have explored this problem in different contexts [10][11][12][13]), or another neighboring swimmer. The interactions between multiple swimmers may significantly impact the performance or cost of locomotion associated with fish schooling, as each swimmer moves in a non-uniform and unsteady flow created by its neighbors.…”

Flow-mediated interactions between two self-propelled flexible fins near sidewalls

“…Kurt et al . (2019) recently performed experimental and numerical studies for a freely movable rigid fin in the lateral direction to identify a lateral equilibrium altitude for a zero when the fin was constrained in the horizontal direction. They showed that a stable equilibrium position of a freely swimming fin with a zero exists in the lateral direction, and the lateral position is similar to that of a laterally constrained fin with a zero .…”

“…As d/A head,l decreases, the fins show a negative due to a time-averaged angled jet away from the wall (not shown) formed by a deflected vortex pair (figure 2 b ), consistent with the jet deflection mechanism of Kurt et al . (2019). As d/A head,l decreases further ( d/A head,l < 2.5 for the leader and d/A head,l ≤ 3.0 for the follower), the sign of acting on the fins is positive due to the enhancement of a positive pressure between the fins and the wall (for example, see the pressure contours around the fins for 1W at t / T = 0.625 and 0.75 in figure 12), consistent with the quasi-static mechanism by Kurt et al .…”

“…Using a numerical and experimental set-up for a freely movable isolated rigid pitching foil in the lateral direction, Kurt et al . (2019) found that the foil near a wall spontaneously settles on a stable equilibrium altitude, where the time-averaged lateral force is zero, and the thrust force is enhanced with high efficiency at the equilibrium position compared to that far from the wall. In addition to a pitching rigid foil, the existence of a stable equilibrium altitude has been identified for a passively flapping fin, which is free to move in the lateral direction (Jeong & Lee 2018).…”