Dynamic shape change of the octopus mantle during fast jet escape manoeuvres results in added mass energy recovery to the energetic advantage of the octopus, giving escape thrust and speed additional to that due to jetting alone. We show through numerical simulations and experimental validation of overall wake behaviour, that the success of the energy recovery is highly dependent on shrinking speed and Reynolds number, with secondary dependence on shape considerations and shrinking amplitude. The added mass energy recovery ratio η_ma, which measures momentum recovery in relation to the maximum momentum recovery possible in an ideal flow, increases with increasing the non-dimensional shrinking parameter σ^∗ = ȧ_max/URe₀, where ȧ_max is the maximum shrinking speed, U is the characteristic flow velocity and Re₀ is the Reynolds number at the beginning of the shrinking motion. An estimated threshold σ^∗∼10 determines whether or not enough energy is recovered to the body to produce net thrust. Since there is a region of high transition for 10 < σ^∗ < 30 where the recovery performance varies widely and for σ^∗ > 100 added mass energy is recovered at diminishing returns, we propose a design criterion for shrinking bodies to be in the range of 50 < σ^∗ < 100, resulting in 61-82% energy recovery.

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The flow mechanisms of shape-changing moving bodies are investigated through the simple model of a foil that is rapidly retracted over a spanwise distance as it is towed at constant angle of attack. It is shown experimentally and through simulation that by altering the shape of the tip of the retracting foil, different shape-changing conditions may be reproduced, corresponding to: (i) a vanishing body, (ii) a deflating body and (iii) a melting body. A sharp-edge, 'vanishing-like' foil manifests strong energy release to the fluid; however, it is accompanied by an additional release of energy, resulting in the formation of a strong ring vortex at the sharp tip edges of the foil during the retracting motion. This additional energy release introduces complex and quickly evolving vortex structures. By contrast, a streamlined, 'shrinking-like' foil avoids generating the ring vortex, leaving a structurally simpler wake. The 'shrinking' foil also recovers a large part of the initial energy from the fluid, resulting in much weaker wake structures. Finally, a sharp edged but hollow, 'melting-like' foil provides an energetic wake while avoiding the generation of a vortex ring. As a result, a melting-like body forms a simple and highly energetic and stable wake, that entrains all of the original added mass fluid energy. The three conditions studied correspond to different modes of flow control employed by aquatic animals and birds, and encountered in disappearing bodies, such as rising bubbles undergoing phase change to fluid.@en

If a moving body were made to vanish within a fluid, its boundary-layer vorticity would be released into the fluid at all locations simultaneously, a phenomenon we call global vorticity shedding. We approximate this process by studying the related problem of rapid vorticity transfer from the boundary layer of a body undergoing a quick change of cross-sectional and surface area. A surface-piercing foil is first towed through water at constant speed, U, and constant angle of attack, then rapidly pulled out of the fluid in the spanwise direction. Viewed within a fixed plane perpendicular to the span, the cross-sectional area of the foil seemingly disappears. The rapid spanwise motion results in the nearly instantaneous shedding of the boundary layer into the surrounding fluid. Particle image velocimetry measurements show that the shed layers quickly transition from free shear layers to form two strong, unequal-strength vortices, formed within non-dimensional time t* = 0:03, based on the foil chord and forward velocity. These vortices are connected to, and interact with, the foil's tip vortex through additional streamwise vorticity formed during the rapid pulling of the foil. Numerical simulations show that two strong spanwise vortices form from the shed vorticity of the boundary layer. The three-dimensional effects of the foil removal process are restricted to the tip of the foil. This method of vorticity transfer may be used for quickly introducing circulation to a fluid to provide forcing for biologically inspired flow control.

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For a body moving within a fluid, its shape and the manner in which it morphs greatly impact the energy transfer between it and the flow. In vanishing bodies, vorticity is globally shed, while added mass-related energy is released into the fluid. We investigate square-tipped, streamlined-tipped, and hollow foils towed at 10◦ angle of attack and quickly retracted in the span-wise direction, as generic models of bodies of different form undergoing rapid shape and volume change. Particle image velocimetry shows that large differences exist in their globally shed wakes. The retracting square-tipped foil forms a wake with energy in excess of the potential flow estimate before retraction starts; the extra energy results in the formation of an additional vortex ring that adds unsteadiness and complexity to the form of the wake. The streamlined-tipped foil avoids creating such ring vortices, but sheds a much less energetic wake: numerical simulation shows that energy is transferred back to the foil during the retraction phase through a thrust force. Circulation calculations show that energy transfer is enabled by the gradual shape change in this foil and is associated with simultaneous pressure gradient-induced and vorticity tilting-induced vorticity annihilation. Finally, the hollow foil combines the advantages of near-complete transfer of the original added mass-related energy to the wake and absence of a vortex ring formation, resulting in an energetic and also cleanly-evolving, stable wake. Hence, modest differences in morphing body shape are shown to result in significantly different flow patterns.@en