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A classic lift decomposition is conducted on potential flow simulations of a near-ground pitching hydrofoil. It is discovered that previously observed stable and unstable equilibrium altitudes are generated by a balance between positive wake-induced lift and negative quasi-steady lift while the added mass lift does not play a role. Using both simulations and experiments, detailed analyses of each lift component's near-ground behaviour provide further physical insights. When applied to three-dimensional pitching hydrofoils the lift decomposition reveals that the disappearance of equilibrium altitudes for AR < 1.5 occurs due to the magnitude of the quasi-steady lift outweighing the magnitude of the wake-induced lift at all ground distances. Scaling laws for the quasi-steady lift, wake-induced lift and the stable equilibrium altitude are discovered. A simple scaling law for the lift of a steady foil in ground effect is derived. This scaling shows that both circulation enhancement and the velocity induced at a foil's leading edge by the bound vortex of its ground image foil are the essential physics to understand steady ground effect. The scaling laws for unsteady pitching foils can predict the equilibrium altitude to within 20% of its value when St < 0.45. For St > 0.45, there is a wake instability effect, not accounted for in the scaling relations, that significantly alters the wake-induced lift. These results not only provide key physical insights and scaling laws for steady and unsteady ground effects, but also for two schooling hydrofoils in a side-by-side formation with an out-of-phase synchronization. 

Abstract When swimming near a solid planar boundary, bio-inspired propulsors can naturally equilibrate to certain distances from that boundary. How these equilibria are affected by asymmetric swimming kinematics is unknown. We present here a study of near-boundary pitching hydrofoils based on water channel experiments and potential flow simulations. We found that asymmetric pitch kinematics do affect near-boundary equilibria, resulting in the equilibria shifting either closer to or away from the planar boundary. The magnitude of the shift depends on whether the pitch kinematics have spatial asymmetry (e.g. a bias angle, θ 0 ) or temporal asymmetry (e.g. a stroke-speed ratio, τ ). Swimming at stable equilibrium requires less active control, while shifting the equilibrium closer to the boundary can result in higher thrust with no measurable change in propulsive efficiency. Our work reveals how asymmetric kinematics could be used to fine-tune a hydrofoil’s interaction with a nearby boundary, and it offers a starting point for understanding how fish and birds use asymmetries to swim near substrates, water surfaces, and sidewalls. 

The Steptoean Positive Carbon Isotope Excursion (SPICE) event at ca. 497−494 Ma was a major carbon-cycle perturbation of the late Cambrian that coincided with rapid diversity changes among trilobites. Several scenarios (e.g., climatic/oceanic cooling and seawater anoxia) have been proposed to account for an extinction of trilobites at the onset of SPICE, but the exact mechanism remains unclear. Here, we present a chemostratigraphic study of carbonate carbon and carbonate-associated sulfate sulfur isotopes (δ13Ccarb and δ34SCAS) and elemental redox proxies (UEF, MoEF, and Corg/P), augmented by secular trilobite diversity data, from both upper slope (Wangcun) and lower slope (Duibian) successions from the Jiangnan Slope, South China, spanning the Drumian to lower Jiangshanian. Redox data indicate locally/regionally well-oxygenated conditions throughout the SPICE event in both study sections except for low-oxygen (hypoxic) conditions within the rising limb of the SPICE (early-middle Paibian) at Duibian. As in coeval sections globally, the reported δ13Ccarb and δ34SCAS profiles exhibit first-order coupling throughout the SPICE event, reflecting co-burial of organic matter and pyrite controlled by globally integrated marine productivity, organic preservation rates, and shelf hypoxia. Increasing δ34SCAS in the “Early SPICE” interval (late Guzhangian) suggests that significant environmental change (e.g., global-oceanic hypoxia) was under way before the global carbon cycle was markedly affected. Assessment of trilobite range data within a high-resolution biostratigraphic framework for the middle-late Cambrian facilitated re-evaluation of the relationship of the SPICE to contemporaneous biodiversity changes. Trilobite diversity in South China declined during the Early SPICE (corresponding to the End-Marjuman Biomere Extinction, or EMBE, of Laurentia) and at the termination of the SPICE (corresponding to the End-Steptoean Biomere Extinction, or ESBE, of Laurentia), consistent with biotic patterns from other cratons. We infer that oxygen minimum zone and/or shelf hypoxia expanded as a result of locally enhanced productivity due to intensified upwelling following climatic cooling, and that expanded hypoxia played a major role in the EMBE at the onset of SPICE. During the SPICE event, global-ocean ventilation promoted marine biotic recovery, but termination of SPICE-related cooling in the late Paibian may have reduced global-ocean circulation, triggering further redox changes that precipitated the ESBE. Major changes in both marine environmental conditions and trilobite diversity during the late Guzhangian demonstrate that the SPICE event began earlier than the Guzhangian-Paibian boundary, as previously proposed. 

Animals and bio-inspired robots can swim/fly faster near solid surfaces, with little to no loss in efficiency. How these benefits change with propulsor aspect ratio is unknown. Here we show that lowering the aspect ratio weakens unsteady ground effect, thrust enhancements become less noticeable, stable equilibrium altitudes shift lower and become weaker and wake asymmetries become less pronounced. Water-channel experiments and potential flow simulations reveal that these effects are consistent with known unsteady aerodynamic scalings. We also discovered a second equilibrium altitude even closer to the wall ( $${<}0.35$$ chord lengths). This second equilibrium is unstable, particularly for high-aspect-ratio foils. Active control may therefore be required for high-aspect-ratio swimmers hoping to get the full benefit of near-ground swimming. The fact that aspect ratio alters near-ground propulsion suggests that it may be a key design parameter for animals and robots that swim/fly near a seafloor or surface of a lake. 

Scaling laws for the thrust production and power consumption of a purely pitching hydrofoil in ground effect are presented. For the first time, ground-effect scaling laws based on physical insights capture the propulsive performance over a wide range of biologically relevant Strouhal numbers, dimensionless amplitudes and dimensionless ground distances. This is achieved by advancing previous scaling laws (Moored & Quinn ( AIAA J. , 2018, pp. 1–15)) with physics-driven modifications to the added mass and circulatory forces to account for ground distance variations. The key physics introduced are the increase in the added mass of a foil near the ground and the reduction in the influence of a wake-vortex system due to the influence of its image system. The scaling laws are found to be in good agreement with new inviscid simulations and viscous experiments, and can be used to accelerate the design of bio-inspired hydrofoils that oscillate near a ground plane or two out-of-phase foils in a side-by-side arrangement. 

The Earth has been beset by many crises during its history, and yet comparing the ecological impacts of these mass extinctions has been difficult. Key questions concern the kinds of species that go extinct and survive, how communities rebuild in the post-extinction recovery phase, and especially how the scaling of events affects these processes. Here, we explore ecological impacts of terrestrial and freshwater ecosystems in three mass extinctions through the mid-Phanerozoic, a span of 121 million years (295–174 Ma). This critical duration encompasses the largest mass extinction of all time, the Permian–Triassic (P–Tr) and is flanked by two smaller crises, the Guadalupian–Lopingian (G–L) and Triassic–Jurassic (T–J) mass extinctions. Palaeocommunity dynamics modelling of 14 terrestrial and freshwater communities through a long sedimentary succession from the lower Permian to the lower Jurassic in northern Xinjiang, northwest China, shows that the P–Tr mass extinction differed from the other two in two ways: (i) ecological recovery from this extinction was prolonged and the three post-extinction communities in the Early Triassic showed low stability and highly variable and unpredictable responses to perturbation primarily following the huge losses of species, guilds and trophic space; and (ii) the G–L and T–J extinctions were each preceded by low-stability communities, but post-extinction recovery was rapid. Our results confirm the uniqueness of the P–Tr mass extinction and shed light on the trophic structure and ecological dynamics of terrestrial and freshwater ecosystems across the three mid-Phanerozoic extinctions, and how complex communities respond to environmental stress and how communities recovered after the crisis. Comparisons with the coeval communities from the Karoo Basin, South Africa show that geographically and compositionally different communities of terrestrial ecosystems were affected in much the same way by the P–Tr extinction. 

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. 

Scaling laws for the thrust production and energetics of self-propelled or fixed-velocity three-dimensional rigid propulsors undergoing pitching motions are presented. The scaling relations extend the two-dimensional scaling laws presented in Moored & Quinn ( AIAA J. , 2018, pp. 1–15) by accounting for the added mass of a finite-span propulsor, the downwash/upwash effects from the trailing vortex system of a propulsor and the elliptical topology of shedding trailing-edge vortices. The novel three-dimensional scaling laws are validated with self-propelled inviscid simulations and fixed-velocity experiments over a range of reduced frequencies, Strouhal numbers and aspect ratios relevant to bio-inspired propulsion. The scaling laws elucidate the dominant flow physics behind the thrust production and energetics of pitching bio-propulsors, and they provide guidance for the design of bio-inspired propulsive systems.