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This paper is associated with a poster winner of a 2023 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, . Published by the American Physical Society2024 

The recognizable shapes of landforms arise from processes such as erosion by wind or water currents. However, explaining the physical origin of natural structures is challenging due to the coupled evolution of complex flow fields and three-dimensional (3D) topographies. We investigate these issues in a laboratory setting inspired by yardangs, which are raised, elongate formations whose characteristic shape suggests erosion of heterogeneous material by directional flows. We combine experiments and simulations to test an origin hypothesis involving a harder or less erodible inclusion embedded in an outcropping of softer material. Optical scans of clay objects fixed within flowing water reveal a transformation from a featureless mound to a yardang-like form resembling a lion in repose. Phase-field simulations reproduce similar shape dynamics and show their dependence on the erodibility contrast and flow strength. Through visualizations of the flow fields and analysis of the local erosion rate, we identify effects associated with flow funneling and the turbulent wake that are responsible for carving the unique geometrical features. This highly 3D scouring process produces complex shapes from simple and commonplace starting conditions and is thus a candidate explanation for natural yardangs. The methods introduced here should be generally useful for geomorphological problems and especially those for which material heterogeneity is a primary factor. 

Abstract Collectively locomoting animals are often viewed as analogous to states of matter in that group-level phenomena emerge from individual-level interactions. Applying this framework to fish schools and bird flocks must account for visco-inertial flows as mediators of the physical interactions. Motivated by linear flight formations, here we show that pairwise flow interactions tend to promote crystalline or lattice-like arrangements, but such order is disrupted by unstably growing positional waves. Using robotic experiments on “mock flocks” of flapping wings in forward flight, we find that followers tend to lock into position behind a leader, but larger groups display flow-induced oscillatory modes – “flonons” – that grow in amplitude down the group and cause collisions. Force measurements and applied perturbations inform a wake interaction model that explains the self-ordering as mediated by spring-like forces and the self-amplification of disturbances as a resonance cascade. We further show that larger groups may be stabilized by introducing variability among individuals, which induces positional disorder while suppressing flonon amplification. These results derive from generic features including locomotor-flow phasing and nonreciprocal interactions with memory, and hence these phenomena may arise more generally in macroscale, flow-mediated collectives. 

Extensive studies of the hydraulics of pipes have focused on limiting cases, such as fully-developed laminar or turbulent flow through long conduits and the accelerating flow through an orifice, for which there exist laws relating pressure drop and flow rate. We carry out experiments on smooth, circular pipes for dimensions and flow rates that interrogate intermediate conditions between the well-studied limits. Organizing this information in terms of dimensionless friction factor, Reynolds number and pipe aspect ratio yields a surface $$f_D(Re,\alpha )$$ that is shown to match the three laws associated with developed laminar, developed turbulent, and orifice flows. While each law fails outside its applicable range of $$(Re,\alpha )$$ , we present a hybrid theoretical–empirical model that includes inlet, development and transition effects, and that proves accurate to approximately 10 % over wide ranges of $Re$ and $$\alpha$$ . We also present simple formulas for the boundaries between the three hydraulic regimes, which intersect at a triple point. Measurements show that sipping through a straw is an everyday example of such intermediate conditions not accounted for by existing laws but described accurately by our model. More generally, our findings provide formulas for predicting frictional resistance for intermediate- $Re$ flows through finite-length pipes. 

Falling paper flutters and tumbles through air, whereas a paper airplane glides smoothly if its leading edge is appropriately weighted. We investigate this transformation from ‘plain paper’ to ‘paper plane’ through experiments, aerodynamic modelling and free flight simulations of thin plates with differing centre of mass (CoM) locations. Periodic modes such as fluttering, tumbling and bounding give way to steady gliding and then downward diving as the CoM is increasingly displaced towards one edge. To explain these observations, we formulate a quasi-steady aerodynamic model whose force and torque coefficients are informed by experimental measurements. The dependencies on angle of attack reflect the transition from attached to separated flow and a dynamic centre of pressure, effects that prove critical to reproducing the observed motions of paper planes in air and plates in water. Because the model successfully accounts for unsteady and steady flight modes, it may be usefully applied to further problems involving actuated motions, feedback control and interactions with ambient flows. 

Flow in the inverted U-shaped tube of a conventional siphon can be established and maintained only if the tube is filled and closed, so that air does not enter. We report on siphons that operate entirely open to the atmosphere by exploiting surface tension effects. Such capillary siphoning is demonstrated by paper tissue that bridges two containers and conveys water from the upper to the lower. We introduce a more controlled system consisting of grooves in a wetting solid, formed here by pressing together hook-shaped metallic rods. The dependence of flux on siphon geometry is systematically measured, revealing behaviour different from the conventional siphon. The flux saturates when the height difference between the two container's free surfaces is large; it also has a strong dependence on the climbing height from the source container's free surface to the apex. A one-dimensional theoretical model is developed, taking into account the capillary pressure due to surface tension, pressure loss due to viscous friction, and driving by gravity. Numerical solutions are in good agreement with experiments, and the model suggests hydraulic interpretations for the observed flux dependence on geometrical parameters. The operating principle and characteristics of capillary siphoning revealed here can inform biological phenomena and engineering applications related to directional fluid transport.