This paper is associated with a poster winner of a 2018 APS/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, https://doi.org/10.1103/APS.DFD.2018.GFM.P0002

The study and control of flow instabilities is a key problem in aerodynamics. Aircrafts are designed not only to generate the lift force needed to balance their weight but, more importantly, to be stable and reasonably steady when in cruise conditions. Similar flow stability properties are naturally achieved by biological flying objects such as the dandelion seeds that are transported by the wind owing to a disklike structure called a pappus. The pappus creates a parachute flow configuration and is a remarkable prototype of how the wake, which would be unsteady if the pappus was completely impermeable, can be stabilized by changing the body structure so as to allow the flow to pass through. We approach the problem using the approximation of an anisotropic and nonhomogeneous rigid porous disk, combined with the linear stability analysis technique. The results show the presence of a mean porosity threshold beyond which the flow is always characterized by a separated, steady, and axisymmetric recirculating vortex ring. We compare our results with those of real dandelion pappi. The threshold is very close to the experimentally observed values of porosity, explaining why the morphology of the pappus promotes a steady wake regime.

This paper investigates the flow of a solidifying liquid film on a solid surface subject to a complex kinematics, a process relevant to pancake making and surface coating. The flow is modeled using the lubrication approximation, with a gravity force whose magnitude and direction depend on the time-dependent orientation of the surface. Solidification is modeled with a temperature-dependent viscosity. Because the flow eventually ceases as the liquid film becomes very viscous, the key question this study aims to address is: what is the optimal surface kinematics for spreading the liquid layer uniformly? Two methods are proposed to tackle this problem. In the first one, the surface kinematics is assumed a priori to be harmonic and parameterized. The optimal parameters are inferred using the Monte Carlo method. This “brute-force” approach leads to a moderate improvement of the film uniformity compared to the reference case when no motion is imposed to the surface. The second method is formulated as an optimal control problem, constrained by the governing partial differential equation, and solved with an adjoint equation. Key benefits of this method are that no assumption is made on the form of the control, and that significant improvement in thickness uniformity are achieved with a comparatively smaller number of evaluations of the objective function.

A bi-frequency open-loop control strategy aiming to combine both high- and low-frequency forcing effects is used to experimentally reduce the drag of a simplified car model at a slight yaw angle of $5^{\circ }$. The unforced mean wake features a lateral asymmetry which induces a low base pressure footprint close to the leeward side and increases drag compared to the aligned model. Forcing is performed with pulsed jets along the windward trailing edge. High-frequency forcing acts as a time-invariant flap. The fluidic flap effect deviates the windward shear layer towards the leeward side and reduces the wake bluffness, but the lateral asymmetry of the near wake is still observed. The drag reduction related to this high-frequency forcing is about 6% with a high actuation efficiency. A modulation of the high-frequency forcing with a low-frequency component is then introduced in order to modify the mass and momentum exchange in the separating shear layer at the windward trailing edge. We find that the modulated forcing provides the ability to manipulate the mean wake orientation while maintaining the fluidic flap effect. Among all wake orientations, those reducing drag are the ones having a mean symmetric wake. The bi-frequency control strategy leads to a maximum drag reduction of 7% for the best choice of frequencies. Importantly, the bi-frequency control is more efficient than the single high-frequency forcing, the actuator requiring only half the actuation energy and presenting an actuation efficiency multiplied by 3. Finally, the physical mechanisms related to drag reduction are carefully analyzed. In particular, we show that the wake symmetrization reduces the global production of turbulent kinetic energy in the shear layers. These results open up opportunities for closed-loop control of wake asymmetries.

Sorting cells based on their intrinsic properties is a highly desirable objective, since changes in cell deformability are often associated with various stress conditions and diseases. Deterministic lateral displacement (DLD) devices offer high precision for rigid spherical particles, while their success in sorting deformable particles remains limited due to the complexity of cell traversal in DLD devices. We employ mesoscopic hydrodynamics simulations and demonstrate prominent advantages of sharp-edged DLD obstacles for probing deformability properties of red blood cells (RBCs). By consecutive sharpening of the pillar shape from circular to diamond to triangular cross-section, a pronounced cell bending around an edge is achieved, serving as a deformability sensor. Bending around the edge is the primary mechanism which governs the traversal of RBCs through such a DLD device. This strategy requires an appropriate degree of cell bending by fluid stresses, which can be controlled by the flow rate, and exhibits good sensitivity to moderate changes in cell deformability. We expect that similar mechanisms should be applicable for the development of novel DLD devices that target intrinsic properties of many other cells.

The power output of wind farms depends strongly on spatial turbine arrangement, and the resulting turbulent interactions with the atmospheric boundary layer. Wind farm layout optimization to maximize power output has matured for small clusters of turbines, with the help of analytical wake models. On the other hand, for large farms approaching a fully developed regime in which the integral power extraction by turbines is balanced through downward transport of the mean kinetic energy, the influence of turbine layout is much less understood. The main goal of this work is to study the effect of turbine layout on the power output for large wind farms approaching a fully developed regime. For this purpose we employ an experimental setup of a scaled wind farm with 100 porous disk models, of which 60 are instrumented with strain gauges. Our experiments cover a parametric space of 56 different layouts for which the turbine-area density is constant, focusing on different turbine arrangements including nonuniform spacings. The strain-gauge measurements are used to deduce surrogate power and unsteady loading on turbines for each layout. Our results indicate that the power asymptote at the end of the wind farm depends on the layout in different ways. Firstly, for layouts with a relatively uniform spacing we find that the power asymptote in the fully developed regime reaches approximately the same value, similarly to the prediction of available analytical models. Secondly, we show that the power asymptote in the fully developed regime can be lowered by inefficient turbine placement, for instance when a large number of the turbines are located in the near wake of upwind turbines. Thirdly, our experiments indicate that an uneven spacing between turbines can improve the overall power output for both the developing and fully developed part of large wind farms. Specifically, we find a higher power asymptote for a turbine layout with a significant streamwise uneven spacing (i.e., a large streamwise spacing between pairs of closely spaced rows that are slightly staggered). Our results thereby indicate that such a layout may promote beneficial flow interactions in the fully developed regime for conditions with a strongly prevailing wind direction.

Nectar-drinking bats and honeybees have tongues covered with hairlike structures, enhancing their ability to take up viscous nectar by dipping. Using a combination of model experiments and theory, we explore the physical mechanisms that govern viscous entrainment in a hairy texture. Hairy surfaces are fabricated using laser cut molds and casting samples with polydimethylsiloxane (PDMS) elastomer. We model the liquid trapped within the texture using a Darcy-Brinkmann-like approach and derive the drainage flow solution. The amount of fluid that is entrained is dependent on the viscosity of the fluid, the density of the hairs, and the withdrawal speed. Both experiments and theory reveal an optimal hair density to maximize fluid uptake.

We present numerical simulations of steady, laminar, axisymmetric convection of a Boussinesq fluid in a shallow, rotating, cylindrical domain. The flow is driven by an imposed vertical heat flux and shaped by the background rotation of the domain. The geometry is inspired by that of tropical cyclones and the global flow pattern consists of a shallow swirling vortex combined with a poloidal flow in the $r\text{−}z$ plane which is predominantly inward near the bottom boundary and outward along the upper surface. Our numerical experiments confirm that, as suggested in our recent work [L. Oruba et al., J. Fluid Mech. 812, 890 (2017)], an eye forms at the center of the vortex which is reminiscent of that seen in a tropical cyclone and is characterized by a local reversal in the direction of the poloidal flow. We establish scaling laws for the flow and map out the conditions under which an eye will, or will not, form. We show that, to leading order, the velocity scales with $V={\left(\alpha g\beta \right)}^{1/2}H$, where $g$ is gravity, $\alpha$ is the expansion coefficient, $\beta$ is the background temperature gradient, and $H$ is the depth of the domain. We also show that the two most important parameters controlling the flow are $\mathrm{Re}=VH/\nu$ and $\mathrm{Ro}=V/\left(\mathrm{\Omega }H\right)$, where $\mathrm{\Omega }$ is the background rotation rate and $\nu$ the viscosity. The Prandtl number and aspect ratio also play an important, if secondary, role. Finally, and most importantly, we establish the criteria required for eye formation. These consist of a lower bound on $\mathrm{Re}$, upper and lower bounds on $\mathrm{Ro}$, and an upper bound on the Ekman number.

This paper is associated with a video winner of a 2016 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2016.GFM.V0055

This paper is associated with a video winner of a 2016 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2016.GFM.V0095

This paper is associated with a video winner of a 2016 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2016.GFM.V0076

We present unifying rules governing the efficient locomotion of swimming fish and marine mammals. Using scaling and dimensional analysis, supported by new experimental data, we show that efficient locomotion occurs when the values of the Strouhal (St) number $\mathrm{St}(=fA/U)$ and $A^{*}(=A/L)$, two nondimensional numbers that relate forward speed $U$, tail-beat amplitude $A$, tail-beat frequency $f$, and the length of the swimmer $L$ are bound to the tight ranges of 0.2–0.4 and 0.1–0.3, respectively. The tight range of 0.2–0.4 for the St number has previously been associated with optimal thrust generation. We show that the St number alone is insufficient to achieve optimal aquatic locomotion, and an additional condition on $A^{*}$ is needed. More importantly, we show that when swimming at minimal power consumption, the Strouhal number of a cruising swimmer is predetermined solely by the shape and drag characteristics of the swimmer. We show that diverse species of fish and cetaceans cruise indeed with the St number and $A^{*}$ predicted by our theory. Our findings provide a physical explanation as to why fast aquatic swimmers cruise with a relatively constant tail-beat amplitude of approximately 20% of the body length, and their swimming speed is nearly proportional to their tail-beat frequency.

A theoretical model for predicting and interpreting blood-spatter patterns resulting from a gunshot wound is proposed. The physical process generating a backward spatter of blood is linked to the Rayleigh-Taylor instability of blood accelerated toward the surrounding air, allowing the determination of the initial distribution of drop sizes and velocities. Then the motion of many drops in air is considered with governing equations accounting for gravity and air drag. Based on these equations, a numerical solution is obtained. It predicts the atomization process, the trajectories of the back-spatter drops of blood from the wound to the ground, the impact angle, and the impact Weber number on the ground, as well as the distribution and location of bloodstains and their shape and sizes. A parametric study is undertaken to predict patterns of backward blood spatter under realistic conditions corresponding to the experiments conducted in the present work. The results of the model are compared to the experimental data on back spatter generated by a gunshot impacting a blood-impregnated sponge.

Miscible liquids commonly contact one another in natural and technological situations, often in the proximity of a solid substrate. In the scenario where a drop of one liquid finds itself on a solid surface and immersed within a second, miscible liquid, it will spread spontaneously across the surface. We show experimental findings of the spreading of sessile drops in miscible environments that have distinctly different shape evolution and power-law dynamics from sessile drops that spread in immiscible environments, which have been reported previously. We develop a characteristic time to scale radial data of the spreading sessile drops based on a drainage flow due to gravity. This time scale is effective for a homologous subset of the liquids studied. However, it has limitations when applied to significantly chemically different, yet miscible, liquid pairings; we postulate that the surface energies between each liquid and the solid surface becomes important for this other subset of the liquids studied. Initial experiments performed with pendant drops in miscible environments support the drainage flow observed in the sessile drop systems.

With the aim to predict energy transport by internal waves incident upon observed density staircases in the ocean, the theory for internal wave tunneling through a single finite-size mixed region is extended to predict the transmission of internal waves through a piecewise-constant density profile with an arbitrary number of steps. An analytic solution is found if all steps have equal vertical extent. From this solution, bounds are established for the relative incident horizontal wave number and frequency of waves that have negligible transmission, a result that is independent of the number of steps. If the step sizes vary randomly about a mean vertical extent, the transmission can be computed numerically for several random realizations. Provided the horizontal wavelength is much longer than the total vertical extent of the staircase, the standard deviation of the computed transmission coefficients is small and the mean agrees well with the analytic prediction for equally spaced steps. The results are applied to thermohaline staircases observed in the ocean in order to put lower bounds on the wavelengths of long inertia gravity waves that significantly transmit to great depth.