Although the mechanics of jumping on water dominated by surface tension are well established, the understanding of water jumping dominated by drag force, as observed in organisms like fishing spiders, remains incomplete despite its potential to achieve high jumping velocity. Here, we demonstrate that simple elastic hoops can achieve drag-dominated jump on water, and use this model system to construct a fundamental framework to theoretically analyze jump dynamics propelled by form drag. In addition to numerically solving the hoop trajectory while interacting with water, we show that the take-off velocity scaled by the hoop's free vibration velocity depends solely on the solid-fluid density ratio. A comparison with hoop jumps on solid ground reveals that the hoop jumps on water are delayed with a lower jumping efficiency. This work can not only contribute to the development of efficient and easily constructible biomimetic robots but also provide a foundation for understanding the optimal design principles and evolutionary pressures that shape biological jumpers.

From microfluidics to fog-harvesting applications, tiny droplets are transported along various solid substrates including hairs, threads, grooves, and other light structures. Driven by gravity, a droplet sliding along a vertical fiber is a complex problem since it is losing volume and speed as it goes down. With the help of an original setup, we solve this problem by tracking in real-time droplet characteristics and dynamics. Single fibers as well as multiple fiber systems are studied to consider the presence of grooves. On both fibers and grooved threads, droplet speed and volume are seen to decay rapidly because the liquid entity is leaving a thin film behind. This film exerts a capillary force able to stop the droplet motion before it is completely drained. A model is proposed to capture the droplet dynamics. We evidence also that multiple vertical fibers are enhancing the droplet speed while simultaneously promoting increased liquid loss on grooves.

Direct numerical simulations of spatially evolving submerged jets with viscoelastic FENE-P fluids at high Reynolds numbers are performed to investigate the development of inertioelastic shear-layer and jet-column instabilities. An analysis of the flow structures, mean and fluctuating velocities, and spectra of perturbation energy at several positions of the flow shows that viscoelasticity has a destabilizing effect at the linear region of perturbation growth but a stabilizing effect at the nonlinear regime. At the linear regime, shorter waves are destabilized first and as the Weissenberg number Wi is increased this effect is propagated towards longer waves until most modes become more unstable. The frequency domain of instability is increased by a factor larger than four for the jet at the highest Wi. At the nonlinear regime, thin sheets of highly stretched polymers at the shear-layer region lead to a suppression of the local velocity gradient and to the formation of additional inflection points in the base flow velocity profile. This is accompanied by lower rates of perturbation growth and a decrease of the characteristic Strouhal number of the jet column mode at the end of the potential core by a factor of 1.8 for the highest Wi jet. The physical mechanisms that explain the observed phenomena are offered but the need for a nonlinear stability theory that also accounts for nonparallel base flow effects is highlighted.

Computer simulations of cardiovascular flows can be key to improving the predicting capabilities of standard diagnostic tools, to refine surgical techniques and perform virtual tests of innovative prosthetic devices. The reliability of simulations, however, depends on the fidelity level of the model, which, for the heart, involves the interconnected multiphysics dynamics of the various systems: the human heart is among the most complex organs, and simulating its dynamics is an ambitious undertaking from both the modeling and computational viewpoints. In this paper we present a multiphysics computational model of the human heart accounting simultaneously for the electrophysiology, the elasto-mechanics, and the hemodynamics, including their multiway coupled interactions referred to as fluid-structure-electro interaction (FSEI). The developed tool embodies accuracy, versatility, and computational efficiency, thus allowing cardiovascular simulations of physiologic and pathologic configurations within a time to solution compatible with the clinical practice and without resorting to large-scale supercomputers. Results are shown for healthy conditions and for myocardial infarction with the aim of assessing the reliability of the model and proving its predicting capabilities, which could be used to anticipate the outcome of surgical procedures or support clinical decisions.

Elastic turbulence is a chaotic flow state observed in dilute polymer solutions in the absence of inertia. It was discovered experimentally in circular geometries and has long been thought to require a finite amplitude perturbation in parallel flows. Here we demonstrate, within the commonly used Oldroyd-B and FENE-P models, that a self-sustaining chaotic state can be initiated via a linear instability in a simple inertia-less shear flow caused by the presence of small but nonzero diffusivity of the polymer stress. Numerical simulations show that the instability leads to a three-dimensional self-sustaining chaotic state, which we believe is the first reported in a wall-bounded, parallel, inertia-less viscoelastic flow.

Low-aspect-ratio revolving wings find applications in miniature robotic flyers and turbo-machinery. At a high angle of attack, the flow separates from a wing's leading edge, forming a leading-edge vortex. On a revolving wing, the leading-edge vortex (LEV) is stabilized by strong rotational acceleration and is known to be the primary source of high and stable aerodynamic forces acting on the wing. While previous studies have characterized the performance of revolving wings, the effects of perturbations on the flow profile and performance have not been explored. This study combined experiments and computational fluid dynamics simulations to investigate the lift, drag, and power coefficients of a wing revolving at a Reynolds number of $\text{Re}=2500$ and undergoing pitch perturbations. Perturbations were systematically varied to investigate the effects of the wing's initial angle, the amplitude and duration of perturbation, and the location of the pitch axis. Simulations provided insights into the flow structures around the wing and their effects on the wing-surface pressures and the aerodynamic forces. Finally, a quasisteady model was used to decompose the effects of wing rotation and pitch perturbations on the lift and drag forces. The decomposition revealed a consistent dependency of the variations in the lift on the pitch angular velocity across all perturbations, irrespective of the initial angle. The transition from the LEV-dominant to the rotation-dominant flow occurs at very low pitch rates, the values of which were found to depend on the initial angle of the revolving wing. For lower initial angles, the transition occurred at lower pitch rates. During the rotation-dominant perturbations, changes in the vortical structures around the wing were found to have a minimal effect on the lift and drag compared to the quasisteady effects. Moreover, the oscillations in the lift and drag during the perturbation could be reduced by appropriately shifting the pitch axis location. These findings highlight the dominant role of inviscid effects on the variations in loads acting on a revolving wing during pitch perturbations.

A direct-adjoint mean flow global stability investigation of self-excited instabilities in an idealized, two-dimensional compressor blade row at off-design conditions is carried out, with a focus on acoustic feedback mechanisms underlying the observed instabilities. This paper is the first part of this work, where nonlinear flows, impulse responses and the global modes are computed for a single-passage system, with good agreement between the linear and nonlinear structures. Structural sensitivities and feedback loops are identified with the aid of wavemakers and show that dominant structures arise due to feedback mechanisms linking the pressure and suction sides of the aerofoil via acoustic waves emanating from the trailing edge. A separate, second part extends this analysis to multiple-blade passages per period window by exploiting the theory of block-circulant matrices and Bloch-wave theory.

A direct-adjoint mean flow global stability investigation of self-excited instabilities in an idealized, two-dimensional compressor blade row at off-design conditions is carried out. In this second part of the paper, the single-passage analysis is extended to multiblade passages by exploiting the properties of block-circulant matrices and Bloch-wave theory. By using this method, analyses for a large number of blade passages become computationally tangible, and the modal and nonmodal single-passage analysis from the first part of the paper can be augmented by considering multiblade effects arising in larger systems. This work shows that multiblade passages introduce additional unstable 10- and five-periodic synchronization structures arising from a tuned optimal phase relationship that is supported by the larger system. Self-excited low-frequency structures, which cannot be represented within a single-passage computation, are also uncovered and analyzed.

Experimental and theoretical studies on wind-wave generation have focused primarily on the air-water interface, where viscous effects are small. Here we characterize the influence of the liquid viscosity on the growth of mechanically generated waves. In our experiment, wind is blowing over a layer of silicon oil, of viscosity 20 and 50 times that of water, and waves of small amplitude are excited by an immersed wave maker. We measure the spatial evolution of the wave slope envelope using Free-Surface Synthetic Schlieren, a refraction-based optical method. Through spatiotemporal band-pass filtering of the surface slope, we selectively determine the spatial growth rate for each forcing frequency, even when the forced wave is damped and coexists with naturally amplified waves at other frequencies. Systematic measurements of the growth rate for various wind velocities and wave frequencies are obtained, enabling precise determination of the marginal stability curve and the onset of wave growth. We show that Miles' model, which is commonly applied to water waves, offers a reasonable description of the growth rate for more viscous liquids. We finally discuss the scaling of the growth rate of the most amplified wave and the critical friction velocity with the liquid viscosity.

We simulate numerically convection in a rectangular cell filled with an ideal gas rotating about an axis perpendicular to the direction of gravity. This configuration corresponds to an experiment with a convection cell placed in a rapidly rotating centrifuge in which the centrifugal force plays the role of gravity. The compressibility of the gas in combination with the rotation of the cell leads to a drifting mode at the onset of convection. The drift persists despite the presence of sidewalls and is rapid enough to cause the anelastic approximation to fail at parameters typical of realizable laboratory experiments. The global spanwise rotation forces the flow to be 2D unless the Rayleigh number is sufficiently large. The main properties of compressible convection in 2D and 3D are compared.

In this article, we investigate the inertial settling of an arbitrarily oriented cylinder settling under gravity. We focus on two regimes: the very short-time and long-time dynamic. Using the generalized Kirchhoff equations to describe the particle motion, we demonstrate that during the very short dynamic regime, a cylinder starting from rest behaves with sedimenting velocities and angular velocity proportional to $t$ and $t^3$, respectively. We then explore the long-time behavior and evaluate the validity of the quasisteady assumption under which the fluid unsteady term can be neglected. Using a dimensional analysis, we establish that the quasisteady assumption only applies to regimes where the Reynolds number is much smaller than 1. However, by comparing the results of quasisteady models to recent experiments and direct numerical simulations, we demonstrate that this assumption is valid for a broader range of Reynolds numbers, particularly for long fibers. We also analyze the effect of particle inertia, and we show that it plays no significant role in the magnitude of the sedimenting velocities and angular velocity. However, for sufficiently large inertia, we reveal that the quasisteady model takes the form of a damped oscillator when the particle approaches its equilibrium position, which is broadside onto its direction of motion. We discuss the relevance of this solution in light of direct numerical simulations.

We present an experimental study of penetrative convection in gases, which allows reaching a lower Prandtl number $\mathrm{Pr}=0.7$ than classical water experiments. A heavy gas (${\mathrm{SF}}_6$) fills the bottom of a meter-sized rectangular tank. Diffusion of ${\mathrm{SF}}_6$ in air establishes a stratified vertical profile in part of the domain. Electric resistors heat the bottom plate of the tank up to a chosen temperature while water circulation fixes the top plate temperature at room temperature. After a short transient, the ${\mathrm{SF}}_6$-rich lower layer convects and progressively invades the upper stably-stratified layer while exciting propagating internal gravity waves. Density and particle image velocimetry (PIV) measurements are performed, allowing us to follow the growth of the convective region as well as the characteristics of the internal waves and convective fields. While mixing at the interface is often modeled in classical penetrative convection with an eddy diffusivity, we find that the convective layer growths here quadratically in time, which contradicts a stationary and homogeneous turbulent diffusion. The analysis of the wave spectra in the stratified domain reveals a peak frequency at the buoyancy frequency, with a clear cutoff above. Running PIV in both layers simultaneously allows us to compute the kinetic energy transfer from the convective zone into the stratified one, which amounts to about $4\%$. We also define a scaling law for the erosion rate as a function of the Froude number.

The temporal linear stability of plane Poiseuille flow modified by spanwise forcing applied at the walls is considered. The forcing consists of a stationary streamwise distribution of spanwise velocity that generates a steady transversal Stokes layer, known to reduce skin-friction drag in a turbulent flow with little energetic cost. A large numerical study is carried out, where the effects of both the physical and the discretization parameters are thoroughly explored, for three representative subcritical values of the Reynolds number Re. Results show that the spanwise Stokes layer significantly affects the linear stability of the system. For example, at $\text{Re}=2000$ the wall forcing is found to more than double the negative real part of the least-stable eigenvalue, and to decrease by nearly a factor of 4 the maximum transient growth of perturbation energy. These observations are Re dependent and further improve at higher Re. Comments on the physical implications of the obtained results are provided, suggesting that spanwise forcing might be effective to obtain at the same time a delayed transition to turbulence and a reduced turbulent friction.

The triple decomposition of a velocity gradient tensor, which extracts local fluid motions of shear, rigid-body rotation, and irrotational strain, is extended to the decomposition of velocity vectors into shear and nonshear components. The present approach adapts the Biot-Savart law to reconstruct shear and nonshear velocities from the vorticity vectors of shear and rigid-body rotation, respectively. These velocities are related to the flows induced by small-scale shear layers or vortex tubes. The decomposed velocities are investigated with direct numerical simulations of isotropic turbulence and temporally evolving planar jets. The r.m.s. values of shear and nonshear velocities are about $70\%$ and $30\%$ of the r.m.s. value of total velocity fluctuations, and shear layers have a greater contribution to velocity fluctuations than vortex tubes. The shear and nonshear velocities are positively correlated at large scales, and the momentum transfer due to their interaction actively occurs at scales greater than 20 times the Kolmogorov scale. The contributions of shear and nonshear velocities to the Reynolds stress hardly depend on flows. The energy spectra of these velocities collapse well at small scales under Kolmogorov normalization. The present analysis of the turbulent jet confirms that shearing motion has dominant contributions to the production and diffusion of turbulent kinetic energy and the turbulent transport of a passive scalar. In addition, the energy transfer across scales is shown to be dominated by the large-scale velocity gradients arising from shearing motion and the small-scale stresses due to the shear velocity and its interaction with the nonshear component.

This article presents the evolutionary history of immersed boundary methods (IBMs), tracing their origins to the very beginning of computational fluid dynamics in the late 1950s all the way to the present day. The article highlights the advancements in this simulation methodology over the last 50 years and explores the interplay between IBMs and body-conformal grid methods during this time. Drawing upon the authors' combined experience of more than 40 years in this arena, the perspective offered is personal and subjective. By employing a critical and comparative approach through the chronological lens, we hope that this article empowers the reader to understand both the capabilities and limitations of these methods, and to pursue advancements that fill the key gaps and break new ground.

The compressible jet over a convex wall is numerically studied using the delayed detached-eddy simulation method based on the two-equation shear-stress transport model. In particular, the current study focuses on the secondary instabilities in the shear layer. The results show that the alternating high-speed and low-speed streaks in the shear layer induced by the streamwise vortices exhibit secondary instabilities similar to those found in other wall-bounded flows. The varicose mode secondary instability induces the thinning and thickening motions of the low-speed regions, whereas the sinuous mode leads to the side-to-side sway motions. The hairpin vortices and the counter-rotating roll-mode, which are often associated with the symmetric (varicose-type) mode, are dominated in the transient stage of the shear layer. However, as the shear layer evolves downstream, there still appear one-sided roll-modes and quasistreamwise vortices with vorticity of alternate sign produced by the spanwise overlapping of the hairpin vortex legs, which are well known to be related to the antisymmetric (sinuous-type) mode. Further, the dynamic mode decomposition analysis performed on the spanwise velocity fluctuation of the instantaneous snapshots reveals the presence of both sinuous- and varicose-type secondary instabilities, as well as their competitions, in the shear layer. Quantitatively, from $\theta ={25}^{\circ }$ to $\theta ={45}^{\circ }$, the proportion of the varicose mode decreases from $84.4\%$ to $50.6\%$, and accordingly, the sinuous mode increases from $15.6\%$ to $49.4\%$. The analysis of the turbulent kinetic energy production terms reveals that both varicose and sinuous modes are influenced by the radial and spanwise shear components of the turbulent energy production term, and they are in the same order of magnitude. Additionally, the mechanism of the instability is due to the velocity fluctuations and Reynolds stress parallel to the local mean flow gradient. The local inflection point instability caused by the mean flow gradient is also the source of turbulent energy that sustains the instabilities.

In our experiment a vortical flow behind a traveling plate turns into turbulence. By exactly repeating this experiment 42 times with a robot, we study the statistics of this transition. In each realization the fate of the flow is followed over 1.7 s when the plate travels with a constant velocity. It suddenly turns turbulent at a scaled traveled distance of $x^{*}\approx 5.5$. We register the vorticity in a plane that divides the plate perpendicularly. We introduce an original Lagrangian measure of variability between the experiment realizations. The finite-time Lyapunov exponent field of a single experiment predicts this variability; thus we confirm ergodicity. Apart from pointwise measures, yielding a distribution over the field of view, we study the statistics of the circulation computed over the upper and lower half of the domain. The almost perfect symmetry both of the mean and of the fluctuations points to their origin as the fluctuating vortex ring trailing behind the plate. During the initial phase long-time correlations exist in the flow, but they cease once the flow turns turbulent. By ordering our repeated experiments we find that extreme circulations are preceded by circulations that are larger than the median.

The root causes for the mechanisms for margination and near-wall platelet accumulation have previously been investigated by numerical simulations and the results pointed to two main contributors. First, the behavior of the red blood cells (RBCs), namely, traveling around the centerline and formation of the cell-free layer (CFL). Second, the multiple interactions between RBCs and platelets. However, these mechanisms remain to be experimentally verified. In this work, we focus on the dynamics of platelet-size particles inside RBC flows through straight-square microchannels. We used rigid particles with nominal diameter of $2.47\mu \mathrm{m}$ to mimic platelets. The three-dimensional (3D) coordinates ($x,y,z$) and velocity components ($v_x,v_y,v_z$) of the platelet-size particles inside the RBC-suspension flows were measured by means of the general defocusing particle tracking method (GDPT). From the 3D particle trajectories, we were able to investigate the root causes for margination and near-wall particle accumulation. The overall picture points to the RBCs as the dictator of the near-wall particle accumulation and margination. We show that the phenomenon of margination is an irreversible, fast, unpredictable and discontinuous process, and more importantly it can be an opportunity-based event.

A mechanism for a microfluidic pump that leverages alternating adverse and favorable thermocapillary stresses along menisci in a (periodically) fully developed transverse flow in a microchannel is exemplified. The transverse ridges are the interdigitated teeth of cold and hot (isothermal) “combs” and free surface menisci span the interstitial regions between them. The teeth are asymmetrically positioned so that the widths of adjacent menisci differ. This architecture is essentially that of the theoretical pump proposed by Adjari [Phys. Rev. E 61, R45(R) (2000)] but exploits thermocapillarity rather than electro-osmotic slip to drive unidirectional pumping. A theoretical model of the multiphysics pumping mechanism is given that is solved in closed form. Two explicit formulas for the pumping speed are provided. One is derived from the exact solution to the full problem; the other follows from the reciprocal theorem for Stokes flow combined with an exact solution to a distinct problem resolving apparent slip over superhydrophobic surfaces [D. G. Crowdy, Phys. Fluids 23, 072001 (2011)]. A conceptual design of the pump is also outlined; this involves no moving parts, requires no external driving pressure, and pumps a continuous stream of liquid through a microchannel, as opposed to a series of discrete droplets. Since there is only a periodic component of the pressure field the microchannel could be made arbitrarily long and the menisci, which would be essentially flat, are more robust than for conventional pressure-driven flow.

We investigate the dynamics of a magnetoelastic robot with a dipolar magnetic head and a slender elastic body as it performs undulatory strokes and burrows through water-saturated granular beds. The robot is actuated by an oscillating magnetic field and moves forward when the stroke amplitude increases above a critical threshold. By visualizing the medium, we show that the undulating body fluidizes the bed, resulting in the appearance of a dynamic burrow, which rapidly closes in behind the moving robot as the medium loses energy. We investigate the applicability of Lighthill's elongated body theory of fish locomotion, and estimate the contribution of thrust generated by the undulating body and the drag incorporating the granular volume fraction-dependent effective viscosity of the medium. The projected speeds are found to be consistent with the measured speeds over a range of frequencies and amplitudes above the onset of forward motion. However, systematic deviations are found to grow with increasing driving, pointing to a need for further sophisticated modeling of the medium-structure interactions.