The effect of prescribed flexural deflection on the propulsive performance of tandem-arranged flapping foils is analyzed by using the vortex impulse formulation in the limit of two-dimensional, linear potential flow theory. Analytical expressions are given for a general configuration of tandem foils undergoing a quadratic flexural deflection coupled with heaving and pitching motions about arbitrary pitching and deflection axes, although quantitative results are focused to the cases pivoting about their leading edges. Flexural deflection may augment not only the thrust and the propulsive efficiency of the individual foils in relation to an otherwise identical rigid-foil configuration, it also modifies the wake behind the front foil, changing the wake interaction with the trailing foil and, consequently, modifying the tandem propulsive performance. The effect of the upstream wake on the thrust force of the trailing foil is analyzed by using the vorticity distributions obtained analytically. Patterns of propulsive performance enhancement in both the spacing-frequency and the spacing-phase shift planes are analyzed and discussed in relation to previous available experimental and numerical results. The present theoretical results provide some new insights for the design of small aerial or aquatic vehicles using biomimetic tandem propulsors.

Colonial physonect siphonophores swim via laterally distributed multijet propulsion at intermediate Reynolds numbers (Re's) on the orders of 1–1000. Here, a computational fluid dynamics approach that assumes steady axisymmetric flow is employed to investigate the underlying fluid mechanics and adaptive values of colonial swimming via laterally distributed multijet propulsion, with comparison with rear-jetting single-jet propulsion. Results show that imposed flow fields, drag coefficients, powers, and efficiencies all vary significantly depending upon Re, jet angle, and way of jetting. For a given Re, two types of optimal jet angles are determined: one in the range of 61°–70° that maximizes the quasipropulsive efficiency (i.e., to minimize the jet power), and another in the range of 34°–45° that maximizes the Froude propulsion efficiency (i.e., to minimize the wake). Comparison with values for a documented siphonophore, Nanomia bijuga, indicates that siphonophores rely upon a spectrum of jet angles between these two theoretical optima. Multiple, laterally directed jets produced by colonial forms are less energetically efficient for propulsion than single, posteriorly directed jets produced by solitary individuals; however, colonial swimming achieves energetic benefits for jetting individuals within the colony because they require significantly lower per-module power than that required by a lone jet module swimming at the same speed. Hence, by sharing propulsive duties, colony formation helps alleviate inherent power constraints that characterize cnidarian muscles. Importantly, multiple jets that are directed obliquely away from the central body axis exert less impact on other colony members within the siphosome that is towed in the wake of the jetting aggregation.

We experimentally investigate the phenomena of large liquid jet rebound, a mode of fluid transfer following oblique jet impacts on superhydrophobic substrates. We initially seek to describe the jet rebound regimes in tests conducted in the weightless environment of a drop tower. A parametric study reveals the dependence of the flow structure on the relevant dimensionless groups such as Reynolds number and Weber number defined on the velocity component perpendicular to the substrate. We show that significantly larger diameter jets behave similarly as much smaller jets demonstrated during previous terrestrial investigations in some parameter ranges while the flow is fundamentally different in others. Level-set numerical predictions are provided for comparisons where practicable. Simple models are developed predicting landing geometry and the onset of instability that are found to yield good agreement with experiments and simulations. Improving our understanding of such jet rebound opens avenues for unique transport capabilities.

Plants and insects use slender conical structures to transport and collect small droplets, which are propelled along the conical structures due to capillary action. These droplets can deposit a fluid film during their motion, but despite its importance to many biological systems and industrial applications, the properties of the deposited film are unknown. We characterize the film deposition by developing an asymptotic analysis together with experimental measurements and numerical simulations based on the lubrication equation. We show that the deposited film thickness depends significantly on both the fiber radius and the droplet size, highlighting that the coating is affected by finite-size effects relevant to film deposition on fibers of any slender geometry. We demonstrate that by changing the droplet size, while the mean fiber radius and the capillary number are fixed, the thickness of the deposited film can change by an order of magnitude or more. We show that self-propelled droplets have significant potential to create passively coated structures.

Capillary bubbles burst at a free surface following a rapid sequence of events occurring at different length scales and timescales: hole nucleation, fast retraction of the micron-thick liquid film in a few microseconds preluding the much slower overall collapse of the millimeter-sized bubble in a matter of milliseconds. Each of these steps is associated with unsteady fluid forces and accelerations, and therefore with sound radiation. In this experimental study we focus on the airborne sound generated during bubble bursting. Investigating the physical mechanism at the root of sound emission with the help of synchronized fast imaging and sound recordings, we quantitatively link the film retraction dynamics with the frequency content of the acoustic signal. We demonstrate that, contrary to a Minnaert resonance scenario, the frequency here drifts and increases, consistent with a Helmholtz-type resonance of the cavity being more and more opened as the thin film retracts. We propose as an extension a simple model based on a collection of drifting Helmholtz resonators capturing the main features of the fizzing sound of an effervescing beverage.

A framework for analyzing energy flux in turbulent channel flows is proposed which enables quantification of the drag reduction efficacy by different control methods. In contrast to the FIK [Fukagata, Iwamoto, and Kasagi, Phys. Fluids 14, L73 (2002)] and the RD [Renard and Deck, J. Fluid Mech. 790, 339 (2016)] identities, this framework expresses the skin friction coefficient in terms of the nondimensionalized dissipation rate and the work done by external excitation. We extend the energy-box analysis of Gatti et al. [J. Fluid Mech. 857, 345 (2018)] through a triple decomposition of energy flux and show how mean (${\epsilon }_M$), coherent (${\epsilon }_C$), and random turbulent (${\epsilon }_R$) dissipations contribute differently to the drag reduction and the net power saving. Three control methods, including our recently developed spanwise opposed wall-jet forcing (SOJF), the spanwise wall oscillation (SWO), and the opposed wall blowing/suction (OBS) controls, are compared at ${\text{Re}}_{\tau }\approx 200$ via direct numerical simulations (DNS). While all methods yield comparable drag reductions ($\sim 20\%$), OBS yields the maximum net power saving, followed by SOJF, and then SWO. Specifically, for SOJF control, ${\epsilon }_C$ (induced by the large-scale swirls) is much smaller than ${\epsilon }_R$ (induced mainly by the small-scale near-wall vortices) and ${\epsilon }_M$ (due to the spanwise vorticity sheet ${\mathrm{\Omega }}_z$). In contrast, for SWO control, ${\epsilon }_C$ (caused by the wall oscillation-induced ${\mathrm{\Omega }}_x$ vortex sheet)—much larger than that of SOJF—is comparable to ${\epsilon }_R$ and ${\epsilon }_M$. For OBS control, ${\epsilon }_R$ is notably suppressed without any introduction of ${\epsilon }_C$ as the energy is injected through the random velocity field. Diagnoses performed at a higher ${\text{Re}}_{\tau }$ (i.e., 2000) for SWO shows that random turbulent dissipation ${\epsilon }_R$ predominates due to the increasing near-wall vortical structures—hence their suppression should be the target for drag control at high ${\text{Re}}_{\tau }$. The analysis also suggests a promising hybrid drag control strategy by incorporating both the random (OBS) and coherent (SOJF or SWO) controls together, an issue for future exploration.

We attempt to address the old problem of plane shear flows: the origin of turbulence and hence transport of angular momentum in accretion flows as well as laboratory flows, such as plane Couette flow. We undertake the problem by introducing an extra force in Orr-Sommerfeld and Squire equations along with the Coriolis force mimicking the local region of the accretion disk. For plane Couette flow, the Coriolis term drops. Subsequently we solve the equations with the WKB approximation method. We investigate the dispersion relation for the Keplerian flow and plane Couette flow for all possible combinations of wave vectors. Due to the very presence of extra force, we show that both flows are unstable for a certain range of wave vectors. However, the nature of instability between the flows is different. We also study the Argand diagrams of the perturbation eigenmodes. This helps us to compare the different timescales corresponding to the perturbations as well as accretion. We ultimately conclude with this formalism that fluid gets enough time to be unstable and hence plausibly turbulent particularly in the local regime of the Keplerian accretion disks. Repetition of the analysis throughout the disk explains the transport of angular momentum and matter along outward and inward directions, respectively.

Three-dimensional (3D) longwave oscillatory Marangoni convection in a heated thin layer with weak heat flux from the free surface is considered. Numerous experiments show that the surface tension is a nonlinear function of temperature. Here we modify the system of nonlinear longwave evolution equations expanding the temperature coefficient of the surface tension into the Taylor series about the surface temperature. Using the weakly nonlinear analysis we explore the patterns formed near the critical value of Marangoni number. Stability of the 3D patterns on square, rhombic, and hexagonal lattices are considered. The nonlinearity of the surface tension's temperature dependence can be a stabilizing factor as well as destabilizing one.

The effect of surface roughness on the steady laminar flow induced by a rotating disk submerged by fluid otherwise at rest is investigated here theoretically and numerically. A theory is proposed where a triple-deck analysis is applied leading to a fast evaluation of the steady-flow modification due to the rough surface. The theory assumes that the roughness is much smaller than the boundary-layer height and is characterized by a significantly longer length scale (slender roughness). Only the leading-order correction is developed here, corresponding to a velocity-field correction that is linear with the roughness height. The proposed theory neglects some curvature terms (here partially accounted by means of a stretching of the radial coordinate and of a scaling of the dependent variables). Numerical simulations performed with different roughness geometries (axisymmetric roughness, radial grooves, and localized bumps) have been used to validate the theory. Results indicate that the proposed theory leads to a good quantification of the flow modifications due to surface roughness at a very low computational cost. A demonstration of the capabilities of the theory is finally proposed where the statistical effects on the flow due to a random (but statistically known) roughness distributed on the surface of a rotating disk are characterized.

Flapping flight and swimming are increasingly studied due to both their intrinsic scientific richness and their applicability to novel robotic systems. Strip theory is often applied to flapping wings, but such modeling is only rigorously applicable in the limit of infinite aspect ratio ($AR$) where the geometry and kinematics are effectively uniform. This work compares the flow features and forces of strip theory and three-dimensional flapping foils, maintaining similitude in the rolling and twisting kinematics while varying the foil $AR$. We find the key influence of finite $AR$ and spanwise varying kinematics is the generation of a time-periodic spanwise flow which stabilizes the vortex structures and enhances the dynamics at the foil root. An aspect-ratio correction for flapping foils is developed analogous to Prandtl finite wing theory, enabling future use of strip theory in analysis and design of finite aspect ratio flapping foils.

We employ the finite-extensible Giesekus viscoelastic constitutive equation to model viscoelastic fluidlike adhesives and study theoretically their response during the debonding process from a rigid surface. We consider a cylindrical sample of soft pressure sensitive adhesive, confined between two solid disks, and assume that small cavities preexist at the adhesive-solid interface due to surface inhomogeneities. When the debonding process is initiated, and the upper disk starts to move, elongating the sample, the cavities expand laterally and weaken the sample. As the debonding process evolves, the cavities start to interact with each other and deform mainly in the direction of elongation; this leads to the formation of thin sheets of material that induce the fibrillation of the sample. At the late stages of the process, these fibrils become very thin, and adhesion is lost. To simulate this complex process that features multiple free surfaces and three-phase contact lines, we solve the full three-dimensional, transient momentum and mass conservation equations coupled with the constitutive equation that accounts for the non-Newtonian stress contribution. The governing equations are expressed in their Lagrangian form and solved with a Petrov-Galerkin stabilized, finite element formulation. The physical domain is discretized with an unstructured mesh that is adaptively reconstructed, allowing us to reach very high deformations of the initial sample. Our results are in qualitative agreement with experimental observations, both regarding the stress-strain curve and the shape of the cavities. Finally, by performing a parametric analysis, we investigate the role of the rheological and geometrical properties of the sample on the adhesion energy of the material.

In this report, results of irreversible mixing efficiency, ${\mathrm{Ri}}_f^{*}$, for a slumping gravity current is presented for a range of Reynolds numbers, $\mathrm{Re}=485$–12 270. Simultaneous velocity and density fields from particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) are used to measure the viscous dissipation ($\epsilon$) and scalar gradients ($\mathbf{\nabla }\rho$, $\mathbf{\nabla }{\rho }^{\prime }$) needed to calculate ${\mathrm{Ri}}_f^{*}$. It is observed that ${\mathrm{Ri}}_f^{*}$ plateaus to ${\mathrm{Ri}}_f^{*}\approx 0.12$, for the range of the buoyancy Reynolds number, ${\mathrm{Re}}_b$, and the gradient Richardson number, ${\mathrm{Ri}}_g$, used in our study. Owing to ambiguities in parametrizing ${\mathrm{Ri}}_f^{*}$ as a function of a single flow parameter, like ${\mathrm{Re}}_b$ or ${\mathrm{Ri}}_g$, a multiparameter space is considered using a turbulent Froude number, ${\mathrm{Fr}}_k$, and a turbulent Reynolds number, ${\mathrm{Re}}_L$. New insights are achieved, wherein it is observed that for a given ${\mathrm{Re}}_b$ or ${\mathrm{Ri}}_g$, ${\mathrm{Ri}}_f^{*}$ can assume different values owing to the turbulent regimes set up by ${\mathrm{Fr}}_k$ and ${\mathrm{Re}}_L$ and the effects of the molecular Prandtl number, Pr. It is also seen that the plateauing value of ${\mathrm{Ri}}_f^{*}$ can be greatly influenced by the flow parameters and fluid properties. We document that mixing efficiency can be increased in strongly stratified flow (${\mathrm{Fr}}_k<0.6$), provided ${\mathrm{Re}}_L$ is sufficiently high. Also, for the parameter range in our study, $3\le {\mathrm{Re}}_b\le 48$ and $0.26\le {\mathrm{Ri}}_g\le 0.9$, we did not notice a drop in the value of ${\mathrm{Ri}}_f^{*}$. This is attributed to the fact that our experiments are in the regime of strongly stratified turbulence with sufficiently high ${\mathrm{Re}}_L$ that could sustain turbulence and mixing. Our study suggests a need for a different parametrization of mixing efficiency in the diffusive ($1\le {\mathrm{Re}}_b\le 10$) and intermediate ($10\le {\mathrm{Re}}_b\le 100$) regimes for a gravity current.

Electrosprays of highly conducting liquids operated in the cone-jet mode produce charged nanodroplets of controllable size and molecular ions. The study of this electrospraying regime is challenging due to the lack of experimental techniques for probing these nanometric systems, and the higher complexity of the physics associated with the onset of ion field emission and self-heating. Jet parameters in the breakup region such as its radius, velocity, potential, and electrification level are key for understanding the formation of droplets and emission of ions, and useful to validate numerical models of cone jets. In the case of micron-sized jets, these quantities can be determined with the values of the retarding potentials and mass-to-charge ratios of the droplets produced by the breakup. This article uses this technique to investigate the parameters of nanometric jets. Retarding potential and mass-to-charge distributions of the beam are measured with retarding potential and time-of-flight analyzers operated in tandem. This combination makes it possible to differentiate between droplets of similar mass-to-charge ratios which, unlike in the case of micrometric jets, are needed to apply the technique. Aside from the jet parameters, the experimental characterization also reveals with great detail the composition of the beam, which includes primary ions emitted from the jet breakup; ions resulting from the desolvation of primary ions; stable primary droplets produced at the breakup; smaller droplets resulting from the Coulomb explosion of unstable primary droplets; and small primary droplets that evaporate a significant fraction of their charge in flight. An analysis of the breakup, parametrized by dimensionless numbers, explains this complexity. Although the experimental characterization only studies the electrosprays of the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide, the analysis is general and can be used to understand the beams of other highly conducting liquids.

This work investigates the mechanisms that underlie transitions to turbulence in a three-dimensional domain in which the variation of flow quantities in the out-of-plane direction is much weaker than any in-plane variation. This is achieved using a model for the quasi-two-dimensional magnetohydrodynamic flow in a duct with moving lateral walls and an orthogonal magnetic field, where three dimensionality persists only in regions of asymptotically small thickness. In this environment, conventional subcritical routes to turbulence, which are highly three dimensional (with large variations from nonzero out-of-plane wave numbers), are prohibited. To elucidate the remaining mechanisms involved in quasi-two-dimensional turbulent transitions, the magnetic field strength and degree of antisymmetry in the base flow are varied, the latter via the relative motion of the lateral duct walls. Introduction of any amount of antisymmetry to the base flow drives the critical Reynolds number infinite, as the Tollmien-Schlichting instabilities take on opposite signs of rotation and destructively interfere. However, an increasing magnetic field strength isolates the instabilities, which, without interaction, permits finite critical Reynolds numbers. The transient growth obtained by similar Tollmien-Schlichting wave perturbations only mildly depends on the base flow, with negligible differences in growth rate for friction parameters $H\gtrsim 30$. Weakly nonlinear analysis determines the local bifurcation type, which is always subcritical at the critical point, and along the entire neutral curve just before the magnetic field strength becomes too low to maintain finite critical Reynolds numbers. Direct numerical simulations, initiated with random noise, indicate that a subcritical bifurcation is difficult to achieve in practice, with only supercritical behavior observed. For $H\le 1$, supercritical exponential growth leads to saturation but not turbulence. For higher $3\le H\le 10$, a turbulent transition occurs and is maintained at $H=10$. For $H\ge 30$, the turbulent transition still occurs, but is short lived, as the turbulent state quickly collapses. In addition, for $H\ge 3$, an inertial subrange is identified, with the perturbation energy exhibiting a $-5/3$ power law dependence on wave number.

Every animal cell is filled with a cytoskeleton, a dynamic gel made of inextensible fibers, such as microtubules, actin fibers, and intermediate filaments, all suspended in a viscous fluid. Numerical simulation of this gel is challenging because the fiber aspect ratios can be as large as ${10}^4$. We describe a method for rapidly computing the dynamics of inextensible slender filaments in periodically sheared Stokes flow. The dynamics of the filaments is governed by a nonlocal slender body theory which we partially reformulate in terms of the Rotne-Prager-Yamakawa hydrodynamic tensor. To enforce inextensibility, we parametrize the space of inextensible fiber motions and strictly confine the dynamics to the manifold of inextensible configurations. To do this, we introduce a set of Lagrange multipliers for the tensile force densities on the filaments and impose the constraint of no virtual work in an $L^2$ weak sense. We augment this approach with a spectral discretization of the local and nonlocal slender body theory operators which is linear in the number of unknowns and gives improved spatial accuracy over approaches based on solving a line-tension equation. For dynamics, we develop a second-order semi-implicit temporal integrator which requires at most a few evaluations of nonlocal hydrodynamics and a few block-diagonal linear solves per time step. After demonstrating the improved accuracy and robustness of our approach through numerical examples, we apply our formulation to a permanently cross-linked actin mesh in a background oscillatory shear flow. We observe a characteristic frequency at which the network transitions from quasistatic, primarily elastic behavior to dynamic, primarily viscous behavior. We find that nonlocal hydrodynamics increases the viscous modulus by as much as 25%. Most of this increase, in contrast to the smaller (about 10%) increase in the elastic modulus, is due to short-ranged intrafiber interactions.

Low-level jets (LLJs) are the wind maxima in the lower regions of the atmosphere with a high wind energy potential. Here we use large-eddy simulations to study the effect of LLJ height on the flow dynamics in a wind farm with $10\times 4$ turbines. We change the LLJ height and atmospheric thermal stratification by varying the surface cooling rate. We find that the first row power production is higher in the presence of a LLJ compared to a neutral reference case without LLJ. Besides, we show that the first row power production increases with decreasing LLJ height. Due to the higher turbulence intensity, the wind turbine wakes recover faster in a neutral boundary layer than in a stably stratified one. However, for strong thermal stratification with a low-height LLJ, the wake recovery can be faster than for the neutral reference case as energy can be entrained from the LLJ. Flow visualizations reveal that under stable stratification the growth of wind farm's internal boundary layer is restricted and the wind flows around the wind farm. Wind farms extract energy from LLJs through wake meandering and turbulent entrainment depending on the LLJ height. Both effects are advantageous for wake recovery, which is beneficial for the performance of downwind turbines. This finding is confirmed by an energy budget analysis, which reveals a significant increase in the kinetic energy flux in the presence of a LLJ. The jet strength reduces as it passes through consecutive turbine rows. For strong stratification, the combined effect of buoyancy destruction and turbulence dissipation is larger than the turbulent entrainment. Therefore, the power production of turbines in the back of the wind farm is relatively low for strong atmospheric stratifications. We find that the pronounced wind veer in stably stratified boundary layers creates asymmetry in the available wind resource, which can only be studied in finite-size wind farm simulations. We emphasize that spanwise-infinite wind farm simulations may underpredict wind farm performance as the additional beneficial effect of LLJ cannot be observed.

The resonant interactions between two gravity wave trains in deep water are studied numerically using a three-dimensional (3D) nonhydrostatic free surface flow model. After model validation, four cases of resonant interactions are simulated and analyzed to study the effect of the primary waves' steepness on the evolutions of the tertiary resonant wave, 3D wave patterns, and velocity profiles. It is found that for primary waves with small steepness, the theories of Longuet-Higgins [J. Fluid Mech. 12, 321 (1962)] predict well the growth of the resonant wave, that the crest and trough lines of wave patterns are basically straight and regular, and that the linear wave theory roughly estimates well the velocity profiles. For primary waves with moderate steepness, the applicable distance of Longuet-Higgins's theory decreases with an increase of the primary waves' nonlinearity. At greater distances, the growth of the resonant wave is smaller in comparison to Longuet-Higgins's predictions. Strong resonant interactions can lead to the bending and then splitting of crests and troughs. The curvatures of the crests and troughs increase with an increase of the primary waves' steepness and the resonant wave's propagation distance. For primary waves with small steepness, the crest and trough lines will eventually split, as long as the propagation distance is sufficiently large. The crest line is split into a longer segment with a larger wave crest and a shorter one with a smaller wave crest. With an increase of the primary waves' nonlinearity, the maximum nondimensionalized wave crest down-wave is found to be larger and more peaked, and its occurrence is earlier, which precisely corresponds to the separated larger wave crest. Meanwhile, the intense resonant and the subsequent quasiresonant interactions have such a significant influence on the velocity profiles that the velocity fields cannot be predicted from the linear predictions.

We present theory and experiments demonstrating the existence of invariant manifolds that impede the motion of microswimmers in two-dimensional fluid flows. One-way barriers are apparent in a hyperbolic fluid flow that block the swimming of both smooth-swimming and run-and-tumble Bacillus subtilis bacteria. We identify key phase-space structures, called swimming invariant manifolds (SwIMs), that serve as separatrices between different regions of long-time swimmer behavior. When projected into $xy$ space, the edges of the SwIMs act as one-way barriers, consistent with the experiments.

The breakup of a jet of a viscous fluid with viscosity ${\mu }_1$ immersed into another viscous fluid with viscosity ${\mu }_2$ is considered in the limit when the viscosity ratio $\lambda ={\mu }_1/{\mu }_2$ is close to zero. We show that, in this limit, a transition from ordinary continuous self-similarity to discrete self-similarity takes place as $\lambda$ decreases. It follows that instead of a single point breakup, the rupture of the inner jet occurs through the appearance of an infinite sequence of filaments of decreasing size that will eventually produce infinite sequences of bubbles of the inner fluid inside the outer fluid. The transition can be understood as the result of a Hopf bifurcation in the system of equations modeling the physical problem.