A free surface, placed in a strong viscous flow (such that viscous forces overwhelm surface tension), often develops ends with very sharp tips. In Courrech du Pont and Eggers [Proc. Natl. Acad. U. S. A. 117, 32238 (2020)] we have shown that the axisymmetric shape of the ends, nondimensionalized by the tip curvature, is governed by a universal similarity solution. The shape of the similarity solution is close to a cone, but whose slope varies with the square root of the logarithmic distance from the tip. Here we develop the calculation of the tip similarity solution to next order, using which we demonstrate matching to previous slender-body analyses, which fail near the tip. This allows us to resolve the long-standing problem, first raised by G. I. Taylor, of finding the global solution of a bubble in a strong hyperbolic flow. We also calculate the tip curvature quantitatively, beyond the scaling behavior of the leading-order solution. Our results are shown to agree in detail with full numerical simulations of the Stokes equation.

When a viscous liquid is released on an inclined solvophilic substrate, it spreads downwards by gravity and tends to coat the substrate. Here we report the gravitational axisymmetric spreading of a viscous liquid with a fixed volume on inclined geometries that cause converging flows, for example, on the inside of a downward-pointing hollow cone (funnel) and the lower part of a sphere (bowl). For the limit that the effect of surface tension is negligible, we analytically determine the thickness profile as well as the time-dependent position of the front of the spreading liquid. In the typical scenario that a liquid spreads on a geometry such as an inclined plate, the thickness of the front of the spreading liquid monotonically decreases in time throughout the spreading and a fingering instability occurs while the liquid film thins. However, we show that on an inclined geometry, where convergence of the flow occurs, the thickness of the spreading front first decreases in time and then increases. We also predict a critical volume $V_c$ such that a fingering instability occurs if the volume of the spreading liquid is less than $V_c$. Experiments of axisymmetric spreading on a downward-pointing cone (funnel) are then performed and the measured position of the front and the critical liquid volume of the fingering instability agree with our theoretical predictions. This study highlights the effect of a geometry that focuses and thickens a thin film.

In this paper we shortly investigate the similarity between states for different fluidized bed regimes, which is an essential requirement for the application of recurrence computational fluid dynamics (rCFD) [Lichtenegger and Pirker, Chem. Eng. Sci. 153, 394 (2016)]. Therefore, bubbling and turbulent fluidization regimes are outlined in the frame of different variable-based recurrence/distance norms (rNorm/dNorm). This last is typically used to quantify the degree of flow similarity within the observation time span. The recurrence plots or the so-called recurrence/distance matrices are accordingly constructed upon the rNorm/dNorm values and show no recurrence tendency for the full-resolved turbulent fluidization regimes. It is reported thereabouts that the high fluctuated nature of turbulent fluidization (interphase small scales) absentees the periodicity, and a disclosing procedure for the superstructure (large-scale) dynamics is vitally needed. To that end, a spatial filtering with the idea of the domain decomposition (recurrence island) has been applied to reveal a proper posterior indicator of turbulent fluidization recurrence. The filtering approach handles in increasing the recurrence prominence without changing the system behavior and makes the recurrence more visible. From other perspectives, a turbulence modeling using the coarse-grained approximate deconvolution model–two-fluid model (ADM-TFM) is employed for the turbulent fluidization case. Following its recurrence investigations, the resultant prominence offered by ADM-TFM is in a very comparable aspect to the same grid spatial filtering.

The dynamics of transitional flows are governed by an interplay between the nonnormal linear dynamics and quadratic nonlinearity in the incompressible Navier-Stokes equations. In this work, we propose a framework for nonlinear stability analysis that exploits the fact that nonlinear flow interactions are constrained by the physics encoded in the nonlinearity. In particular, we show that nonlinear stability analysis problems can be posed as convex feasibility and optimization problems based on Lyapunov matrix inequalities, and a set of quadratic constraints that represent the nonlinear flow physics. The proposed framework can be used to conduct global stability, local stability, and transient energy growth analysis. The approach is demonstrated on the low-dimensional Waleffe-Kim-Hamilton model of transition and sustained turbulence. Our analysis correctly determines the critical Reynolds number for global instability. For local stability analysis, we show that the framework can estimate the size of the region of attraction as well as the amplitude of the largest permissible perturbation such that all trajectories converge back to the equilibrium point. Additionally, we show that the framework can predict bounds on the maximum transient energy growth. Finally, we show that careful analysis of the multipliers used to enforce the quadratic constraints can be used to extract dominant nonlinear flow interactions that drive the dynamics and associated instabilities.

To investigate the influence of the orifice geometry on near-field coherent structures in a jet, Fourier proper orthogonal decomposition (Fourier-POD) is applied. Velocity and vorticity snapshots obtained from tomographic particle image velocimetry at the downstream distance of two equivalent orifice diameters are analyzed. Jets issuing from a circular orifice and from a fractal orifice are examined, where the fractal geometry is obtained from a repeating fractal pattern applied to a base square shape. While in the round jet energy is mostly contained at wave number $m=0$, associated to the characteristic Kelvin-Helmholtz vortex rings, in the fractal jet modal structures at the fundamental azimuthal wave number $m=4$ capture the largest amount of energy. In addition, energy is scattered across a wider range of wave numbers than in the round jet. The radial Fourier-POD profiles, however, are nearly insensitive to the orifice geometry, and collapse to a universal distribution when scaled with a characteristic radial length. A similar collapse was recently observed in POD analysis of turbulent structures in pipe flow. However, unlike in pipe flow, the azimuthal-to-radial aspect ratio of the Fourier-POD structures is not constant and varies greatly with the wave number. The second part of the paper focuses on the relationship between streamwise vorticity and streamwise velocity, to characterize the role of the orifice geometry on the lift-up mechanism recently found to be active in turbulent jets [P. Nogueira, A. Cavalieri, P. Jordan, and V. Jaunet, Large-scale streaky structures in turbulent jets, J. Fluid Mech. 873, 211 (2019)]. The averaging of the streamwise vorticity conditioned on intense positive fluctuations of streamwise velocity reveals a pair of vorticity structures of opposite sign flanking the conditioning point, inducing a radial flow towards the jet periphery. This pair of structures is observed in both jets, even if the azimuthal extent of this pattern is $30\%$ larger in the jet issuing from the circular orifice. The coupling between streamwise vorticity and velocity motions is also examined using Fourier-POD. The analysis reveals that in the jet with a circular orifice lower wave-number modes, corresponding to structures at larger scales, capture a larger fraction of the vorticity-velocity coupling. This evidences that the orifice geometry directly influences the interaction between velocity and vorticity.

Flow separation control of a sweeping jet actuator in a backward-facing ramp was studied using two-dimensional and stereoscopic particle-image velocimetry. The actuator was operated at a single supply rate pertaining to a jet velocity of 7.3 m/s and positioned at the streamwise location of 0.8 and 3.7 boundary layer thickness upstream of the separating edge. Three wind tunnel reference velocities corresponding to Reynolds numbers based on the boundary layer thickness of ${\mathrm{Re}}_{\delta }=2400$, 5200, and 9800 (jet-to-reference velocity ratios of 1, 0.5, and 0.3) were investigated, and the control effectiveness was assessed based on the size of the separation bubble. For all three Reynolds numbers, positioning the actuator nearer to the separating edge offered poorer flow separation control for measurement planes near the jet centerline. This was attributed to the upwash effect of the jet which directed high momentum fluid away from the wall leading to lower levels of entrainment, and the formation of a localized low-pressure region that coincided with the sharp change in ramp geometry leading to stronger adverse pressure gradients and lower streamwise velocities that were more likely to undergo flow reversal. At high jet-to-reference velocity ratios, the effect was accentuated, and a secondary separation bubble was observed. When the actuator was positioned further upstream, the primary streamwise vortices produced by the sweeping jet lifted away from the wall, and secondary flow structures induced near the wall contributed to higher levels of near-wall entrainment and improved flow control along the jet centerline. In contrast, for measurement planes far from the jet centerline, positioning the actuator nearer the separating edge was preferable. This was attributed to milder decay of the primary streamwise vortices, leading to stronger downwash effect and higher entrainment levels that were able to affect a wider spanwise area.

The flow past a fixed finite-length circular cylinder, the axis of which makes a nonzero angle with the incoming stream, is studied through fully resolved simulations, from creeping-flow conditions to strongly inertial regimes. The investigation focuses on the way the body aspect ratio $\chi$ (defined as as the length-to-diameter ratio), the inclination angle $\theta$ with respect to the incoming flow, and the Reynolds number Re (based on the cylinder diameter) affect the flow structure past the body and therefore the hydrodynamic loads acting on it. The configuration $\theta =0^{\circ }$ (where the cylinder is aligned with the flow) is first considered from creeping-flow conditions up to $\text{Re}=400$, with aspect ratios up to 20 (10) for $\text{Re}\le 10$ ($\text{Re}\ge 10$). In the low-to-moderate Reynolds-number regime ($\text{Re}\lesssim 5$), influence or the aspect ratio, inclination (from $0^{\circ }$ to ${30}^{\circ }$), and inertial effects are examined by comparing numerical results for the axial and transverse force components and the spanwise torque with theoretical predictions based on the slender-body approximation, possibly incorporating finite-Reynolds-number corrections. Semiempirical models based on these predictions and incorporating finite-length and inertial corrections extracted from the numerical data are derived. For large enough Reynolds numbers ($\text{Re}\gtrsim {10}^2$), separation takes place along the upstream part of the lateral surface of the cylinder, deeply influencing the surface stress distribution. Numerical results are used to build empirical models for the force components and the torque, valid for moderately inclined cylinders ($\left|\theta \right|\lesssim {30}^{\circ }$) of arbitrary aspect ratio up to $\text{Re}\approx 300$ and matching those obtained at low-to-moderate Reynolds number.

In this paper we develop a methodology for the mesoscale simulation of strong electrolytes. The methodology is an extension of the fluctuating immersed-boundary approach that treats a solute as discrete Lagrangian particles that interact with Eulerian hydrodynamic and electrostatic fields. In both algorithms the immersed-boundary method of Peskin is used for particle-field coupling. Hydrodynamic interactions are taken to be overdamped, with thermal noise incorporated using the fluctuating Stokes equation, including a “dry diffusion” Brownian motion to account for scales not resolved by the coarse-grained model of the solvent. Long-range electrostatic interactions are computed by solving the Poisson equation, with short-range corrections included using an immersed-boundary variant of the classical particle-particle particle-mesh technique. Also included is a short-range repulsive force based on the Weeks-Chandler-Andersen potential. This methodology is validated by comparison to Debye-Hückel theory for ion-ion pair correlation functions, and Debye-Hückel-Onsager theory for conductivity, including the Wien effect for strong electric fields. In each case, good agreement is observed, provided that hydrodynamic interactions at the typical ion-ion separation are resolved by the fluid grid.

Patterns observed in correlation measurements provided early indications of organized structures in turbulent boundary layers, later supplemented by imaging studies. It is recognized that correlation patterns could in some instances reflect transient flow processes rather than structures, but discrimination among the possible origins of various correlation patterns has not been addressed systematically. Here this is done from three complementary perspectives. First, a conceptual framework termed cascade analogy is shown to imply three processes, all devoid of organized-structure influences, that might induce such patterns. Second, hierarchical parcel swapping (HiPS), a stochastic model that is likewise devoid of such influences, is shown to produce the correlation patterns that are implied by these processes. The HiPS formulation used here is a highly reduced version of a previous formulation, highlighting the elementary nature of the pattern-inducing processes. Third, experimental indications of all these patterns are noted. One pattern, an obliquely oriented ridge of peak cross-correlation between streamwise velocity at various heights and wall stress, is known by other means to be associated with organized structure. The results indicate that the oblique ridge does not in itself uniquely imply this interpretation. This inference is shown to have substantive consequences. The other two patterns are marginally discernible in reported measurements, but there has been no prior assessment of their significance, nor are they obviously associated with organized structure in boundary layers. Here they are identified as possible analogs of the inertial-range inverse cascade (backscatter) and the effects of the fluctuating rate of forward cascading, respectively. Further investigations to delineate more clearly the origins and the circumstances of occurrence of such patterns are suggested.

Shock wave propagation in a variable cross-section channel is a recurrent issue in the literature. Seminal work regarding this flow configuration has been proposed by Whitham (1958) through the derivation of a one-dimensional approach connecting the shock Mach number and the area channel: the A-M relation. It is based on strong theoretical restrictions: (i) shock equations applied on a $C^{+}$, (ii) omission of the postshock influence, and (iii) initial conditions at rest. It has been the focus of many studies aimed at generalizing it. However, very little attention has been paid to the study of the shock motion outside the varying cross-sectional region since Russell (1967). The objective of the current work is to describe and to explain the shock wave behavior in a constant area channel behind a convergent or divergent channel. It is found that the shock propagation in the downstream uniform area region is influenced by the postshock flow unsteadinesses. Therefore, the Whitham model is not suited to the shock motion study in a constant area region downstream of a convergent or divergent area region. A detailed flow description is provided and a quasisteady model for determining the waves intensity at large times is proposed. This model gives accurate results without any assumptions on the shock strength, area variation or the shock upstream state. Finally, this study points out the limits of the use of Whitham's theory in a variable area channel with increasing section variation rate (where $\left|dA/A(x+dx)\right|\ge \left|dA/A\left(x\right)\right|$).

The dynamics of a polarizable spheroid in a shear flow subjected to a magnetic field is determined by a balance between the hydrodynamic torque and the magnetic torque due to the induced magnetic moment. The magnetic moment of the particle is an odd function of $\mathit{H}·\widehat{\mathit{z}}$ which saturates to constant for $|\mathit{H}·\widehat{\mathit{z}}|\gg 1$, where $\mathit{H}$ is the magnetic field and $\widehat{\mathit{z}}$ is the orientation vector of the particle. Three different models are used, the realistic Langevin model and the simpler linear and signum approximations. These models contain two dimensionless parameters, $\mathrm{\Sigma }=\left({\mu }_0\chi \right|\mathit{H}{|}^2/\mathrm{\Gamma })$ and ${\mathrm{\Sigma }}_s=({\mu }_0{m}_s\left|\mathit{H}\right|/\mathrm{\Gamma })$, where $\mathrm{\Gamma }$ is the characteristic hydrodynamic torque, ${\mu }_0$ is the magnetic permeability of free space, $\chi$ is the polarizability for low magnetic field, and $m_s$ is the saturation moment. The dynamics of the spheroid is analyzed for the case where the magnetic field is aligned along the flow plane. For the linear model, an analytical solution for the evolution of the particle orientation is obtained; there is a continuous transition between a rotating state and a static state when the parameter $\mathrm{\Sigma }$ exceeds a critical value which depends on the orientation of the magnetic field and the aspect ratio of the particle. The phase portrait for the signum model exhibits a rich variety in dynamical behavior, including continuous and discontinuous transitions between the rotating and static states, and the possibility of multiple steady states. The transition between stationary and rotating states, and the orientation and magnetic torque in both states, are numerically determined for the Langevin model.

Water entry studies traditionally employ homogeneous projectiles of varying impactor shape, entry speed, and surface roughness. Surface heterogeneity is yet another means to manipulate splash dynamics. In this experimental study, we systematically investigate the water entry of smooth, free-falling, hemispherically coated spheres for Froude numbers in the range of $2.8-6.7$. Hydrophilic spheres are hemispherically coated with a hydrophobic compound and in-turn produce deep seal cavities, provoke changes in super-surface splash features, and alter sphere trajectories. Generally, flow separation is initialized when hydrophobic surfaces make contact with the fluid, leading to air-entrainment across the range of entry speeds and impact orientations on test. Cavity formation induced by the hydrophobic portion of a hemispherically coated sphere promotes flow separation across the hydrophilic surface at impact velocities well below the threshold of 8 m/s required for air-entrainment by completely hydrophilic spheres. Spheres having partially hydrophilic and partially hydrophobic surfaces entering the fluid simultaneously, experience asymmetric cavities and horizontal forces that result in lateral migration from straight-line trajectories. Such observations augur well for water entry applications where the coupled dynamics of flow separation and passive trajectory control are desirable.

Immobilized electrocatalytic surfaces are capable of generating reaction-driven fluid flow by electrochemical energy conversion. A well-known system concerns the gold-platinum bimetallic motor driven by hydrogen peroxide conversion. In this work, we focus on experimental and numerical analyses that provide fundamental insight on the key elements that control the resulting transport characteristics in this system, including the generated electric field, reaction kinetics, and diffusio-electro-osmotic phenomena. The current between the electrodes and the induced potential that governs the reactive fluxes are measured electrochemically, while the fluid flow is analyzed using particle tracking velocimetry. Numerical simulations based on the Poisson-Nernst-Planck and Navier-Stokes equations reveal the interplay of the individual electrode surface reactivity, represented by the dimensionless Damköhler numbers, with the electrokinetic phenomena.

Particle-resolved direct numerical simulations of monodisperse settling suspensions of cubes and spheres are performed for Galileo numbers $\text{Ga}=70$ and $\text{Ga}=160$, and solid volume fractions in the range $0.01⩽\varphi ⩽0.2$. The solid-to-fluid density ratio $m={\rho }_s/{\rho }_f$ is taken to be fixed at 2, representing liquid-solid suspensions. Strong columnar clustering is observed for $\text{Ga}=160$ and $\varphi =0.01$ in a sphere suspension, whereas similar vertical structures are not present as prominently in a cube suspension. We find that in all cases, cube suspensions tend to be more homogeneous compared to sphere suspensions, as indicated by both their microstructure and momentum transfer properties. The enhanced homogeneity is associated with the pronounced angular velocities of cubes and the resulting orientation- and rotation-induced lift forces, which promote transverse motions and the likelihood of escaping from clusters. Higher rotation rates of cubes thus play a major role in the transfer of momentum from the gravity to the transverse direction, demonstrated by the lower anisotropy of particle velocity fluctuations in cube suspensions. In more dilute cases, cubes induce significantly stronger pseudoturbulence in the flow, especially in the transverse direction. The drag of dynamic cube suspensions is found to be generally similar to static beds of cubes, the reason for which is speculated to be relevant to their motion freedom and the more homogeneous microstructure.

The extensional effective viscosity, ${\eta }_{\mathrm{e}}$, of a suspension of solid cylindrical fibers in a Newtonian liquid is measured from the gravitational stretching of a quasisteady jet. We vary the length-to-diameter aspect ratio of the fibers, $a$, from $\sim 10$ to $\sim {10}^2$, and the particle volume fraction, $\varphi$, in the range $a\varphi \sim 0.1–2$. For low values of $\varphi$, the extensional viscosity is found to agree with Batchelor's model for the dilute regime, which assumes noninteracting fibers aligned with the stretching direction, but for higher concentrations, ${\eta }_{\mathrm{e}}$ is found to increase much more strongly with increasing $\varphi$ than predicted by available models assuming purely hydrodynamics interactions between the fibers. Additional experiments are performed on the breakup of an unstable capillary bridge for $a=11$. Although the variability in the bridge shape and the deviation from a viscous Newtonian dynamics in the late stage of the breakup increase significantly with increasing $\varphi$, it is found that the mean total duration of the breakup is in good agreement with a Newtonian effective dynamics limited by the extensional viscosity, ${\eta }_{\mathrm{e}}$.

By employing dimensional analysis, we scale the equations of the mesoscopic model of finite temperature superfluid hydrodynamics. Based on this scaling, we set up three problems that depict the effects of kinematic, normal-fluid strain fields on superfluid vortex loops, and characterize small-scale processes in fully developed turbulence. We also develop a formula for the computation of energy spectra corresponding to superfluid vortex tangles in unbounded domains. Employing this formula, we compute energy spectra of superfluid vortex patterns induced by uniaxial, equibiaxial, and simple-shear normal-fluid flows. By comparing the steady-state superfluid spectra and vortex structures, we conclude that normal-flow strain fields do not play an important role in explaining the phenomenology of fully developed superfluid turbulence. This is in sharp contrast with the role of vortical normal-flow fields in offering plausible, structural explanations of superfluid vortex patterns and spectra entailed in numerical turbulent solutions of the mesoscopic model.

Numerical simulations supported by previously published experimental data are used to compare the impact of the internal fluid viscosity and the membrane viscosity on a tank-treading red blood cell. The method used is based on a continuum framework both for the fluid and the membrane, their interaction being ensured thanks to the immersed boundary method. The finite-strain model implemented to account for membrane viscosity assumes a free energy form that leads to an additive decomposition of the equilibrium and nonequilibrium stresses. It also assumes that the stress tensor can be separated into a deviatoric part and a hydrostatic part, which are independent. Only the deviatoric part is accounted for in this study. Both the viscosities of the cytoplasm and of the membrane yield a decrease of the tank-treading frequency, with only moderate changes in the deformation of the red blood cell. However, it is shown that the values of tank-treading frequency from the literature cannot be explained by the internal fluid viscosity only. On the contrary, adding the membrane dissipation produces a good agreement with experimental results when using acceptable values of the internal fluid and membrane viscosities. In addition, this study proposes a direct inference of the value of the membrane viscosity as a function of the shear rate from the comparison between simulations and experiments and confirms experimental results that highlighted the shear-thinning behavior of the red blood cell membrane.

We perform numerical simulations to examine settling and fluid transport by a pair of particles passing through a thin density interface of a two-layer fluid. As the particles settle through the interface, they deform the interface and carry upper layer fluid into the lower layer. This increased buoyancy hinders the particle settling such that the trailing particle collides with the leading particle at strong stratification and when the particles are nearly vertically aligned. When descending into the lower layer, the upper layer fluid detaches from the particles, returning upward within a wake whose width is on the order of two particle diameters. Due to the added buoyancy and the returning wake, particle settling is hindered and the trailing particle separates away from the leading particle when aligned within or near the wake of the leading particle. Meanwhile, the trailing particle re-entrains fluid detached from the leading particle. Consequently, the transport of upper layer fluid into the lower layer increased by up to 40% in the case of weak stratification.

We present an experimental study on the settling velocity of dense sub-Kolmogorov particles in active-grid-generated turbulence in a wind tunnel. Using phase Doppler interferometry, we observe that the modifications of the settling velocity of inertial particles, under homogeneous isotropic turbulence and dilute conditions [i.e., small liquid fraction ${\varphi }_v\le O{\left(10\right)}^{-5}$], is controlled by the Taylor-Reynolds number ${\text{Re}}_{\lambda }$ of the carrier flow. Meanwhile, we did not find a strong influence of the ratio between the fluid and gravity accelerations on the particle settling behavior. Remarkably, we find that that the degree of hindering experienced by the particles (i.e., the measured particle settling velocity is smaller in magnitude than its respective one in still fluid conditions) increases with ${\text{Re}}_{\lambda }$. This observation is contrary to previous works at intermediate values of ${\text{Re}}_{\lambda }$ that report the opposite effect: settling enhancement. Nonetheless, our trend is observed at all particle sizes investigated, and when previous experimental data is included into the analysis, our data suggest that the particle settling behavior may be nonmonotonic with ${\text{Re}}_{\lambda }$: inducing enhancement at moderate values of ${\text{Re}}_{\lambda }$, and at promoting hindering at higher values of ${\text{Re}}_{\lambda }$. Moreover, at the highest ${\text{Re}}_{\lambda }$ studied, the settling enhancement regime ceases to exist. Finally, we find that the difference between the measured particle settling velocity $\left(V_p\right)$ and the particle terminal velocity in still fluid conditions $\left(V_T\right)$, normalized by the carrier phase rms fluctuations, $(V_p-V_T)/u$ scales linearly with the Rouse number $\text{Ro}=V_T/u$ (i.e., the ratio between the particles settling velocity and the fluid rms fluctuations). However, such behavior $(V_p-V_T)/u\sim -\text{Ro}$ appears only to be valid for moderate values of the Rouse number.