Steady polygonal hydraulic jumps have a complex flow structure and are formed when a circular jump loses stability through an increase in the downstream liquid height beyond a critical value. We report the experimental observation of a universal corner shape in polygonal hydraulic jumps over a wide range of experimental conditions that include the flow rate, weir geometry, and flow history, as defined by the tip radius of curvature and the corner angle. The tip radius of curvature is nearly constant over all experimental conditions, whereas the corner angle weakly depends on gravitational effects. Knowledge of the corner angle allows one to determine the global jump shape, as defined by a dimensionless geometry number related to the isoperimetric inequality, thus giving a complete description of the jump shape.

Locomotion of biological and artificial microswimmers has received considerable attention due to its fundamental biological relevance and promising biomedical applications such as drug delivery and microsurgery. Purcell's well-known discussion on “Life at Low Reynolds Number” [Am. J. Phys. 45, 3 (1977)] elucidated the stringent fluid dynamical constraints on swimming at the microscopic scale. He also presented the “simplest animal,” now known as Purcell's swimmer, that can swim in the absence of inertia, which has now become a useful model for exploring different fundamental aspects of microscopic locomotion. While extensive studies have improved our understanding of locomotion in Newtonian fluids, microswimmers often encounter biological fluids that display complex (non-Newtonian) rheological behaviors, and much less is known about swimming in complex fluids. In this work, we utilize Purcell's swimmer as a model swimmer to probe the impacts of shear-thinning rheology, a ubiquitous non-Newtonian behavior of biological fluids such as blood and mucus, on swimming at low Reynolds numbers. We show how the propulsion characteristics of Purcell's swimmer in a shear-thinning fluid differ from those in a Newtonian fluid in terms of both the magnitude and direction of propulsion, depending on the details of the swimming strokes. The simplicity of Purcell's swimmer allows us to rationalize the results by examining how the shear-thinning effect manifests in different swimming strokes in a cycle. We also demonstrate how unequal arm rotational rates can couple with the shear-thinning effect to induce a net vertical displacement of the swimmer, which is not possible in a Newtonian fluid. These results suggest modulating the arm rotational rates as a way to enable different two-dimensional motions of Purcell's swimmer in a shear-thinning fluid.

Slender objects are commonplace in microscale flow problems, from soft deformable sensors to biological filaments such as flagella and cilia. While much research has focused on the local translational motion of these slender bodies, relatively little attention has been given to local rotation, even though it can be the dominant component of motion. In this study, we explore a classically motivated ansatz for the Stokes flow around a rotating slender body via superposed rotlet singularities, which leads us to pose an alternative ansatz that accounts for both translation and rotation. Through an asymptotic analysis that is supported by numerical examples, we determine the suitability of these flow ansatzes for capturing the fluid velocity at the surface of a slender body, assuming local axisymmetry of the object but allowing the cross-sectional radius to vary with arclength. In addition to formally justifying the presented slender-body ansatzes, this analysis reveals a markedly simple relation between the local angular velocity and the torque exerted on the body, which we term resistive torque theory. Though reminiscent of classical resistive force theories, this local relation is found to be algebraically accurate in the slender-body aspect ratio, even when translation is present, and is valid and required whenever local rotation contributes to the surface velocity at leading asymptotic order.

We present a high-order numerical study of the dependence of the dynamo onset on electromagnetic boundary conditions in convecting Boussinesq flows forced by temperature gradients. Perfectly conducting boundaries, vacuum, and mixed boundary conditions are considered, treating fields and boundary conditions with close to spectral accuracy. Having one or two conducting boundaries greatly facilitates dynamo action. For the mixed case it is shown that the critical magnetic Reynolds number becomes independent of the Rayleigh number Ra for sufficiently large Ra.

When carbon dioxide (${\mathrm{CO}}_2$) is layered on top of brine, the diffusion occurring at the interface generates an intermediate layer denser than the brine one. This may generate a convective process that accelerates ${\mathrm{CO}}_2$ dissolution into the brine. Here, we use the shadowgraph method and a sample cell geometry with a large width/height aspect ratio to investigate the 3D behavior of the convective dissolution of ${\mathrm{CO}}_2$ in brine in a free medium. This process is driven by the instability of the denser boundary layer formed at the interface between the two phases and is totally independent of the overall vertical size. When the purely diffusive mass transfer get disrupted, we observe the development of complex 3D structures, consisting of ${\mathrm{CO}}_2$-rich falling sheets at the liquid-liquid interface. This pattern could not be detected in 2D Hele-Shaw studies, mainly used in the literature. The experiments have been performed over a broad range of ${\mathrm{CO}}_2$ pressures, close to the process-relevant conditions, and show that the convective mass transfer is governed by the critical thickness of the mixing layer at the onset of convection, and that the process can be described by a scale-free universal model.

Thermal plumes arising from localized buoyancy sources are very common in nature and industrial settings. They have been extensively studied experimentally, theoretically, and numerically, mostly focusing on entrainment and mixing processes in fully developed turbulent regimes. Here, we focus on the primary instabilities of laminar plumes and their transitions as the strength of the buoyancy source (quantified by a Rayleigh number) is increased. Numerous prior studies in this transitional regime have reported a myriad of disparate spatiotemporal plume characteristics. We show that this wide variety of behavior is tied to the various ways an $O\left(2\right)$ axisymmetric system can undergo symmetry breaking. Our equivariant dynamical systems theory analyzing the breaking of $O\left(2\right)$ symmetry accounts for the spatiotemporal characteristics of the plumes we compute solving the Navier–Stokes–Boussinesq equations. We find that the nature of the ambient stratification plays an important role in determining how $O\left(2\right)$ symmetry is broken with increasing Rayleigh number, and this in turn determines the details of the plume spatiotemporal characteristics.

We have performed direct numerical simulations for the flow past a streamwise and transversely rotating sphere at a Reynolds number $\mathrm{Re}=500$. To investigate the effect of low to very high rotation rates on the flow dynamics, we have varied the dimensionless streamwise $\left({\mathrm{\Omega }}_x\right)$ and transverse $\left({\mathrm{\Omega }}_z\right)$ rotation rates between 0.5 and 5. The streamwise rotation of the sphere causes twisting of the vortex structures in the wake and results in centrifugal instabilities. The wake consists of two intertwined spiral vortices at ${\mathrm{\Omega }}_x=0.5$, whereas the vortex structures form threads and bifurcate into large-scale shear layers for ${\mathrm{\Omega }}_x\ge 2$. The shedding pattern during the transverse rotation is subject to turning. The structures at the aiding side of the motion experience tearing, whereas they squeeze at the opposing side. We found single-sided shedding of the hairpin structure at ${\mathrm{\Omega }}_z=0.5$. The wake deforms into numerous small-scale vortex filaments for ${\mathrm{\Omega }}_x=2$, whereas it becomes complex, constituting stretched hairpins at ${\mathrm{\Omega }}_x=5$. During the rotation cycle of the sphere, the wake shows steady flow at ${\mathrm{\Omega }}_x=0.5$. In contrast, at ${\mathrm{\Omega }}_z=0.5$, we found one-sided shedding of hairpin vortices in the near wake, which becomes ringlike vortices in the far wake. The wake at ${\mathrm{\Omega }}_z=2$ forms randomly oriented vorticity patches, which cannot cope with the sphere's rotation, thereby retaining their shape and orientation during the rotation cycle. The line-time reconstruction of vertical velocity signals shows discontinuity in vortex formation for higher ${\mathrm{\Omega }}_{x,z}$. We have formulated a method for tracking the trajectories of the vortices. In the near wake at ${\mathrm{\Omega }}_x=0.5$, the vortex trajectories move in a circular path, whereas it settles at a larger radius in the far wake. We observe that for ${\mathrm{\Omega }}_x\ge 2$, the local rotation center of the near-wake vortices cannot cope with high rotational speeds, and the fluid particles partially obey the effects of solid-body rotation. A higher degree of mixing of the fluid particles in the near wake at ${\mathrm{\Omega }}_x=5$ decreases the localized rotation of the vortex trajectories, and the vortex centers settle along the radial lines in the far wake. We found the symmetric distribution of the vortex trajectories at all transverse planes during ${\mathrm{\Omega }}_z$ rotation. Our results indicate that a rotating sphere always experiences a positive drag irrespective of the rotational direction. The time average normalized angular velocity of the vortices at various transverse planes reveals that the near wake vortices could cope with the sphere's rotation for ${\mathrm{\Omega }}_x=0.5$. However, it decays marginally for ${\mathrm{\Omega }}_x=2$. In contrast, most of the rotational speed is lost for ${\mathrm{\Omega }}_x=5$. We have calculated the penetration depth as the downstream length for which $10\%$ of the sphere's angular speed is preserved by the downstream vortices, which reveals rapid reduction for increasing ${\mathrm{\Omega }}_x$. At various downstream locations, the normalized angular frequency of the vortices renders the asynchronous rotation of the vortex structures. We found a minimal impact of ${\mathrm{\Omega }}_z$ on the rotation of the downstream vortices. However, the wake fluctuations are triggered with increasing rotation rate, although fluctuations are lesser for ${\mathrm{\Omega }}_z$ rotation. The near wake vortices reveal low-frequency rotation for all ${\mathrm{\Omega }}_z$, and the asynchronous motion of the vortices triggers its asynchronicity for increasing ${\mathrm{\Omega }}_z$.

The Pi Chamber generates moist turbulent Rayleigh-Bénard flow in order to replicate steady-state cloud conditions. We take inspiration from this setup and consider a particle-laden, convectively driven turbulent flow using direct numerical simulation. The aim of our paper is to develop a simple stochastic model that can accurately describe the residence times of the particles in the flow, this time being determined by the complex competition between the gravitational settling of the particles, and the interaction of the particles with the turbulent structures in the flow. A simple conceptual picture underlies the stochastic model, namely that the particles take repeated trips between the top and bottom boundaries, driven by the convective cells that occur in Rayleigh-Bénard turbulence, and that their residence times are determined by the time it takes to complete one of these trips, which varies from one trip to another, and the probability of falling out to the bottom boundary after each trip. Despite the simplicity of the model, it yields quantitatively accurate predictions of the distribution of the particle residence times in the flow. We independently vary the Stokes numbers and settling velocities in order to shed light on the independent roles that gravity and inertia play in governing these residence times.

We show the impact that scalar structure deformation and mixing have on the fate of plumes of waterborne contaminant transported through a chemically heterogeneous, partially adsorbing porous medium at a typical Péclet number characterizing saturated flows in subsurfaces, $\text{Pe}=O\left(1\right)$. Via pore-scale lattice Boltzmann simulations, we follow the dynamic of a passive scalar injected in a packed bed consisting of a mixture of chemically inert and adsorbing spherical particles. By varying the fraction of adsorbers $\xi$ randomly and uniformly distributed in the porous volume, we find that the waterborne solute forms concentration plumes emerging between pairs of adsorbing particles. This deformation is a consequence of the different mechanisms of transport characterizing the transport of molecules in the proximal and remote pores relative to the adsorbers, diffusion and advection, respectively. The resulting isoscalar surface embedding the plumes grows at a rate proportional to the average pore-scale velocity $U$ and inversely proportional to the adsorbers' interparticle dimensionless distance, i.e., $\gamma \propto U/{\ell }_{\xi }$. We provide a quantification of the characteristic diffusive timescale of the plume $t_{\eta }\propto {\ell }_{\xi }^2/D_m$, which dissipates the concentration differences in the vicinity of the adsorbers, with $D_m$ being the molecular diffusion coefficient. Thus, by quantifying the relative importance of the advection-sustained stretching rate $\gamma$ and plume mixing rate $1/t_{\eta }$ for different values of fractions of adsorbers $\xi$, we establish a transition from diffusion- to advection-dominated macroscopic adsorption, whose time evolutions scale as $\propto \sqrt{t}$ and $\propto t$, respectively. Such a transition is determined by the number of adsorbers within the medium, with diffusion and advection dominating at high and low fractions, respectively. Our numerical analysis provides ${\ell }_{\xi }/d\approx 4/ln\left(2\right){\text{Pe}}^{-1}$ as the critical distance between adsorbers that sets the transition, with $d$ being the pore size.

High-resolution wind detection plays a crucial role in aviation safety and aerodynamic research. A pulsed coherent Doppler wind lidar (CDWL) with sub-meter/sub-second resolution is demonstrated. The pseudorandom modulation (PRM) method is used to break the link between laser pulse duration and spatial resolution. Benefiting from the flexible pulse duration, the detection accuracy degradation related to the short pulse is largely mitigated. The backscattered spectra and wind profiles measured by the proposed lidar are compared with those obtained by a conventional pulsed CDWL, validating its capacity of radial wind detection within 700 m at 0.9 m/0.5 s resolution. With the help of the proposed high-resolution lidar, the meter-scale perturbation on the wind field from an electric fan is detected in a field experiment.

We demonstrate that, as in the forward cascade of three-dimensional turbulence that displays intermittency (a lack of self-similarity) due to the concentration of energy dissipation in a small set of fractal dimension less than three, the inverse cascade of two-dimensional turbulence can also display a lack of self-similarity and intermittency if the energy injection is constrained in a fractal set of dimension less than two. A series of numerical simulations of two-dimensional turbulence are examined, using different forcing functions of the same forcing length scale but different fractal dimension $D$ that varies from the classical $D=2$ case to the point vortex case $D=0$. It is shown that as the fractal dimension of the forcing is decreased from $D=2$, the self-similarity is lost and intermittency appears. The present model thus provides a unique example that intermittency is controlled and can thus shed light and provide test beds for multifractal models of turbulence.

Aggregation and disaggregation of clusters of attractive particles under flow are studied from numerical and theoretical points of view. Two-dimensional molecular dynamics simulations of both Couette and Poiseuille flows highlight the growth of the average steady-state cluster size as a power law of the adhesion number, a dimensionless number that quantifies the ratio of attractive forces to shear stress. Such a power-law scaling results from the competition between aggregation and disaggregation processes, as already reported in the literature. Here we rationalize this behavior through a model based on an energy function, which minimization yields the power-law exponent in terms of the cluster fractal dimension, in good agreement with the present simulations and with previous works.

We describe the shape of moderately flexible fibers settling under inertial conditions in dilute and semidilute suspension and examine the hydrodynamic forces on the fibers that create different fiber shapes. The analysis is based on numerical simulations, using an immersed boundary method, to couple the motion of the fibers to the fluid dynamics. The direct numerical simulation results show that while fiber curvature can have a nonmonotonic dependence on fiber concentration, fiber torsion monotonically increases with increasing the concentration of fibers. Based on the concept of splitting the total forces into a mean and a stochastic part, we propose a reduced-order, stochastic model that can, with a reasonable accuracy, model the three-dimensional fiber shapes at different fiber concentrations, flexibility, and inertia. This model also helps us understand how random hydrodynamic fluctuations and fluid-mediated forces due to the presence of neighboring fibers contribute to the total forces on the fibers and fiber shapes.

We use the mean-bacterial-velocity model to investigate the irreversibility of two-dimensional (2D) bacterial turbulence and to compare it with its 2D fluid-turbulence counterpart. We carry out extensive direct numerical simulations of Lagrangian tracer particles that are advected by the velocity field in this model. We demonstrate how the statistical properties of these particles help us to uncover an important, qualitative way in which irreversibility in bacterial turbulence is different from its fluid-turbulence counterpart: For large but negative (or large and positive) values of the activity (or friction) parameter, the probability distribution functions of energy increments, along tracer trajectories, or the power are positively skewed; so irreversibility in bacterial turbulence can lead, on average, to particles gaining energy faster than they lose it, which is the exact opposite of what is observed for tracers in 2D fluid turbulence.

A granular raft—a two-dimensional (2D) particle layer floating at a fluid-fluid interface—collapses when losing its stability under compression. Although granular rafts are frequently encountered in various natural and engineering settings, how a raft fails under compression is still an open question. Here, by combining experiments with theoretical modeling, we examine the failure modes of granular rafts without free periphery under quasistatic biaxial compression. Different from granular rafts with open periphery, granular rafts in our study remain stable under finite compressive stresses. More surprisingly, under large compression, granular rafts made of small particles sink gradually by expelling individual particles, whereas rafts of large particles collapse catastrophically by forming large-scale creases. The collective creasing is enhanced by the 2D particle density and is suppressed by the density difference of the two fluids. We develop a one-dimensional continuum model for the shape of the granular rafts and the concentration of particles along the fluid-fluid interface, which provides quantitative explanations of our experimental findings.

With the availability of new high-Reynolds-number ($Re$) databases of turbulent boundary layers (TBLs) it has been possible to identify in detail certain regions of the boundary layer with more complex behavior. In this study we consider a unique database at moderately-high $Re$, with a nearconstant adverse pressure gradient (APG) [Pozuelo et al., J. Fluid Mech. 939, A34 (2022)], and perform spectral analysis of the Reynolds stresses, focusing on the streamwise component. We assess different regions of the APG TBL, comparing this case with the zero-pressure-gradient (ZPG) TBL, and identify the relevant scaling parameters as well as the contribution of the scales of different sizes. The small scales in the near-wall region up to the near-wall spectral peak have been found to scale using viscous units. In APG TBLs, the largest scales close to the wall have a better scaling with the boundary-layer thickness (${\delta }_{99}$), and they are significantly affected by the APG. In the overlap and wake regions of the boundary layer, the small energetic scales exhibit a good scaling with the displacement thickness (${\delta }^{*}$) while the larger scales and the outer spectral peak are better scaled with the boundary-layer thickness. Also, note that the wall-normal location of the spectral outer peak scales with the displacement thickness rather than the boundary layer thickness. The various scalings exhibited by the spectra in APG TBLs are reported here, and shed light on the complex phenomena present in these flows of great scientific and technological importance.

The time-dependent oscillating convection leading to the formation of reverse flowing cells is a special phenomenon induced by viscoelasticity in the Rayleigh-Bénard convection (RBC). The causes and the evolution of this overstability problem have not yet been investigated in-depth. Numerical simulations of the viscoelastic Rayleigh-Bénard convection (VRBC) have been conducted in this work with viscoelastic working fluids abiding by the nonlinear Phan-Thien-Tanner (PTT) constitutive structure in two-dimensional cavities. To understand the impact of the nonlinearity and the rheological parameters on the mechanism of the regular reverse flow numerical simulations have been performed over the range of $\beta =(0.1,0.2)$ (where $\beta ={\mu }_s/{\mu }_0$, ${\mu }_s$ is the solvent viscosity, ${\mu }_0={\mu }_s+{\mu }_p$ is sum of solvent viscosity ${\mu }_s$ and polymer viscosity ${\mu }_p$) and Weissenberg number $(We\in [0.075,0.25\left]\right)$, using an in-house finite-difference code. The remaining constitutive parameters of the (PTT) fluid representing elongational and slippage characteristics of the fluid were kept fixed at $\epsilon =0.1$ and $\xi =0.05$, respectively. A viscoelastic kinetic-energy budget method was used to analyze the energy transport in this time-dependent reverse flow process. An original parametric analysis is developed to gain an insight into the dynamics of the reversal flow observed recently in our work, Zheng et al. [Phys. Rev. Fluids 7, 023301 (2022)], as well as observed by Park and Ryu [Rheol. Acta 41, 427 (2002)] and Lappa and Boaro [J. Fluid Mech. 904, A2 (2020)]. The emergence of the reversal convection can be explained by the transfer of potential energy between flow and fluid elasticity during the reversal process. The existence of time phase differences of different potentials in the evolution drive this potential-energy transfers.

This work examines the dynamics of elliptical vortices in two-dimensional ideal fluid using an adaptively refined and remeshed vortex method. Four examples are considered comprising two compact vortices denoted by MMZ (smooth) and POLY (nonsmooth), and two noncompact vortices denoted by Gaussian and smooth Kirchhoff. The vortices all have the same maximum vorticity and 2:1 initial aspect ratio, but unlike the top-hat Kirchhoff vortex, they have continuous profiles with different degrees of regularity. In each case the phase portrait of the vortex in a corotating frame has two hyperbolic points, and the separatrix divides space into four regions, a center containing the vortex core, two crescent-shaped lobes next to the core, and the exterior. As the vortices start to rotate, two spiral filaments emerge and form a halo of low-amplitude vorticity around the core; this is attributed to vorticity advection along the unstable manifolds of the hyperbolic points. In the case of the Gaussian vortex the core rapidly axisymmetrizes, but later it starts to oscillate and two small lobes enclosing weak vortical fluid form within the halo; this is attributed to a resonance stemming from the core oscillation. In the case of the MMZ, POLY, and smooth Kirchhoff vortices, the core remains elliptical for longer time, and the filaments entrain weak vortical fluid into two large lobes which together with the core form a nonaxisymmetric tripole; afterwards, however, the lobes repeatedly detrain some of their fluid into the halo; the repeated detrainment is attributed to a heteroclinic tangle near the hyperbolic points. While prior work suggested that elliptical vortices could evolve to become either an axisymmetric monopole or a nonaxisymmetric tripole, the current results suggest they may oscillate between these states.

Dense suspensions of swimming bacteria exhibit chaotic flow patterns that promote the mixing and transport of resources and signaling chemicals within cell colonies. While the importance of active turbulence is widely recognized, the structure and dynamics of the resulting collective flows are the subject of intense investigation. Here, we combine microfluidic experiments with proper orthogonal decomposition (POD) analysis to quantify the dynamical flow structure of this model active matter system under a variety of conditions. In isotropic quasi-two-dimensional turbulence, the modal analysis encompasses the most energetic spatiotemporal flow structures across a range of suspension activity levels and benchmarks the potential for low-dimensional order representations of active turbulence. In confined geometries, POD analysis illustrates the role of boundary interactions for the transition to bacterial turbulence, and it quantifies the evolution of coherent active structures in externally applied flows. Beyond establishing the physical flow structures underpinning the complex dynamics of bacterial turbulence, the low-dimensional representation afforded by this modal analysis will facilitate data-driven modeling of active turbulence.

Recent literature shows that chiral particles driven by vorticity gradients of a base Newtonian liquid can separate only in nonlinear or nonstationary flows. Here, we show that a base Newtonian liquid endowed with rotational degrees of freedom can give rise to chiral particle propulsion and separation even in the Stokes flow approximation. We consider active mechanisms generating spatially inhomogeneous vorticity in the base liquid in a channel such as a magnetic torque, a pressure gradient, and a sliding wall. These mechanisms generate regions of spatially inhomogeneous vorticity maintained by the internal angular momentum, propelling the chiral particles according to their handedness. Similar conclusions can be reached when one of the channel walls is replaced by a free surface acted on by surface shear. This behavior is in contrast to the case of standard Newtonian liquids where chiral particle propulsion generated by vorticity gradients is not possible in Stokes flow. This effect can find applications in industry, biology, and medicine.