Vorticity Direction Research Articles

The Relations Between Hölder Continuity Assumptions on the Direction of Vorticity and Energy Equality

The Relations Between Hölder Continuity Assumptions on the Direction of Vorticity and Energy Equality

Precise and accurate speed measurements in rapidly flowing dense suspensions

We introduce a method for precise and accurate measurements of particle speeds in dense suspensions flowing at high rates and demonstrate the utility of the approach for revealing complex flow fluctuations during shearing in a setup that combines imaging with a confocal microscope and shearing with a rheometer. We scan the focal point in one dimension, aligned with direction of flow, producing absolute measurements of speed that are independent of suspension structure and particle shape. We compare this flow-direction line scanning approach with a complementary method we introduced previously, measuring speed using line scanning in the vorticity direction. By comparing results in various flow conditions, including shear-thinning and thickening regimes, we demonstrate the efficacy of our new approach. We find that both approaches exhibit qualitatively similar flow profiles, but a comparative analysis reveals a 15%–25% overestimation in speed measurement using vorticity line scanning, with discrepancies generated by anisotropic suspension microstructure under flow. Moreover, in the thickening regime where complex flow fields are present, both approaches capture local speed fluctuations. However, line scanning in the flow direction reveals and precisely captures stagnation and backflows, a capability not achievable with vorticity line scanning. The approach introduced here not only provides a refined technique for speed measurement in fast-flowing suspensions but also emphasizes the significance of accurate measurement techniques in advancing our understanding of flow behavior in dense suspensions, particularly in contexts where strong non-affine flows are prevalent.

Stress and flow inhomogeneity in shear-thickening suspensions

HypothesisThe viscosity of dense suspensions surges when the applied stress surpasses a material-specific critical threshold. There is growing evidence that the thickening transition involves non-uniform flow and stress with considerable spatiotemporal complexity. Nevertheless, it is anticipated that dense suspensions of calcium carbonate particles with purely repulsive interactions may not conform to this scenario, as indicated by local pressure measurements with millimeter spatial resolution. ExperimentHere we utilize Boundary Stress Microscopy (BSM), a technique capable of resolving stresses down to the micron scale, to search for evidence of stress heterogeneity. In addition, we measure the flow field at the lower boundary of the suspension where the boundary stress is measured. FindingsWe find localized regions of high-stresses that are extended in the vorticity direction and propagate in the flow direction at a speed approximately half that of the rheometer's top plate. These high-stress regions proliferate with the applied stress accounting for the increased viscosity. Furthermore, the velocity of particles at the lower boundary of the suspension shows a significant and complex nonaffine flow that accompanies regions of high-stresses. Hence, our findings demonstrate that stress and flow inhomogeneity are intrinsic characteristics of shear-thickening suspensions, regardless of the nature of interparticle interactions.

Scaling law for a buckled elastic filament in a shear flow.

We analyze the three-dimensional (3D) buckling of an elastic filament in a shear flow of a viscous fluid at low Reynolds number and high Péclet number. We apply the Euler-Bernoulli beam (elastica) theoretical model. We show the universal character of the full 3D spectral problem for a small perturbation of a thin filament from a straight position of arbitrary orientation. We use the eigenvalues and eigenfunctions for the linearized elastica equationin the shear plane, found earlier by Liu etal. [Phys. Rev. Fluids 9, 014101 (2024)2469-990X10.1103/PhysRevFluids.9.014101] with the Chebyshev spectral collocation method, to solve the full 3D eigenproblem. We provide a simple analytic approximation of the eigenfunctions, represented as Gaussian wave packets. As the main result of the paper, we derive the square-root dependence of the eigenfunction wave number on the parameter χ[over ̃]=-ηsin2ϕsin^{2}θ, where η is the elastoviscous number and the filament orientation is determined by the zenith angle θ with respect to the vorticity direction and the azimuthal angle ϕ relative to the flow direction. We also compare the eigenfunctions with shapes of slightly buckled elastic filaments with a non-negligible thickness with the same Young's modulus, using the bead model and performing numerical simulations with the precise hydromultipole numerical codes.

Secondary flow characteristics in confluent streams with vegetation

Vegetation commonly exists in river confluences and alters flow structures, affecting the strength and direction of secondary flows. This study investigated the impact of vegetation on the secondary flow structures of a confluence by measuring three-dimensional instantaneous velocities under different vegetative conditions. By utilizing downstream and horizontal flow velocity characteristics, a secondary flow coefficient concept was introduced to describe secondary flow vorticity directions and strengths. The influence of vegetation was assessed in the context of Reynolds stress, the relative strength of secondary flows, and the direction of secondary flow vorticities to clarify the mechanisms by which vegetation affects secondary flows. The findings reveal opposing vertical forces in the confluent section due to incoming tributary flows, resulting in secondary flow generation. Vegetation redistributes cross-sectional water energy, increasing energy convergence within vegetated areas. This amplifies secondary flow strengths and alters vorticity directions. The impact of vegetation on secondary flows is evident in the increase in rotational intensity. Considering various factors, such as the confluence ratio, flow velocity, and distance from the confluence, is crucial, as the influence of vegetation on flows is multifaceted.

The Spatial Variation of Large‐ and Meso‐Scale Plasma Flow Vorticity Statistics in the High‐Latitude Ionosphere and Implications for Ionospheric Plasma Flow Models

AbstractThe ability to understand and model ionospheric plasma flow on all spatial scales has important implications for operational space weather models. This study exploits a recently developed method to statistically separate large‐scale and meso‐scale contributions to probability density functions (PDFs) of ionospheric flow vorticity measured by the Super Dual Auroral Radar Network (SuperDARN). The SuperDARN vorticity data are first sub‐divided depending on the Interplanetary Magnetic Field (IMF) direction, and the separation method is applied to PDFs of vorticity compiled in spatial regions of size 1° of geomagnetic latitude by 1 hr of magnetic local time, covering much of the high‐latitude ionosphere in the northern hemisphere. The resulting PDFs are fit by model functions using maximum likelihood estimation (MLE) and the spatial variations of the MLE estimators for both the large‐scale and meso‐scale components are presented. The spatial variations of the large‐scale vorticity estimators are ordered by the average ionospheric convection flow, which is highly dependent on the IMF direction. The spatial variations of the meso‐scale vorticity estimators appear independent of the senses of vorticity and IMF direction, but have a different character in the polar cap, the cusp, the auroral region, and the sub‐auroral region. The paper concludes by discussing the sources of the vorticity components in the different regions, and the consequences for the fidelity of ionospheric plasma flow models.

Highly elastic fibers in a shear flow can form double helices

The long-time behavior of highly elastic fibers in a shear flow is investigated experimentally and numerically. Characteristic attractors of the dynamics are found. It is shown that for a small ratio of bending to hydrodynamic forces, most fibers form a spinning elongated double helix, performing an effective Jeffery orbit very close to the vorticity direction. Recognition of these oriented shapes, and how they form in time, may prove useful in the future for understanding the time history of complex microstructures in fluid flows and considering processing steps for their synthesis.

Optical momentum distributions in monochromatic, isotropic random vector fields

Abstract We investigate the decomposition of the electromagnetic Poynting momentum density in three-dimensional random monochromatic fields into orbital and spin parts, using analytical and numerical methods. In sharp contrast with the paraxial case, the orbital and spin momenta in isotropic random fields are found to be identically distributed in magnitude, increasing the discrepancy between the Poynting and orbital pictures of energy flow. Spatial correlation functions reveal differences in the generic organization of the optical momenta in complex natural light fields, with the orbital current typically forming broad channels of unidirectional flow, and the spin current manifesting larger vorticity and changing direction over subwavelength distances. These results are extended to random fields with pure helicity, in relation to the inclusion of electric-magnetic democracy in the definition of optical momenta.

Geometric regularity criteria for the Navier–Stokes equations in terms of velocity direction

In this paper, we are inspired by a famous result by Constantin and Fefferman who proved that a simple geometrical assumption on the direction of the vorticity leads to the regularity of weak solutions of the 3D Navier–Stokes equations. We show that the same result can be achieved if the vorticity direction is replaced by the velocity direction. We further strengthen this result and prove that in fact it is not necessary to consider the velocity direction in all close space points but only in the points whose distance equals to a small positive number dependant on the data. In the second part of the paper, we extend a result by Berselli and C rdoba concerning the role of the helicity for the regularity of the weak solutions of the Navier–Stokes equations.

A Study of the Relationship between Dipole Noise Sources and the Flow Field Parameters around the Rearview Mirror of Passenger Cars

When air flows through the mirrors, A-pillars, and other surfaces of a passenger car, airflow separation occurs to generate vorticity and generates aerodynamic noise. The dipole noise source is the main source of aerodynamic noise when the passenger car is travelling at high speed. In order to reveal the relationship between the physical quantities in the flow field and the intensity of the dipole noise source, this paper equates each dipole noise source to a sphere radiating noise to the outside. The acoustic wave fluctuation equations expressed as spherical coordinates are combined with the acoustic boundary conditions and the equations of motion of an ideal fluid medium to obtain the relationship between the intensity of the dipole noise source and the flow velocity and vorticity in the flow field. Then, through flow field simulation, we establish a method of identifying the dipole noise source and its distribution area, and analyze the generation mechanism of the dipole noise source. Through the analysis, it is concluded that the dipole noise sources are mainly concentrated in the airflow separation areas, which easily generate vortices. The size of the vorticity is the key factor affecting the intensity of the dipole noise source. When the intensity of the dipole noise source reaches its peak, the direction of the flow vorticity is perpendicular to the direction of the flow velocity and the peak of the flow velocity occurs before the peak of the dipole noise source, which indicates that the angle between the flow vorticity and the flow velocity, as well as the flow velocity, also has a certain effect on the generation of the dipole noise source.

Study on the Suppression Effect on Vortex-Induced Vibration of Double-Deck Truss Girder by the Spatial Position of the Deflector Plate

This paper carried out wind tunnel tests and numerical analysis to study the effect of the spatial position of deflector plates on the vortex-induced vibration (VIV) of a double-deck truss girder. The wind tunnel tests found that setting the web deflector plate and the lower chord deflector plate significantly suppressed the VIV. In order to study the suppression mechanism of the deflector plate on VIV, numerical simulations were conducted using the computational fluid dynamics (CFD) method. We analyzed the suppression mechanism of the deflector plate on VIV by combining the vertical amplitude obtained by numerical simulation with the change in the vorticity magnitude and direction. The results showed that the flow velocity around the lower surface of the airflow was reduced, resulting in significantly lower vorticity at the exact position of the lower chord deflector plate and web deflector plate section compared to the original section. The web deflector plate and the lower chord deflector plate broke the vortex shedding mode in the wake flow region, and the vortex shedding frequency was far away from the self-oscillation frequency of the double-deck truss girder, thus suppressing the VIV.

Morphology of Anisotropic Banded Structures in an Emulsion under Simple Shear

The formation of flow-induced, oriented structures in two-phase systems, as in this study, is a phenomenon of considerable interest to the scientific and industrial sectors. The main difficulty in understanding the formation of bands of droplets is the simultaneous interplay of physicochemical, hydrodynamic, and mechanical effects. Additionally, banded structure materials frequently show multiple length scales covering several decades as a result of complex time-dependent stress fields. Here, to facilitate understanding a subset of these structures, we studied water in oil emulsions and focused on the effects of three variables specifically: the confinement factor (Co=2R/H), the viscosity ratio (p), and the applied shear rate (γ˙). The confinement (Co) is the ratio between the drop’s diameter (2R) and the separation of (the gap between) the circular rotating disks (H) containing the emulsion. We carried out (a) observations of the induced structure under different simple shear rates, as well as (b) statistical and morphological analysis of these bands. At low shear rates, the system self-assembles into bands along the direction of the flow and stacked normal to the velocity gradient direction. At higher shear rates is possible to observe bands normal to the vorticity direction. Here, we show that a detailed analysis of the dynamics of the band structures is amenable, as well as measurements of flow field anomalies simultaneously observed. The local emulsion viscosity varies in time, increasing in regions of higher droplet concentration and subsequently inducing velocity components perpendicular to the main flow direction. Thus, the emulsion morphology evolves and changes macroscopically. A relatively plausible explanation is attributed to the competitive effects of coalescence and the rupture of drops, where p values less than one predominate coalescence.

On the vorticity direction and the regularity of 3D Navier–Stokes equations

This short paper presents a simplified and alternative proof of the regularity of weak solutions to the 3D Navier–Stokes equations with ‘sufficiently small’ jumps in the vorticity direction. Although the main result is very similar to a previously proven one, there are some relevant differences. Specifically, we prove that the smallness condition regarding the angle spanned by the vorticity direction needs to be checked, for each point x in the domain, only over a discrete set of surrounding points. These points lie in the direction of the coordinate axes and have a fixed positive distance from x. This is achieved by using a more direct approach which does not rely on the use of singular integrals theory, but which requires estimates on higher-order derivatives of the velocity.

Learning to swim efficiently in a nonuniform flow field.

Microswimmers can acquire information on the surrounding fluid by sensing mechanical queues. They can then navigate in response to these signals. We analyze this navigation by combining deep reinforcement learning with direct numerical simulations to resolve the hydrodynamics. We study how local and nonlocal information can be used to train a swimmer to achieve particular swimming tasks in a nonuniform flow field, in particular, a zigzag shear flow. The swimming tasks are (1) learning how to swim in the vorticity direction, (2) learning how to swim in the shear-gradient direction, and (3) learning how to swim in the shear-flow direction. We find that access to laboratory frame information on the swimmer's instantaneous orientation is all that is required in order to reach the optimal policy for tasks (1) and (2). However, information on both the translational and rotational velocities seems to be required to accomplish task (3). Inspired by biological microorganisms, we also consider the case where the swimmers sense local information, i.e., surface hydrodynamic forces, together with a signal direction. This might correspond to gravity or, for microorganisms with light sensors, a light source. In this case, we show that the swimmer can reach a comparable level of performance to that of a swimmer with access to laboratory frame variables. We also analyze the role of different swimming modes, i.e., pusher, puller, and neutral.

A study on the dynamic characteristics of surface suction vortices in an open inlet pool

The surface suction vortices in the open pump intakes were systematically investigated by using numerical and experimental methods. A 3D open inlet pool model has been applied to numerically simulate the flow pattern in the sump based on the shear stress transfer k–ω model, and the volume of fluid method was used to analyze flow fluctuations in the free surface in order to capture and identify the developing status and the evolution process of surface suction vortices as well. The results show that the surface suction vortices easily occur at large flow rates, and the suction ability of these vortices has a positive linear relationship with the flow rate, submerged depth, and the Froude constant. Moreover, it can be observed that the extended direction of the dynamic vorticity is determined by the vortex component along the Z axis (ωz), which played a major role in the stretching effect during the vortex deformation.

Potential Vorticity Generation in Breaking Gravity Waves

Potential vorticity (PV) is an important quantity in stratified flows because it is conserved following the flow in the absence of forcing and viscous and diffusive effects. However, as shown by previous work for unstratified turbulence, viscosity and diffusion, when present, are not purely dissipative and can create potential vorticity even when none is present initially. In this work, we use direct numerical simulations to investigate the viscous and diffusive generation of potential vorticity and potential enstrophy (integrated square PV) in stratified turbulence. Simulations are initialized with a two-dimensional standing internal gravity wave, which has no potential vorticity apart from some low-level random noise; as a result, all potential vorticity and enstrophy comes from viscous and diffusive effects. Significant potential enstrophy is found when the standing wave breaks, and the maximum potential enstrophy increases with increasing Reynolds number. The mechanism for the initial PV generation is spanwise diffusion of buoyancy perturbations, which grow as the standing wave three-dimensionalizes, into the direction of spanwise vorticity. The viscous and diffusive terms responsible are small-scale and are sensitive to under-resolution, so high resolution is required to obtain robust results.

Shear rheology of a dilute suspension of thin rings

The rheology of suspensions of rings (tori) rotating in an unbounded low Reynolds number simple shear flow is calculated using numerical simulations at dilute particle number densities ( n ≪ 1 ). Suspensions of non-Brownian rings are studied by computing pair interactions that include hydrodynamic interactions modeled using slender body theory and particle collisions modeled using a short-range repulsive force. Particle contact and hydrodynamic interactions were found to have comparable influences on the steady-state Jeffery orbit distribution. The average tilt of the ring away from the flow-vorticity plane increased during pairwise interactions compared to the tilt associated with Jeffery rotation and the steady-state orbit distribution. Particle stresses associated with the increased tilt during the interaction were found to be comparable to the stresses induced directly by particle contact forces and the hydrodynamic velocity disturbances of other particles. The hydrodynamic diffusivity coefficients in the gradient and vorticity directions were also obtained and were found to be two orders of magnitude larger than the corresponding values in fiber suspensions at the same particle concentrations. Rotary Brownian dynamics simulations of isolated Brownian rings were used to understand the shear rate dependence of suspension rheology. The orbit distribution observed in the regime of weak Brownian motion, P e ≫ ϕ T − 3, was surprisingly similar to that obtained from pairwise interaction calculations of non-Brownian rings. Here, the Peclet number P e is the ratio of the shear rate and the rotary diffusivity of the particle and ϕ T is the effective inverse-aspect ratio of the particle (approximately equal to 2 π times the inverse of its non-dimensional Jeffery time period). Thus, the rheology results obtained from pairwise interactions should retain accuracy even for weakly Brownian rings ( n ≪ 1 and ϕ T − 3 ≪ P e ).

Single-orientation colloidal crystals from capillary-action-induced shear.

We study the crystallization of colloidal dispersions under capillary-action-induced shear as the dispersion is drawn into flat walled capillaries. Using confocal microscopy and small angle x-ray scattering, we find that the shear near the capillary walls influences the crystallization to result in large random hexagonal close-packed (RHCP) crystals with long-range orientational order over tens of thousands of colloidal particles. We investigate the crystallization mechanism and find partial crystallization under shear, initiating with hexagonal planes at the capillary walls, where shear is highest, followed by epitaxial crystal growth from these hexagonal layers after the shear is stopped. We then characterize the three-dimensional crystal structure finding that the shear-induced crystallization leads to larger particle separations parallel to the shear and vorticity directions as compared to the equilibrium RHCP structure. Confocal microscopy reveals that competing shear directions, where the capillary walls meet at a corner, create differently oriented hexagonal planes of particles. The single-orientation RHCP colloidal crystals remain stable after formation and are produced without the need of complex shear cell arrangements.

Vortex Pinning in Neutron Stars, Slipstick Dynamics, and the Origin of Spin Glitches

We study pinning and unpinning of superfluid vortices in the inner crust of a neutron star using three-dimensional dynamical simulations. Strong pinning occurs for certain lattice orientations of an idealized, body-centered-cubic lattice and occurs generally in an amorphous or impure nuclear lattice. The pinning force per unit length is ∼1016 dyn cm−1 for a vortex–nucleus interaction that is repulsive and ∼1017 dyn cm−1 for an attractive interaction. The pinning force is strong enough to account for observed spin jumps (glitches). Vortices forced through the lattice move with a slipstick character; for a range of superfluid velocities, the vortex can be in either a cold, pinned state or a hot, unpinned state, with strong excitation of Kelvin waves on the vortex. This two-state nature of vortex motion sets the stage for large-scale vortex movement that creates an observable spin glitch. We argue that the vortex array is likely to become tangled as a result of repeated unpinnings and repinnings. We conjecture that during a glitch, the Kelvin-wave excitation spreads rapidly along the direction of the mean superfluid vorticity and slower in the direction perpendicular to it, akin to an anisotropic deflagration.

Migration of non-Brownian particles localized inside sheared droplets

• Particles inside sheared droplets migrate along the vorticity direction. • The migration direction depends on the viscosity ratio. • The migration kinetics depends on Ca, interfacial tension and particle concentration. • VOF simulations provide velocity and shear rate distribution in a particle-free droplet. • Shear-induced migration plays a major role. The migration of non-Brownian particles inside a droplet subjected to shear flow is investigated. The viscosity ratio, particle concentration, particle to droplet size ratio and capillary number are systematically varied. It was observed that particles migrate in the vorticity direction either towards or away from the equatorial plane. The main factor determining the migration direction is the viscosity ratio. The particle concentration and applied capillary number have no influence on the equilibrium distribution and only affect the time necessary to reach this distribution. In order to identify the flow profile, both velocity and shear rate magnitudes to which the particles inside the droplet are subjected, are numerically simulated using the Volume-of-Fluid method in a particle-free droplet/matrix system. The numerical predictions of the flow are used to evaluate the presence of possible driving mechanisms for cross-streamline particle motion, such as particle inertia and shear rate gradients. Depending on the conditions, the simulations reveal significant differences in the streamline profiles and shear rate gradients within the droplet. The observed steady state particle distributions can partially be explained by shear-induced migration towards zones of low shear rates and/or low streamline curvature. However, in complex flows, such as inside a deformed droplet, different migration mechanisms can occur simultaneously. Hence, confinement inside the droplet and potential secondary flows may also play a role.