Finite Vorticity Research Articles

Stabilized equal lower-order finite element methods for simulating Brinkman equations in porous media

This paper demonstrates the mixed formulation of the Brinkman problem using linear equal-order finite element methods in porous media modelling. We introduce Galerkin least-squares (GLS) and least-squares (LS) finite element methods to address the incompatibility of finite element spaces, treating velocity, pressure, and vorticity as independent variables. Theoretical analysis examines coercivity and continuity, providing error estimates. Demonstrating resilience in theoretical findings, these methods achieve optimal convergence rates in the L 2 norm by incorporating stabilization terms with low-order basis functions. Numerical experiments validate theoretical predictions, showing the effectiveness of the GLS method and addressing finite element space incompatibility. Additionally, the GLS method exhibits promising capabilities in handling the Brinkman equation at low permeability compared to the LS method. The study reveals an increase in the average pressure difference in the Brinkman problem compared to the Stokes equations as the inlet velocity rises, providing insights into the behaviour of Brinkman equations.

Stagnation Points Beneath Rotational Solitary Waves in Gravity-Capillary Flows

Stagnation points beneath solitary gravity-capillary waves in the weakly nonlinear weakly dispersive regime in a sheared channel with finite depth and constant vorticity are investigated. A Korteweg-de Vries equation that incorporates the surface tension and the vorticity effects is obtained asymptotically from the full Euler equations. The velocity field in the bulk fluid is approximated which allow us to compute stagnation points in the solitary wave moving frame. We show that stagnation points bellow the crest of elevation solitary waves exist for large values of the vorticity and Bond numbers less than a critical value that depends on the vorticity. Remarkably, the positions of these stagnation points do not depend on the surface tension. Besides, we show that when there are two stagnation points located at the bottom of the channel, they are pulled towards the horizontal coordinate of the solitary wave crest as the Bond number increases until its critical value.

Defect self-propulsion in active nematic films with spatially varying activity.

We study the dynamics of topological defects in active nematic films with spatially varying activity and consider two set-ups: (i) a constant activity gradient and (ii) a sharp jump in activity. A constant gradient of extensile (contractile) activity endows the comet-like +1/2 defect with a finite vorticity that drives the defect to align its nose in the direction of decreasing (increasing) gradient. A constant gradient does not, however, affect the known self-propulsion of the +1/2 defect and has no effect on the -1/2 that remains a non-motile particle. A sharp jump in activity acts like a wall that traps the defects, affecting the translational and rotational motion of both charges. The +1/2 defect slows down as it approaches the interface and the net vorticity tends to reorient the defect polarization so that it becomes perpendicular to the interface. The -1/2 defect acquires a self-propulsion towards the activity interface, while the vorticity-induced active torque tends to align the defect to a preferred orientation. This effective attraction of the negative defects to the wall is consistent with the observation of an accumulation of negative topological charge at both active/passive interfaces and physical boundaries.

Complex flow structures beneath rotational depression solitary waves in gravity-capillary flows

Particle trajectories beneath depression solitary gravity-capillary waves in the weakly nonlinear weakly dispersive regime in a sheared channel with finite depth and constant vorticity are investigated. A fifth-order Korteweg–de Vries equation that incorporates the surface tension and the vorticity effects is derived asymptotically from the full Euler equations when the Bond number is nearly a critical value that depends on the vorticity. The velocity field in the bulk fluid is approximated which allow us to study the submarine structures beneath depression solitary waves. The dynamical system of particle trajectories is reformulated in the moving wave frame and its features are seen through the streamlines. We show that for large values of the vorticity parameter there are always stagnation points in the bulk fluid, which produce rich cat’s-eyes structures. In this case, particle trajectories can undergo vertical excursions, describing closed orbits or undergo pure horizontal transport. Furthermore, bifurcation diagrams according to the number of stagnation points and complex flow structures beneath depression solitary waves with multiple local extrema are shown.

Numerical method for steady ideal 2‐D flows of finite vorticity with applications to vertical‐axis wind turbine aerodynamics

AbstractThis paper presents a new method for approximately modeling 2‐D ideal steady fluid flows with finite vorticity induced by actuator curves of arbitrary shape. An actuator curve is an infinitesimally thin region containing a body force density acting on the flow, while the rest of the flow is force‐free. The approach can be used for any flow satisfying this description, but, like other actuator methods, it is naturally suited for modeling turbines or propellers. We derive a weak formulation of the governing equations in the Lagrange streamfunction and solve it using finite elements. Compared to related methods such as the actuator cylinder (AC) approach, our formulation is uniquely suited for computations involving wake–wake or wake–turbine interactions. We validate the method by computing the flow through a single Darrieus vertical‐axis wind turbine (VAWT) and comparing with previous work. To demonstrate the ability to simulate interacting actuators of arbitrary configuration, we simulate a three‐VAWT array. The turbines are modeled in a freestream, and the loading is chosen to represent ideal airfoils. The standard VAWT results are consistent with previous work, validating the method. The three‐VAWT array demonstrates a higher efficiency than the single VAWT (0.56 vs. 0.52), with differing optmal tip speed ratios for the upwind and downwind turbines (upwind: 3.9, downwind: 3.1. The optimum for a single turbine is 3.6). The flow field of the three‐VAWT array shows expected features such as an acceleration of flow between the two counter‐rotating upwind turbines.

Strain pattern and vorticity analysis in the transpressional Kamandan area within the Sanandaj-Sirjan Metamorphic Belt, Iran

New structural data on radiolarite and quartz mylonite rocks from the well-exposed Kamandan area are presented with the aim to shed light on the quantitative finite strain and vorticity analyses and strain partitioning along the Zagros transpression zone. Duplex structures, imbricate fans, thrust sheets and shear zones are well developed in the Kamandan region, located in the Sanandaj-Sirjan Metamorphic Belt, western Iran. Kinematic shear sense indicators associated with Kamandan shear zone show top-to-the-NE sense of ductile shearing deformation. Integrated quantitative finite strain and kinematic vorticity analyses of deformed rocks indicate deformation pattern and geometry. The strain parameter measurements vis. strain ratios and strain ellipsoid shape (k) show that radiolarite and quartz mylonite rocks have deformed in the constrictional to approximately plane-strain conditions. The quartz mylonite rocks highlight general-shear (sub-simple shear) deformation (Wm = 0.68–0.81) associated with the spatial increase in simple-shear component (47%–60%) from NE to SW. Our results of structural, strain, and vorticity analyses confirm a dextral transpression with strain partitioning into the pure-shear and simple-shear components in the Kamandan shear zone. Estimated Wm-values display the θ angle between the transpressional boundary and the maximum instantaneous strain axis (ISA) is the range from 63 to 69°. Accordingly, the oblique convergence angle (α) between the flow apophyses was estimated at about 35–48° that causes a horizontal shortening of ∼32–42% perpendicular to the boundaries of the Kmandan shear zone.

Chiral vortical effect in extended Rarita-Schwinger field theory and chiral anomaly

We consider the theory of Rarita-Schwinger field interacting with a field with spin 1/2, in the case of finite temperature, chemical potential and vorticity, and calculate the chiral vortical effect for spin 3/2. We have clearly demonstrated the role of interaction with the spin 1/2 field, the contribution of the terms with which to CVE is 6. Since the contribution from the Rarita-Schwinger field is -1, the overall coefficient in CVE is 6-1=5, which corresponds to the recent prediction of a gauge chiral anomaly for spin 3/2. The obtained values for the coefficients $\mu^2$ and $T^2$ are proportional to each other, but not proportional to the spin, which indicates a possible new universality between the temperature-related and the chemical potential-related vortical effects. The results obtained allow us to speculate about the relationship between the gauge and gravitational chiral anomalies.

Kinematic vorticity, finite strain, and deformation thermometry analyses of the exhumed mylonites in the Samen ductile shear zone (Sanandaj-Sirjan Metamorphic Belt, Iran)

Quantitative microstructural investigations involving finite strain and vorticity analyses of quartz-rich mylonites provide significant information regarding the kinematic characteristics of the Samen shear zone (SSZ) within the Sanandaj–Sirjan Metamorphic Belt, Zagros Mountain of Iran. A dominant top-to-the-SE sense shear in the study area is recognized by several kinematic indicators. The results of the finite strain analyses indicate approximately plane strain deformation conditions (Rxz = 2.46–3.53). The mylonitic granitoid rocks record general-shear deformation (Wm = 0.37–0.94) associated with a spatial increase in simple-shear component (23%–78%) from W to E. In the study area, kinematic analyses indicate spatial variations of finite strain, deformation temperature, and the kinematic vorticity numbers resulted in partitioned progressive deformation. These spatial variations reveal an increase of all values towards the Samen thrust sheet. Ductile SSZ developed under greenschist-amphibolite facies metamorphic conditions (464–619 °C), as indicated by the presence of quartz, feldspar, biotite, muscovite, hornblende mineral assemblages, opening angles (OAs) of quartz c-axis fabrics and recrystallization regimes. The dynamic and kinematic characteristics of the study area were generally controlled by ongoing oblique convergence of the Afro-Arabian plate and the Iranian plateau with estimation of a horizontal shortening of ∼20–38% measured perpendicular to the boundaries of the SSZ.

Local spin polarizations in relativistic heavy-ion collisions

Based on a generalized side-jump formalism for massless chiral fermions, which naturally takes into account the spin-orbit coupling in the scattering of two chiral fermions and the chiral vortical effect in a rotating chiral fermion matter, we have developed a covariant and total-angular-momentum-conserved chiral transport model to study both the global and local polarizations of this matter. For a system of massless quarks of random spin orientations and finite vorticity in a box, we have demonstrated that the model can exactly conserve the total angular momentum of the system and dynamically generate the quark spin polarization expected from a thermally equilibrated quark matter. Using this model to study the spin polarization in relativistic heavy-ion collision, we have found that the local quark spin polarizations depend strongly on the reference frame where they are evaluated as a result of the nontrivial axial charge distribution caused by the chiral vortical effect. We have further shown that because of the anomalous orbital or side-jump contribution to the quark spin polarization, the local quark polarizations calculated in the medium rest frame are qualitatively consistent with the local polarizations of Lambda hyperons measured in experiments.

Probing vorticity in heavy ion collision with dilepton production

We study the effect of vorticity present in heavy ion collisions (HICs) on the temperature evolution of hot quark-gluon plasma in the presence of spin-vorticity coupling. The initial global rotation entails a nontrivial dependence of the longitudinal flow velocity on the transverse coordinates and also develops a transverse velocity component that depends upon the longitudinal coordinate. Both of these velocities lead to a 2+1 dimensional expansion of the fireball. It is observed that with finite vorticity and spin-polarization the fireball cools faster as compared to the case without vorticity. Furthermore, we discuss the consequence of this on the production of thermal dileptons.

Transpression tectonics in the eastern Binalud Mountains, northeast Iran; Insight from finite strain analysis, vorticity and 40Ar/39Ar dating

Different tectonic episodes from Late Triassic to recent times in the eastern Binalud Mountains have resulted from convergence and transpression between the Turan and Central Iran plates. Heterogeneous deformation and variable portions of pure and simple shear, demonstrated by finite strain and vorticity analysis in the Mashhad metamorphic rocks, indicate strain partitioning during the first tectonic episode. Modern strain partitioning is characterized by reverse and strike-slip faulting along the Neyshabur fault system and Shandiz fault zone in the southern and northern flanks of the eastern Binalud, respectively. Time-transgressive regional deformation migrated from the hinterland of the belt into the foreland basin, from northeast to the southwest of the mountains. Different generations of deformation resulted in obliteration of the subduction-related accretionary wedge, and growth of an orogenic wedge resulted from collision between the Central Iran and Turan plates.

Nonlinear Electrostatic Waves in PIE and PI Plasmas With Field-Aligned Shear Flow

Nonlinear low-frequency ion acoustic (IA) wave and pair plasma convective cell (PPCC) mode are investigated in pair-ion (PI) plasmas with and without electrons in the presence of sheared flows. IA wave forms both KdV solitons and dipolar vortices in PI-electron plasma, and their amplitude depends upon electron density and sheared flow. But when electron density is too low, the structures disappear, because IA does not exist in pure PI plasma. On the other hand, PPCC mode cannot form pulse-type solitary structures in the pair plasma, while it forms dipolar vortices due to finite vorticity. The nonlinear analysis has been performed assuming the presence of electrons in fullerene PI plasma and limit of zero electron density is also considered for a comparison.

THE NATURE OF DUCTILE DEFORMATION IN THE PHYLLITE-QUARTZITE UNIT (EXTERNAL HELLENIDES)

This work describes the nature of ductile deformation in the Phyllite-Quartzite (PQ) unit in terms of structural evolution and spatial variation of finite strain and vorticity of flow. The PQ unit is affected by at least three ductile deformation (D1, 2, 3) phases. However, the D2 is the dominant phase resulting in the formation of a penetrative foliation (S2) which is by far the most common structural feature in all scales of observation. A stretching lineation (L2), which trends perpendicular to the structural grain of the belt, is well-developed within the S2 plane. Numerous kinematic criteria clearly indicate west (or south)-directed transport of the PQ unit during D2. This phase is also characterized by a systematic non-linear increase of strain ratio (Rxz) with proximity to the Basal thrust. Spatial variation of kinematic vorticity number reveals an increase of pure shear component of D2 deformation towards the middle structural levels of the unit. These results are used to discuss the validity of various geodynamic models related to the exhumation of the PQ unit.

Event-by-event generation of vorticity in heavy-ion collisions

In a noncentral heavy-ion collision, the two colliding nuclei have a finite angular momentum in the direction perpendicular to the reaction plane. After the collision, a fraction of the total angular momentum is retained in the produced hot quark-gluon matter and is manifested in the form of fluid shear. Such fluid shear creates finite flow vorticity. We study some features of such generated vorticity, including its strength, beam energy dependence, centrality dependence, and spatial distribution.

Highlights from STAR heavy ion program

Recent experimental results obtained in STAR experiment at the Relativistic heavy-ion collider (RHIC) with ion beams will be discussed. Investigations of different nuclear collisions in some recent years focus on two main tasks, namely, detail study of quark-gluon matter properties and exploration of the quantum chromodynamics (QCD) phase diagram. Results at top RHIC energy show clearly the collective behavior of heavy quarks in nucleus-nucleus interactions. Jet and heavy hadron measurements lead to new constraints for energy loss models for various flavors. Heavy-ion collisions are unique tool for the study of topological properties of theory as well as the magneto-hydrodynamics of strongly interacting matter. Experimental results obtained for discrete QCD symmetries at finite temperatures confirm indirectly the topologically non-trivial structure of QCD vacuum. Finite global vorticity observed in non-central Au+Au collisions can be considered as important signature for presence of various chiral effects in sQGP. Most results obtained during stage I of the RHIC beam energy scan (BES) program show smooth behavior vs initial energy. However certain results suggest the transition in the domain of dominance of hadronic degrees of freedom at center-of-mass energies between 10--20 GeV. The stage II of the BES at RHIC will occur in 2019--2020 and will explore with precision measurements in the domain of the QCD phase diagram with high baryon densities. Future developments and more precise studies of features of QCD phase diagram in the framework of stage II of RHIC BES will be briefly discussed.

Short-lived polyphase deformation during crustal thickening and exhumation of a collisional orogen (Ribeira Belt, Brazil)

The Ribeira Belt (Brazil) is a Neoproterozoic collisional-related feature that was located in a south-central position in West Gondwana. We present quantitative data on finite strain, flow vorticity and deformation temperatures for the Curitiba Terrane, a major segment of the southern Ribeira Belt. Six deformation phases (D1-D6) related with crustal thickening and exhumation were recognized. D1 and D2-related microstructures are preserved exclusively within porphyroblasts, in part grown during stages of high-pressure (∼9–12 kbar) isobaric heating after crustal thickening. D3 phase was active from peak metamorphism attained in contrasting crustal levels (810–400 °C), to the early stage of exhumation (500–400 °C), as indicated by petrological, microstructural and quartz c-axis fabric evidence. Kinematic vorticity results indicate that the SL3 mylonitic fabric resulted from a simple shear-dominated deformation related with westward thrusting. North-verging overturned D4 folds with E-W-trending subhorizontal axes derived from a pure shear-dominated deformation. Regional D5 open folds with subvertical axes and NNE-SSW-trending traces were produced by indentation tectonics. D6 phase comprises retrograde orogen-parallel transcurrent shear zones related with scape tectonics. Geochronological data indicate that D3-D6 phases occurred between 584 and 580 Ma, suggesting a fast exhumation rate of ∼8 mm/year for the deepest rocks from the southern Ribeira Belt.

Primordial magnetic field and kinetic theory with Berry curvature

We study the generation of magnetic field in the primordial plasma of the standard model (SM) particles at temperature $T>80$~TeV much higher than the electroweak scale. It is assumed that there is an excess number of right-handed electrons over left-handed positrons in the plasma. Using the Berry-curvature modified kinetic theory to incorporate the effect of the Abelian anomaly, we show that this chiral-imbalance leads to generation of hyper-magnetic field in the plasma in both the collision dominated and the collisionless regimes. It is shown that in the collision dominated regime the chiral-vorticity effect can generate finite vorticity in the plasma together with the magnetic field. Typical strength of the generated magnetic field is $10^{27}$~Gauss at $T\sim 80$~TeV with the length scale $10^5/T$ whereas the Hubble length scale is $10^{13}/T$. Further the instability can also generate the magnetic field of order $10^{31}$~Gauss at typical length scale $10/T$. But there may not be any vorticity generation in this regime. We show that the estimated values of the magnetic field are consistent with the bounds obtained from present observations.

Spatiotemporal complexity of electroconvection patterns in nematic liquid crystals.

We investigate a number of complex patterns driven by the electroconvection instability in a planarly aligned layer of a nematic liquid crystal. They are traced back to various secondary instabilities of the ideal roll patterns bifurcating at onset of convection, whereby the basic nematohydrodynamic equations are solved by common Galerkin expansion methods. Alternatively these equations are systematically approximated by a set of coupled amplitude equations. They describe slow modulations of the convection roll amplitudes, which are coupled to a flow field component with finite vorticity perpendicular to the layer and to a quasihomogeneous in-plane rotation of the director. It is demonstrated that the Galerkin stability diagram of the convection rolls is well reproduced by the corresponding one based on the amplitude equations. The main purpose of the paper is, however, to demonstrate that their direct numerical simulations match surprisingly well new experiments, which serves as a convincing test of our theoretical approach.

A minimal flow-elements model for the generation of packets of hairpin vortices in shear flows

AbstractPackets of hairpin-shaped vortices and streamwise counter-rotating vortex pairs (CVPs) appear to be key structures during the late stages of the transition process as well as in low-Reynolds-number turbulence in wall-bounded flows. In this work we propose a robust model consisting of minimal flow elements that can produce packets of hairpins. Its three components are: simple shear, a CVP having finite streamwise vorticity magnitude and a two-dimensional (2D) wavy (in the streamwise direction) spanwise vortex sheet. This combination is inherently unstable: the CVP modifies the base flow due to the induced velocity forming an inflection point in the base-flow velocity profile. Consequently, the 2D wavy vortex sheet is amplified, causing undulation of the CVP. The undulation is further enhanced as the wave continues to be amplified and eventually the CVP breaks down into several segments. The induced velocity generates highly localized patches of spanwise vorticity above the regions connecting two consecutive streamwise elements of the CVP. These patches widen with time and join with the streamwise vortical elements situated beneath them forming a packet of hairpins. The results of the unbounded (having no walls) model are compared with pipe and channel flow experiments and with a direct numerical simulation of a transition process in Couette flow. The good agreement in all cases demonstrates the universality and robustness of the model.

Dynamics of the innermost accretion flows around compact objects: magnetosphere-disc interface, global oscillations and instabilities

We study global non-axisymmetric oscillation modes and instabilities in magnetosphere- disc systems, as expected in neutron star X-ray binaries and possibly also in accreting black hole systems. Our two-dimensional magnetosphere-disc model consists of a Keplerian disc in contact with an uniformly rotating magnetosphere with low plasma density. Two types of global overstable modes exist in such systems, the interface modes and the disc inertial-acoustic modes. We examine various physical effects and parameters that influence the properties of these oscillation modes, particularly their growth rates, including the magnetosphere field configuration, the velocity and density contrasts across the magnetosphere-disc interface, the rotation profile (with Newtonian or General Relativistic potential), the sound speed and magnetic field of the disc. The interface modes are driven unstable by Rayleigh-Taylor and Kelvin-Helmholtz in- stabilities, but can be stabilized by the toroidal field (through magnetic tension) and disc differential rotation (through finite vorticity). General relativity increases their growth rates by modifying the disc vorticity outside the magnetosphere boundary. The interface modes may also be affected by wave absorption associated with corotation resonance in the disc. In the presence of a magnetosphere, the inertial-acoustic modes are effectively trapped at the innermost region of the relativistic disc just outside the interface. They are driven unstable by wave absorption at the corotation resonance, but can be stabilized by modest disc magnetic fields. The overstable oscillation modes studied in this paper have characteristic properties that make them possible candidates for the quasi-periodic oscillations observed in X-ray binaries.