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We discuss a phenomenological self-consistent model of a turbulent magnetized conducting fluid for mean flow and magnetic field in geophysical and astrophysical contexts. This model is designed to study spirality and dynamo effect in the study of astro-geophysical magnetic fields. It is believed that the very existence of cosmic magnetic fields is largely explained by the chirality of background turbulence, the simplest measure of which is the non-vanishing helicity of small-scale turbulence. The mean velocity and magnetic fields are modelled using averaged MHD-equations and phenomenological differential equations for the four bulk turbulence quantities (hydro magnetic turbulent energy, magnetic and cross helicity and residual helicity). These model equations, combined with the mean-field equations, allow the most complete construction of a self-consistent model of the turbulent dynamo. These problems and open questions are considered, especially those concerning the model transport equations for the determination of the alpha effect in astrophysical magnetic fields. The presented work is mainly aimed at modelling rotation effects in hydro magnetic turbulent flows of spiral space and thermonuclear plasma. [ABSTRACT FROM AUTHOR]

We prove weighted analytic regularity of Leray--Hopf variational solutions for the stationary, incompressible Navier--Stokes equations (NSEs) in plane polygons, subject to analytic body forces. We admit mixed boundary conditions which may change type at each corner. The weighted analytic regularity results are established in scales of corner-weighted Kondrat'ev spaces of finite order. The proofs rely on a priori estimates for the corresponding linearized boundary value problem in sectors in corner-weighted Sobolev spaces and on an induction argument for the weighted norm estimates on the quadratic nonlinear term in the NSE in a polar frame. [ABSTRACT FROM AUTHOR]

Low Reynolds number fluid flows are governed by the Stokes equations. In two dimensions, Stokes flows can be described by two analytic functions, known as Goursat functions. Brubeck and Trefethen [SIAM J. Sci. Comput., 44 (2022), pp. A1205-A1226] recently introduced a lightning Stokes solver that uses rational functions to approximate the Goursat functions in polyg- onal domains. In this paper, we present the LARS algorithm (lightning-AAA rational Stokes) for computing two-dimensional (2D) Stokes flows in domains with smooth boundaries and multiply con- nected domains using lightning and AAA rational approximation [Y. Nakatsukasa, O. Sète, and L. N. Trefethen, SIAM J. Sci. Comput., 40 (2018), pp. A1494-A1522]. After validating our solver against known analytical solutions, we solve a variety of 2D Stokes flow problems with physical and engineering applications. Using these examples, we show rational approximation can now be used to compute 2D Stokes flows in general domains. The computations take less than a second and give solutions with at least 6-digit accuracy. [ABSTRACT FROM AUTHOR]

The ideal magnetohydrodynamics (MHD) as well as the ideal fluid dynamics is governed by a Hamilton equation with respect to the Lie–Poisson bracket. The Nambu bracket manifestly represents the Lie–Poisson structure in terms of derivatives of the Casimir invariants. We construct a compact Nambu bracket representation for the 3D ideal MHD equations with the use of three Casimirs for the second Hamiltonians, the total entropy, and the magnetic and cross-helicities, whose coefficients are all constant. The Lie–Poisson bracket induced by this Nambu bracket does not coincide with the original one, but is supplemented by terms with an auxiliary variable. The supplemented Lie–Poisson bracket qualifies the cross-helicity as the Casimir. By appealing to Noether's theorem, we show that the cross-helicity is an integral invariant associated with the particle-relabeling symmetry. Employing a Lagrange label function as the independent variable in the variational framework facilitates implementation of the relabeling transformation. By incorporating the divergence symmetry, other known topological invariants are put on the same ground as Noether's theorem. [ABSTRACT FROM AUTHOR]

It has long been thought that shear band (SB) formation in amorphous solids initiates from relatively "soft" regions in the material in which large-scale non-affine deformations become localized. The test of this hypothesis requires an effective means of identifying "soft" regions and their evolution as the material is deformed to varying degrees, where the metric of "softness" must also account for the effect of temperature on local material stiffness. We show that the mean square atomic displacement on a caging timescale ⟨u2⟩, the "Debye–Waller factor," provides a useful method for estimating the shear modulus of the entire material and, by extension, the material stiffness at an atomic scale. Based on this "softness" metrology, we observe that SB formation indeed occurs through the strain-induced formation of localized soft regions in our deformed metallic glass free-standing films. Unexpectedly, the critical strain condition for SB formation occurs when the softness (⟨u2⟩) distribution within the emerging soft regions approaches that of the interfacial region in its undeformed state, initiating an instability with similarities to the transition to turbulence. Correspondingly, no SBs arise when the material is so thin that the entire material can be approximately described as being "interfacial" in nature. We also quantify relaxation in the glass and the nature and origin of highly non-Gaussian particle displacements in the dynamically heterogeneous SB regions at times longer than the caging time. [ABSTRACT FROM AUTHOR]

We analyze the anisotropy of turbulence in an electrically conducting fluid in the presence of a uniform magnetic field, for low magnetic Reynolds number, using the quasistatic approximation. In the linear limit, the kinetic energy of velocity components normal to the magnetic field decays faster than the kinetic energy of component along the magnetic field [H. K. Moffatt, “On the suppression of turbulence by a uniform magnetic field,” J. Fluid Mech. 28, 571 (1967)]. However, numerous numerical studies predict a different behavior, wherein the final state is characterized by dominant horizontal energy. We investigate the corresponding nonlinear phenomenon using direct numerical simulations. The initial temporal evolution of the decaying flow indicates that the turbulence is very similar to the so-called two-and-a-half-dimensional flow [D. Montgomery and L. Turner, “Two-and-a-half-dimensional magnetohydrodynamic turbulence,” Phys. Fluids 25, 345 (1982)] and we offer an explanation for the dominance of horizontal kinetic energy. [ABSTRACT FROM AUTHOR]

In a previous paper [R. González, L. G. Sarasua, and A. Costa, “Kelvin waves with helical Beltrami flow structure,” Phys. Fluids 20, 024106 (2008)] we analyzed the formation of Kelvin waves with a Beltrami flow structure in an ideal fluid. Here, taking into account the results of this paper, the topological analogy between the role of the magnetic field in Woltjer’s theorem [L. Woltjer, “A theorem on force-free magnetic fields,” Proc. Natl. Acad. Sci. U.S.A. 44, 489 (1958)] and the role of the vorticity in the equivalent theorem is revisited. Via this analogy we identify the force-free equilibrium of the magnetohydrodynamics with the Beltrami flow equilibrium of the hydrodynamic. The stability of the last one is studied applying Arnold’s theorem. We analyze the role of the enstrophy in the determination of the equilibrium and its stability. We show examples where the Beltrami flow equilibrium is stable under perturbations of the Beltrami flow type with the same eigenvalue as the basic flow one. The enstrophy variation results invariant with respect to a uniform rotating and translational frame and the stability is conserved when the flow experiences a transition from a Beltrami axisymmetric flow to a helical one of the same eigenvalue. These results are discussed in comparison with that given by Moffatt in 1986 [H. K. Moffatt, “Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations,” J. Fluid Mech. 166, 359 (1986)]. [ABSTRACT FROM AUTHOR]

Motivated by the observation that dynamo is a conversion mechanism between kinetic and magnetic energy, we develop a new approach to unravel dynamo mechanism based on local (in space, scale, and time) energy budget describing dissipation and scale-by-scale energy transfers. Our approach is based upon a new filtering approach that can be used effectively for any type of meshes, including unstructured ones. The corresponding formalism is very general and applies to any geometry or boundary conditions. We further discuss the interpretation of these energy transfers in the context of fast dynamo and anomalous dissipation. We apply it to the results from direct numerical simulations of the von Kármán Sodium setup (referred to as VKS) using a finite element code, showing dynamo action for two types of impellers (steel or soft iron) in the magnetic field growth and saturation phases. Although the two types of dynamo hardly differ from the mean-field theory point of view (the velocity fields are the same in both cases), the locality of our formalism allows us to trace the origin of the differences between these two types of dynamo: for steel impellers, the dynamo is due to the transfer of velocity energy both in the bulk and in the vicinity of the impellers, whereas for soft iron impellers, the dynamo effect mainly comes from the rotation of the blades. We finally discuss possible signatures of precursors to anomalous dissipation and fast dynamo, which could become relevant in the inviscid limit. [ABSTRACT FROM AUTHOR]

The stretch-twist-fold (STF) flow is a variant of the dynamo model describing the generation and behavior of magnetic fields in celestial bodies such as stars and planets. This study seeks to provide fresh insights into the integrable STF flow within the framework of dynamical systems theory and Poisson geometry. Our results include (i) the establishment of Poisson structures, Hamilton–Poisson realizations, and a Lax formulation for the STF flow; (ii) a comprehensive classification of phase portraits for the STF flow restricted to its symplectic leaf; (iii) a description of the asymptotic behavior of the STF flow on the Poincaré sphere, revealing the occurrence of bifurcations at infinity; (iv) a characterization of the energy-Casimir mapping of the STF flow and its connections with dynamical elements. These findings have the potential to deepen our understanding of the intricate and diverse dynamics exhibited by the STF flow in the context of dynamo theory. [ABSTRACT FROM AUTHOR]

We examine the flow in and around a falling fluid droplet in a vertically oscillating flow. We assume axisymmetric Stokes flow, and for small deformations to the droplet, the governing equations can be linearized leading to an infinite system of linear ordinary differential equations. In this study, we have analytically solved the problem in the small-capillary limit. We note that the solution locally breaks down at the poles of the droplet. The drag and center of the mass were also obtained. In the case when only odd modes are present, the droplet shows three-dimensional axisymmetric heart-shaped solutions oscillating vertically in time. When only even modes are present, the droplet exhibits axisymmetric stretching and squeezing. [ABSTRACT FROM AUTHOR]

There is growing recognition that integrating clients' religion and spirituality (RS) in mental health practice can contribute to positive outcomes. Given that intrinsic religiosity predicts faculty attitudes/behaviors regarding training students on such integration within social work education, it is worth understanding their RS beliefs and practices. Thus, our current national study describes the RS beliefs and practices of 807 MSW faculty in accredited programs. Interestingly, faculty consider RS to be important within their lives, are frequently involved in RS activities, and tend to be more religiously diverse than the general population. Implications for training and research are discussed. [ABSTRACT FROM AUTHOR]

Studies of forced homogeneous isotropic turbulence (HIT) of multiphase systems rely on a comprehensive understanding of the single-phase HIT flow to quantify any turbulence modifications due to injection of the dispersed phase. Here, we compare external forcing schemes to generate and sustain single-phase HIT. The considered forcing schemes, Lundgren, Arnold–Beltrami–Childress, and Mallouppas, are based on the application of the body force in physical space to inject energy into the flow at large length scales. Direct numerical simulations are performed in cubic periodic domains of 1283 and 2563 size using a lattice Boltzmann method. The range of the Taylor's Reynolds number achieved is R e λ T = 24.4 – 75.4. The Lundgren force takes the longest time to generate turbulence and produces significant fluctuations in the turbulence properties in the statistically stationary state. Additionally, this force interacts with the velocity field in the entire range of wavenumbers, which is not the case for the other two forces. However, the scale-by-scale analysis shows that for the considered forces, the behavior of the non-linear energy transfer, dissipation, and energy injection terms differs only within the initial 16% of the wavenumbers that represent large length scales. After that, all terms behave consistently among each other for different forcing schemes. We conclude that the three considered large-scale forcing schemes do not affect the generated turbulent flow fields at small scales and can be used to study turbulence modification by the dispersed phase. [ABSTRACT FROM AUTHOR]

The correlation between helicity and turbulent transport in turbulent flows is probed with the use of direct numerical simulation and Lagrangian scalar tracking. Channel flow and plane Couette flow at friction Reynolds number 300 and Lagrangian data along the trajectories of fluid particles and passive particles with Schmidt numbers 0.7 and 6 are used. The goal is to identify characteristics of the flow that enhance turbulent transport from the wall, and how flow regions that exhibit these characteristics are related to helicity. The relationship between vorticity and relative helicity along particle trajectories is probed, and the relationship between the distribution of helicity conditioned on Reynolds stress quadrants is also evaluated. More importantly, the correlation between relative helicity density and the alignment of vorticity with velocity vectors and eigenvectors of the rate of strain tensor is presented. Separate computations for particles that disperse the farthest into the flow field and those that disperse the least are conducted to determine the flow structures that contribute to turbulent dispersion. The joint distribution of helicity and vertical velocity, and helicity and vertical vorticity depends on the location of particle release and the Schmidt number. The trajectories of particles that disperse the least are characterized by a correlation between the absolute value of the relative helicity density and the absolute value of the cosine between the vorticity vector and the eigenvectors of the rate of strain tensor, while the value of this correlation approaches zero for the particles that disperse the most. [ABSTRACT FROM AUTHOR]

A volume penalization-based immersed boundary technique is developed and thoroughly validated for fluid flow problems, specifically flow over bluff bodies. The proposed algorithm has been implemented in an open source field operation and manipulation (OpenFOAM), a computational fluid dynamics solver. The immersed boundary method offers the advantage of inserting a complex solid object inside a Cartesian grid system, and therefore, the governing equations can be applied to such a simpler grid arrangement. For capturing the fluid–solid interface more accurately, the grid is refined near the solid surface using topoSetDict and refineMeshDict utilities in OpenFOAM. In order to avoid any numerical oscillation and to compute the gradients accurately near the interface, the present volume penalization method (VPM) is integrated with a signed distance function, which is also referred to as a level-set function. Benchmark problems, such as flows around a cylinder and a sphere, are considered and thoroughly validated with the results available in the literature. For the flow over a stationary cylinder, the Reynolds number is varied so that it covers from a steady two-dimensional flow to an unsteady three-dimensional flow. The capability of the present solver has been further verified by considering the flow past a vibrating cylinder in the cross-stream direction. In addition, a flow over a sphere, which is inherently three-dimensional due to its geometrical shape, is validated in both steady and unsteady regimes. The results obtained by the present VPM show good agreement with those obtained by a body-fitted grid using the same numerical scheme as that of the VPM, and also with those reported in the literature. The present results indicate that the VPM-based immersed boundary technique can be widely applicable to scientific and engineering problems involving flow past stationary and moving bluff bodies of arbitrary geometry. [ABSTRACT FROM AUTHOR]

An off-source volumetrically heated turbulent transient plume, known as transient diabatic plume (TDP), is compared with an unheated transient plume (TP). Both the TDP and TP are simulated using direct numerical simulations at a source Reynolds number (Re) of 2000. The flow is sufficiently resolved till the Kolmogorov (η) scale. The radius of the TP shows a self-similar behavior of linear increase with height after about five diameters from the source hot-patch. However, the velocity does not show a self-similar behavior. The addition of off-source buoyancy in the TDP triples the vertical velocity and also causes an order of magnitude increase in the vorticity magnitude (ω) due to the effect of the baroclinic torque. Compared to the TP, the entrainment coefficient and radius of the TDP increase and this shows enhanced entrainment due to heating. The transient flows fields are analyzed using local scales based on integral quantities of volume, momentum, and buoyancy. Normalizing the vorticity with these integral scales results in a more uniform scaled ωl for both flows. Hence, for both TP and TDP, we use the same values of ωl to quantify the inner and outer boundaries of the turbulent non-turbulent layer (TNTL). The width of the TNTL (δTNTL) decreases by ∼25% due to heating. The conditionally averaged velocity profiles suggest that very close to the outer irrotational boundary (IB) of the TNTL, the TDP exhibits stronger updrafts and downdrafts in comparison to the TP. Entrainment is studied using the mean relative velocity (⟨ v n ⟩) defined at the IB. The analysis of the components of ⟨ v n ⟩ reveal that the viscous diffusion component, which is of the order of the Kolmogorov velocity ( u η ), is balanced by the baroclinic and viscous dissipation components, while the inviscid term is negligible in comparison. [ABSTRACT FROM AUTHOR]

Artificial and living microswimmers encounter a large variety of geometric confinements and surfaces in the biological world. Here, we study the low-Reynolds-number dynamics of a microswimmer enclosed by a wedge-shaped free-slip interface. For various opening angles of the wedge, we derive an exact solution for the resulting flow fields using the method of images. In this way, the hydrodynamic interactions between the swimmer and the confining interfaces are examined. In particular, we find attraction or repulsion by the wedge depending on the propulsion mechanism (pusher- or puller-type) and the opening angle of the wedge. Our description should be related to the dynamics of microswimmers in free-standing liquid films of spatially varying thickness. [ABSTRACT FROM AUTHOR]

Chemical erosion, one of the two major erosion processes along with mechanical erosion, occurs when a soluble rock-like salt, gypsum, or limestone is dissolved in contact with a water flow. The coupling between the geometry of the rocks, the mass transfer, and the flow leads to the formation of remarkable patterns, like scallop patterns in caves. We emphasize the common presence of very sharp shapes and spikes, despite the diversity of hydrodynamic conditions and the nature of the soluble materials. We explain the generic emergence of such spikes in dissolution processes by a geometrical approach. Singularities at the interface emerge as a consequence of the erosion directed in the normal direction, when the surface displays curvature variations, like those associated with a dissolution pattern. First, we demonstrate the presence of singular structures in natural interfaces shaped by dissolution. Then, we propose simple surface evolution models of increasing complexity demonstrating the emergence of spikes and allowing us to explain at long term by coarsening the formation of cellular structures. Finally, we perform a dissolution pattern experiment driven by solutal convection, and we report the emergence of a cellular pattern following well the model predictions. Although the precise prediction of dissolution shapes necessitates performing a complete hydrodynamic study, we show that the characteristic spikes which are reported ultimately for dissolution shapes are explained generically by geometrical arguments due to the surface evolution. These findings can be applied to other ablation patterns, reported for example in melting ice. [ABSTRACT FROM AUTHOR]

This article investigates whether there are differences in religious and spiritual (R/S) beliefs, attitudes, practices, training, and self-assessed competence between counselors and psychologists in Canada. Researchers surveyed 307 mental health professionals in Canada with two standardized measures (the Assessment of Spirituality and Religious Sentiments Scale and the Duke University Religion Index) and various other questions corresponding to variables investigated or alluded to in past research. We hypothesized that, compared with psychologists, counselors would (a) have stronger personal R/S beliefs, (b) demonstrate more positive attitudes about the appropriateness of using R/S techniques with clients, (c) utilize R/S techniques more in sessions, (d) possess more positive attitudes toward training in this area, and (e) have higher self-assessed competence for working with R/S clients. These hypotheses were generally supported except for the last one: there were no significant differences found between counselors and psychologists in self-assessed competence in working with R/S clients. We compare our findings to those of extant research, particularly the study by Plumb who examined counselors in Canada. On the basis of our findings, we advocate for more systematic cultivation of R/S competence in programs for both counselors and psychologists in Canada. [ABSTRACT FROM AUTHOR]

Understanding the origin and structure of mean magnetic fields in astrophysical conditions is a major challenge. Shear flows often coexist in such astrophysical conditions, and the role of flow shear on the dynamo mechanism is of great interest. Here, we present a direct numerical simulation study of the effect of flow shear on dynamo instability for EPI2D flows [Yoshida et al., Phys. Rev. Lett. 119, 244501 (2017)] with controllable mirror symmetry (i.e., fluid helicity). Our numerical observations suggest that for helical base flows, the effect of shear is to reduce the small-scale dynamo (SSD) growth rate moderately. For non-helical base flows, flow shear has the opposite effect of amplifying the SSD action. The magnetic energy growth rate (γ) for non-helical base flows has been found to follow an algebraic nature of the form, γ = − a S + b S 2 3 , where a , b > 0 are real constants, S is the shear flow strength, and γ is found to be independent of the scale of flow shear. Studies with different shear profiles and shear scale lengths for non-helical base flows have been performed to test the universality of our finding. [ABSTRACT FROM AUTHOR]

We introduce and analyze a statically condensed iterated penalty (SCIP) method for solving incompressible flow problems discretized with pth order Scott--Vogelius elements. While the standard iterated penalty method is often the preferred algorithm for computing the discrete solution, it requires inverting a linear system with O (pd) unknowns at each iteration. The SCIP method reduces the size of this system to O (pd-1) unknowns while maintaining the geometric rate of convergence of the iterated penalty method. The application of SCIP to Kovasznay flow and Moffatt eddies shows good agreement with the theory. [ABSTRACT FROM AUTHOR]

The equations of multimoment hydrodynamics, supplemented by stochastic components, are used to study the chaotic distortion of a regular flow in the wake of a sphere. The mutual influence of the Reynolds number and the intensity of weak disordered perturbations in the incident flow, characterized by the turbulence coefficient, is investigated. The calculations show that the turbulent flow pattern is formed due to the excessive growth of disordered perturbations in the unstable recirculating zone in the near wake behind the sphere. The transition from laminar to turbulent motion has a considerable length on the Reynolds number scale. The turbulence coefficient is a key factor influencing the formation of a turbulent flow pattern. Low values of the turbulence coefficient can block the occurrence of turbulence even at arbitrarily high values of the Reynolds number. On the contrary, high values of the turbulence coefficient can initiate turbulence even at relatively low values of the Reynolds number. The degree of the development of turbulence is interpreted in terms of randomness coefficients depending on the Reynolds number and the turbulence coefficient. The previously formulated idea on the nature of turbulence is confirmed. The regular component of turbulence is formed as a result of unstable motion of coherent structures. Excessively expanding disordered perturbations form the chaotic component of turbulence. [ABSTRACT FROM AUTHOR]

This paper identifies a new and previously unidentified trend changing corporate governance: board liability for misconduct based on operational risk. Operational risk is serious business. When boards slumber, hundreds of people die in airline accidents, pipeline explosions cause massive environmental damage, and mine collapses leave families with grief unimaginable. These and other corporate disasters were entirely preventable, but board members were asleep at the wheel while the conditions were set for disaster. This Article argues that courts are only now starting to fully recognize the peril of operational risk as a source of liability for boards of directors. Operational misconduct should take center stage alongside financial mismanagement as a critical source of director liability. After closely reviewing the key cases, this Article shows how operational risk heralds a fundamental shift in the way boards respond to monitoring the firm. This Article also identifies how subtle changes in judicial doctrine are changing the way boards manage operational risk, avoid liability, and protect the lives of stakeholders of the company and society at large. [ABSTRACT FROM AUTHOR]

The relation between the helicity and the rate of dissipation of turbulent kinetic energy in turbulent flows has been a matter of debate. Herein, direct numerical simulations of turbulent Poiseuille and Couette flow were used in combination with the tracking of helicity, helicity density, and dissipation along the trajectories of passive scalar markers to probe the correlation between helicity and dissipation in anisotropic turbulence. The Schmidt number of the scalar markers varied between 0.7, 6, and infinite (i.e., fluid particles), while the friction Reynolds number for both simulations was 300. The probing tools were the autocorrelation coefficients, the cross correlation coefficients between helicity and dissipation, and the joint probability density function calculated in the Lagrangian framework along the positions of the scalar markers. These markers were released at different locations within the flow field, including the viscous wall sublayer, the transition layer, the logarithmic region, and the outer flow. In addition, conditional statistics for scalar markers that dispersed most or least in the flow field were also calculated. It was found that helicity and dissipation changed along the trajectories of scalar markers; however, helicity and dissipation were not correlated in the Lagrangian framework. There was anticorrelation between helicity and dissipation in the near wall region, which was less obvious in the logarithmic region. More importantly, helicity could be used to characterize the alignment of the fluctuating velocity and vorticity vectors along the trajectories of scalar markers that disperse the farthest in the direction normal to the channel wall. [ABSTRACT FROM AUTHOR]

This paper presents a straightforward and efficient numerical simulation method for solving the Navier–Stokes equations for weakly viscous incompressible fluids describing steady flow. Our approach utilizes isogeometric finite elements to handle higher-order partial differential operators associated with weakly viscous incompressible flow problems. Specifically, our numerical formulation employs a principle of virtual power (PVP)-based weak formulation that utilizes a stream-function field, which distinguishes it from the more commonly used bi-harmonic type formulations. The usage of a stream-function field ensures a pointwise divergence-free velocity condition, making the present method suitable for low to moderately high Reynolds number flow problems. In contrast to the bi-harmonic formulation, which is typically used for describing internal flow and requires special treatment of outflow boundary conditions, the PVP-based formulation is more general and does not require special treatment at the outflow boundary. It is also demonstrated that both bi-harmonic and PVP-based weak formulations yield identical results for internal flow problems. Our method employs non-uniform rational B-spline basis functions, and we present a simple stitching technique for imposing no-slip Dirichlet boundary conditions. Finally, we solve Poisson's equation to recover the pressure field. Furthermore, we use an appropriate Gaussian quadrature that is exact for splines to speed up the computation of various element matrices, especially for high polynomial degrees. The proposed formulation is evaluated by solving a set of numerical problems, including internal flow and channel flow problems. [ABSTRACT FROM AUTHOR]

The two-dimensional solutions and stability analysis are presented for an evaporating thin viscous liquid film flowing inside a uniformly heated rotating horizontal cylinder. A non-linear, fourth-order, partial differential evolution equation is obtained by simplifying mass, momentum, and energy conservation equations within the lubrication approximation. The effect of evaporation, gravity, viscous drag, surface tension, thermocapillary stress, and intermolecular forces has been taken into account. The numerical solutions of the model are validated against the existing experimental as well as the numerical results, along with the analytical result for the limiting cases of the present model. The film thickness model is solved to elucidate two-dimensional spatiotemporal solutions and their stability for a wide range of thermal and other parameters. The evaporative mass flux at the liquid–air interface results in unsteady solutions which are oscillatory in nature, and the amplitude of the oscillations increases with an increase in the evaporative flux. The film ruptures after some time and the rupture time is found to be inversely proportional to the evaporation number, a non-dimensional number quantifying the rate of evaporation. The linear stability analysis shows that the thermocapillary stresses as well as the long-range molecular forces destabilize the film. A negative disjoining pressure is shown to reduce the rupture time and vice versa. Evaporation (condensation) plays a destabilizing (stabilizing) role in the thin film flow. Non-linear computations are carried out for the steady profiles, validating the growth rates obtained from the linear stability analysis. [ABSTRACT FROM AUTHOR]

The flow characteristics of Taylor–Couette–Poiseuille flow induced by supercritical carbon dioxide in an annular gap play a pivotal role in determining the overall performance of the rotating machinery. To accurately design the structural components of rotating machinery and enhance its efficiency, this study employs the large eddy simulation method to investigate the flow behavior of Taylor–Couette–Poiseuille flow with supercritical carbon dioxide within an annular gap. The results reveal that vortices are predominantly generated near the inner wall. Initially, the flow exhibits small swirl vortices, spiral ring vortices, and annular vortices along the flow direction. As the flow progresses, these small vortices at the inlet region transition into hairpin swirl vortices. Finally, turbulent flow disturbances lead to the fragmentation and merging of spiral and annular vortices, resulting in a flow field characterized by high-frequency hairpin swirl vortices and small vortices with strong randomness. An increase in the swirl number causes the initial position of the Taylor vortex to shift toward the inlet, while the turbulent kinetic energy is more active on the outer wall side than the inner wall side. Along the flow direction, the vortices experience a developmental process involving stabilization, diffusion, and mixing. Varying the radius ratio affects the magnitude of vorticity, reduces velocity fluctuations in a regular pattern, and alters the distribution of helicity bands from wide and sparse to compact and dense groupings. As the axial Reynolds number increases, the magnitude of vortices grows, leading to more severe velocity fluctuations and the transformation of the helicity bands from a regular annular pattern to fluctuating vortices bands, accompanied by a decrease in helicity. [ABSTRACT FROM AUTHOR]

The so-called stretch-twist-fold flow consists in a Stokes flow depending on two parameters defined in a unit closed ball B that is associated with the motion of a fluid particle coming from the dynamo theory, and it models a mechanism for studying the magnetic field of the Earth and the Sun. Here for the first time, we classify all the local phase portraits of its equilibrium points, and we provide the global phase portraits on the 2-dimensional sphere of the boundary of the ball B. [ABSTRACT FROM AUTHOR]

The original UNIFAES, as any exponential-type scheme, applies to the combined advective and diffusive terms of the viscous fluid transport equations. This work generalizes the scheme by making explicit the first and second derivatives of its interpolating curve, so that it can be applied, alongside classic central differencing schemes, to the statistical correlations of the transport equations of fluctuating kinetic energy, helicity and enstrophy. Tests are performed in a perturbed laminar incompressible Couette flow, obtained with a three-dimensional primitive variables solver using the original UNIFAES, the semi-staggered mesh, the Poisson equation for pressure and the forth order Runge-Kutta time-wise integration. Both the asymptotic tendencies of the correlations at low Reynolds number and the numerical stability of the solver for any Reynolds number are demonstrated with modest meshes. [ABSTRACT FROM AUTHOR]

Vortex instability in cavity flow is a fundamental component of microfluidic applications such as flow mixing, nanoparticle synthesis, and cell/particle manipulation. In contrast to Newtonian fluids, non-Newtonian fluids exhibit significantly different flow behaviors due to their non-linear flow dynamics. This study experimentally investigates the flow dynamics of polymer solutions with distinct rheological properties through a microcavity and quantifies the influence of the rheological degree on the evolution dynamics of vortices. We find three typical vortex evolution patterns in the cavity flow of polymer solutions and show that the rheological degree mediates the transitions among these patterns. The vortex evolution in the cavity flow of all polymer solutions tested in this study shifts from a basic increasing logistic function to one of three typical patterns as the polymer concentration increases. It is clarified that the pattern transition is related to the elasticity number and shear-thinning index of the fluids, and the phase difference between identical patterns is due to differences in the viscosity and elasticity of the fluids. These results extend our understanding of the vortex dynamics of complex fluids in cavity flow and provide theoretical guidance for enhancing the working efficiency of cavity-structured microfluidic applications using polymer solutions. The results of this study may also inspire developments in the flow regulation of drug delivery in blood through the vascular system. [ABSTRACT FROM AUTHOR]

For magnetic knots and links in plasmas, we introduce an internal twist and study their dynamical behavior in numerical simulations. We use a set of helical and non-helical configurations and add an internal twist that cancels the helicity of the helical configurations or makes a non-helical system helical. These fields are then left to relax in a magnetohydrodynamic environment. In line with previous works, we confirm the importance of magnetic helicity in field relaxation. However, an internal twist, as could be observed in coronal magnetic loops, does not just add or subtract helicity, but also introduce an alignment of the magnetic field with the electric current, which is the source term for helicity. This source term is strong enough to lead to a significant change in magnetic helicity, which for some cases leads to a loss of the stabilizing properties expressed in the realizability condition. Even a relatively weak internal twist in these magnetic fields leads to a strong enough source term for magnetic helicity that for various cases even in a low diffusion environment, we observe an inversion in sign of magnetic helicity within timescales much shorter than the diffusion time. We conclude that in solar and stellar fields, an internal twist does not automatically result in a structurally stable configuration and that the alignment of the magnetic field with the electric current must be taken into account. [ABSTRACT FROM AUTHOR]

This paper studies the problem of finding a three-dimensional solenoidal vector field such that both the vector field and its curl are tangential to a given family of toroidal surfaces. We show that this question can be translated into the problem of determining a periodic solution with periodic derivatives of a two-dimensional linear elliptic second-order partial differential equation on each toroidal surface and prove the existence of smooth solutions. Examples of smooth solutions foliated by toroidal surfaces that are not invariant under continuous Euclidean isometries are also constructed explicitly, and they are identified as equilibria of anisotropic magnetohydrodynamics. The problem examined here represents a weaker version of a fundamental mathematical problem that arises in the context of magnetohydrodynamics and fluid mechanics concerning the existence of regular equilibrium magnetic fields and steady Euler flows in bounded domains without continuous Euclidean isometries. The existence of such configurations represents a key theoretical issue for the design of the confining magnetic field in nuclear fusion reactors known as stellarators. [ABSTRACT FROM AUTHOR]

In this work, on the one hand, we continue with the study of the dynamic property of Beltrami flows [R. González, "Dynamics of non-axisymmetric Beltrami flows," Phys. Fluids 26, 114104 (2014)], extending its scopes to non-stationary flows in the rotating system, which allowed us to classify the rotating waves on the basis of their phase velocities. On the other hand, and in accordance with this classification, we study the resonant triadic interaction of these waves. For this purpose, we use the expansion in a Chandrasekhar–Kendall basis for an infinite tube, in an analogous procedure to the one carried out by Waleffe ["The nature of triad interactions in homogeneous turbulence," Phys. Fluids A 4, 350–363 (1992)], to study the interaction of plane Beltrami waves. Taking an equilibrium of the resulting non-linear equations for the amplitudes of the waves, we consider their linear and non-linear stability. Regarding their linear stability, we see that unlike plane Beltrami waves, their stability depends not only on the relative helicities but also on an interaction factor that depends on the properties and the co-rotating or counter-rotating character of the interacting waves. On the other hand, for non-linear stability dependent on the same parameters as those of linear stability, we find, for one case of analysis, that there is non-linear instability only for some interactions of two co-rotating waves with a counter-rotating one and we exhibit criteria that are sufficient conditions of non-linear stability or non-linear instability. [ABSTRACT FROM AUTHOR]

The vortex structure of an electrically conducting liquid flowing past a localized magnetic obstacle wake is simulated. When the field strength exceeds a critical value, a localized Lorentz breaking force produces a virtual body filled with a pair of counter-rotating vortices. It is shown that a pair of tail vortices forms behind the body vortex pair to produce a four-vortex pattern if the field strength exceeds a second critical value. Before and after separation of the tail vortex from the body vortex, new vortices of two types emerge between them to produce six-vortex patterns. [ABSTRACT FROM AUTHOR]

After more than 70 years of development, holography has become an essential tool of modern optics in many applications. In fact, for various applications of different kinds of holographic techniques, stability and antijamming ability are very important. Here, optical topological structures are introduced into holographic technology, and an entirely new concept of optical topological holography is demonstrated to solve stability and antijamming problems. Based on the optical knots and links, the topological holography is not only developed in theory, but also demonstrated experimentally. In addition, a new topological holographic coding is established by regarding each knotted/linked topological structure as an information carrier. Due to the variety of knotted and linked structures and their characteristics of topological protection, such coding can have high capacity as well as robust properties. Furthermore, with writing the hologram into the liquid crystal, robust information storage of 3D topological holography is realized. [ABSTRACT FROM AUTHOR]

We demonstrate a universal mechanism of a class of instabilities in infrared regions for massless Abelian p-form gauge theories with topological interactions, which we call generalized chiral instabilities. Such instabilities occur in the presence of initial electric fields for the p-form gauge fields. We show that the dynamically generated magnetic fields tend to decrease the initial electric fields and result in configurations with linking numbers, which can be characterized by non-invertible global symmetries. The so-called chiral plasma instability and instabilities of the axion electrodynamics and (4 + 1)-dimensional Maxwell-Chern-Simons theory in electric fields can be described by the generalized chiral instabilities in a unified manner. We also illustrate this mechanism in the (2+1)-dimensional Goldstone-Maxwell model in electric field. [ABSTRACT FROM AUTHOR]

The University of Warwick has been subjected to two apparently contradictory critiques. The first, associated with social historian EP Thompson, is that the university had been captured by a cabal of industrialists intending to use its faculties to reproduce capitalistic managers. A second, more general critique of universities in Britain since 1945 is that their elite liberal education in the arts and abstract sciences had little contribution to make to meeting the national economic and social needs for technological 'manpower'. Neither of these accounts satisfactorily explains the early development at Warwick. An alliance between educators and local Midlands' industrialists at Warwick developed an education in the virtues of liberal capitalism, reinventing the traditional university education in moral character to face the challenges of the mid-twentieth century. In the midst of the Cold War, only with such an education could students help meet the needs of local and national industry. [ABSTRACT FROM AUTHOR]

This study examines the viscous fingering phenomenon of immiscible displacement in Hele-Shaw cells using the volume of fluid approach (HSC). The displaced fluid has various power law indices and is shear-thinning. Both the distribution properties of pressure and velocity were examined during the development process as well as the morphological evolution characteristics of non-Newtonian fluid when the air was moved. The findings indicate that pressure decreases in the fingering direction throughout the whole non-Newtonian fluid region. The non-Newtonian fluid's velocity close to the HSC pipe wall is virtually zero, and the highest velocity in the air phase is scattered throughout the finger's center. Its relative width gets less as development progresses. Viscous fingering then exhibits a high degree of stability and practically constant relative breadth. The outstretched fingers are shorter and thicker under different power-law indices, and the displacement efficiency is higher. The lower the power-law index n, the better the shear thinning properties. According to the aforementioned features, high-quality and high-efficiency oil displacement can be achieved in petroleum engineering by using new power rate fluid. [ABSTRACT FROM AUTHOR]

A new Cloud Imaging and Particle Size (CIPS) gravity wave (GW) variance data set is available that facilitates automated analysis of GWs entering the mesosphere. This work examines several years of CIPS GW variances from 50 to 55 km in the context of the Arctic and Antarctic polar vortices. CIPS observes highest GW activity in the vortex edge region where horizontal wind speeds are largest, consistent with previously published GW climatologies in the stratosphere and mesosphere. CIPS observes the well‐documented planetary wave (PW)‐1 patterns in GW activity in both hemispheres. In the Northern Hemisphere, maximum GW activity occurs over the North Atlantic and western Europe. In the Southern Hemisphere, maximum GW activity stretches from the Andes over the South Atlantic and Indian Oceans, as expected. In the NH, CIPS GW spatial patterns are highly correlated with horizontal wind speed. In the SH, CIPS GW patterns are less positively correlated with the winds due to increased zonal symmetry and orographic forcing. The Andes Mountains and Antarctic Peninsula, South Georgia Island, Kerguelen/Heard Islands, New Zealand, and Tasmania are persistent sources of orographic GWs. Atmospheric Infrared sounder observations of stratospheric GWs are analyzed alongside CIPS to explore vertical GW coherence and to infer GW propagation and sources. NH midlatitude GW activity is reduced during the January 2021 SSW, as expected. This reduction in GWs leads to a simultaneous reduction in traveling ionospheric disturbances (TIDs), providing more evidence that weak polar vortex events with weak GW activity leads to reduced daytime TID activity. Plain Language Summary: A new satellite gravity wave (GW) variance data set is available that facilitates automated analysis of GWs entering the mesosphere. This work examines several years of GW variances from 50 to 55 km in the context of the Arctic and Antarctic polar vortices. Highest GW activity is observed in the vortex edge region where horizontal wind speeds are largest, consistent with previous work. Known planetary wave‐1 patterns are confirmed in the new data set. In the Northern Hemisphere, maximum GW activity occurs over the North Atlantic and western Europe. In the Southern Hemisphere, maximum GW activity stretches from the Andes over the South Atlantic and Indian Oceans. In the Arctic winter, GW spatial patterns are highly correlated with horizontal wind speed. In the Antarctic winter, GW patterns are less positively correlated with the winds due to smaller variations around a latitude circle and larger orographic forcing. We show that Arctic midlatitude GW activity is reduced during the January 2021 SSW, as expected. This reduction in GWs leads to a simultaneous reduction in traveling ionospheric disturbances (TIDs), providing more evidence that weak polar vortex events with weak GW activity leads to reduced daytime TID activity. Key Points: This is the first work to present gravity waves (GWs) from 50 to 55 km observed by AIM CIPS with a focus on the winter polar vorticesDuring the 2020–2021 Arctic winter the longitude of maximum GW activity, maximum horizontal wind speed, and the polar vortex are co‐locatedReduced GW activity during the January 2021 SSW leads to simultaneous reductions in daytime traveling ionospheric disturbances [ABSTRACT FROM AUTHOR]

Classical analogs of chiral vortical and magnetic effects, generated by the currents possessing the hydrodynamical helicity are considered. The earlier found phenomenon of helicity separation in heavy-ion collisions leads to the appearance of currents of opposite signs at the different sides of reaction plane, accompanied by the current parallel to the plane. We discuss briefly relation between classical and quantum chiral effects. [ABSTRACT FROM AUTHOR]

Magnetic helicity plays a tremendously important role when it is different from zero on average. Most notably, it leads to the phenomenon of an inverse cascade. Here, we consider decaying magnetohydrodynamic (MHD) turbulence as well as some less common examples of magnetic evolution under the Hall effect and ambipolar diffusion, as well as cases in which the magnetic field evolution is constrained by the presence of an asymmetry in the number density of chiral fermions, whose spin is systematically either aligned or anti-aligned with its momentum. In all those cases, there is a new conserved quantity: the Hosking integral. We present quantitative scaling results for the magnetic integral scale as well as the magnetic energy density and its spectrum. We also compare with cases were a magnetic version of the Saffman integral is initially finite. Rotation in MHD turbulence tends to suppress nonlinearity and thereby also inverse cascading. Finally, the role of the Hosking and magnetic Saffman integrals in shell models of turbulence is examined. [ABSTRACT FROM AUTHOR]

Objective: While previous research indicates that negative religious coping relates with distress, it is unclear if this represents generalized spiritual struggles or a specific vulnerability activated by negative events. Moreover, past research treats coping as a stable phenomenon, although it likely fluctuates. This research simultaneously tested both models longitudinally and examined the relationship between coping and distress., Methods: The current study is a secondary analysis of longitudinal data collected online over 3 years from 397 participants. Life events, negative religious coping, and depressive symptoms were assessed on six occasions, and linear mixed-effect models were used to analyze data., Results: Negative religious coping was largely stable with increases at times of stress. Participants with higher mean negative coping reported more depressive symptoms regardless of life circumstances (i.e., main effect), likely reflecting generalized spiritual struggles. In addition, those with higher mean coping or with particularly high levels at a given time reported even higher levels of symptoms when they experienced more negative life events (i.e., moderation effect)., Conclusion: Results suggest that previous research merges two distinct phenomena-spiritual struggles and negative coping. This has important theoretical and research implications and suggests that integrating spirituality and religion into treatment can be warranted., (© 2024 Wiley Periodicals LLC.)

This article describes a national sample of 989 current mental health clients' views regarding whether and how their mental health care providers integrated the client's religion/spirituality (RS) into treatment. Within the online Qualtrics survey, two open-ended items asked respondents what (if anything) the client perceived their therapist having done regarding the client's RS that was (1) helpful/supportive or (2) hurtful/harmful. Participants also reported various ways therapists included the topic of RS in practice, if any. Nearly half freely described helpful ways their providers integrated the client's RS, and half indicated it was not discussed or applicable. Although 9.6% described hurtful experiences, most indicated their provider had not done anything harmful related to integrating RS. Implications for practice and training across mental health disciplines are discussed., (© 2024. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

While kinetic helicity is not Galilean invariant locally, it is known [Moffatt, J. Fluid Mech. 35, 117 (1969)] that its spatial integral quantifies the degree of knottedness of vorticity field lines. Being a topological property of the flow, mean kinetic helicity is Galilean invariant. Here, we provide a direct mathematical proof that kinetic helicity is Galilean invariant when spatially integrated over regions enclosed by vorticity surfaces, i.e., surfaces of zero vorticity flux. We also discuss so-called relative kinetic helicity, which is Galilean invariant when integrated over any region in the flow. [ABSTRACT FROM AUTHOR]