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We examine the mechanisms responsible for the onset of the three-dimensional mode B instability in the wake behind a circular cylinder. We show that it is possible to explicitly account for the stabilising effect of spanwise viscous diffusion and then demonstrate that the remaining mechanisms involved in this short-wavelength instability are preserved in the limit of zero wavelength. Using the resulting simplified equations, we show that perturbations in different fluid particles interact only through the in-plane viscous diffusion which turns out to have a destabilising effect. We also show that in the presence of viscous diffusion, the closed trajectories which had been conjectured to play a crucial role in the onset of the mode B instability are not actually a prerequisite for the growth of mode B type perturbations. We combine these observations to identify the three essential ingredients for the development of the mode B instability: (i) the amplification of perturbations in the braid regions due to the stretching mechanism; and the spreading of perturbations through (ii) viscous diffusion, and (iii) cross-flow advection which transports fluid between the two braid regions on either side of the cylinder. Finally, we develop a simple criterion that allows the prediction of the regions where three-dimensional short-wavelength perturbations are amplified by the stretching mechanism. The approach used in our study is general and has the potential to give insights into the onset of three-dimensionality via short-wavelength instabilities in other flows. [ABSTRACT FROM AUTHOR]

The article in the Journal of Fluid Mechanics delves into the stability of different steady flows in an electrolyte layer driven by the Lorentz force in an annular channel. It identifies a new flow state, type 3, which sustains free-surface vortices and undergoes transitions as the Reynolds number increases. The study highlights the role of the type 3 flow in the development of free-surface vortices and contributes to understanding electromagnetically driven flows in fluid dynamics. Other researchers have also explored fluid behavior in rotating systems and spherical Couette flows, offering valuable insights into vortices and shear layers in diverse fluid environments. [Extracted from the article]

In this paper, the classical problem of two-dimensional flow in a cylindrical domain, driven by a nonuniform tangential velocity imposed at the boundary, is reconsidered in straightforward manner. When the boundary velocity is a pure rotation Ω plus a small perturbation ηΩf(θ) and when the Reynolds number based on Ω is large (Re ≫1), this flow is of "Prandtl-Batchelor" type, namely, a flow of uniform vorticity ωc in a core region inside a viscous boundary layer of thickness O(Re)-1/2. The O(η²) contribution to ωc is determined here by asymptotic analysis up to O(Re−1). The result is in good agreement with numerical computation for Re ≳400. [ABSTRACT FROM AUTHOR]

Eddy-viscosity-based turbulence models provide the most commonly used modeling approach for computational fluid dynamics simulations in the aerospace industry. These models are very accurate at a relatively low cost for many cases but lack accuracy in the case of highly rotational leading edge vortex flows for mid to low aspect-ratio wings. An enhanced adaptive turbulence model based on the one-equation Spalart–Allmaras turbulence model is fundamental to this work. This model employs several additional coefficients and source terms, specifically targeting vortex-dominated flow regions, where these coefficients can be calibrated by an optimization procedure based on experimental or high-fidelity numerical data. To extend the usability of the model from single or cluster-wise calibrated cases, this work presents a preconditioning approach of the turbulence model via a neural network. The neural network provides a case-unspecific calibration approach, enabling the use of the model for many known or unknown cases. This extension enables aircraft design teams to perform low-cost Reynolds-averaged Navier–Stokes simulations with increased accuracy instead of complex and costly high-fidelity simulations. [ABSTRACT FROM AUTHOR]

In this paper we discuss the dynamics of vorticity at partial-slip boundaries. We consider the total vector circulation, which includes both the total vorticity of the fluid and the slip velocity at the boundary (the interface vortex sheet). The generation of vector circulation is an inviscid process, which does not depend on either viscosity or the slip length at the boundary. Vector circulation is generated by the inviscid relative acceleration between the fluid and the solid, due to either tangential pressure gradients or tangential acceleration of the partial-slip wall. While the slip length does not affect the creation of vector circulation, it governs how vector circulation is distributed between the total vorticity of the fluid and the interface vortex sheet. Specifically, the partial-slip boundary condition prescribes the ratio between boundary vorticity and the strength of the interface vortex sheet, and the viscous boundary flux transfers vector circulation between the interface vortex sheet and the fluid interior to maintain this condition. The interaction between a vortex ring and a partial-slip wall is examined to highlight various aspects of this formulation. For the head-on collision, the quantity of vector circulation diffused into the fluid as secondary vorticity increases as the slip length is decreased, resulting in a stronger secondary vortex and increased rebound of the vortex ring. For the oblique interaction, the extent to which the vortex ring connects to the boundary increases as the slip length is increased. [ABSTRACT FROM AUTHOR]

Continuum models of media with zero pressure are widely used in various branches of physics and mechanics, including studies of a dilute dispersed phase in multiphase flows. In zero-pressure media, the particle trajectories may intersect, "folds" and "puckers" of the phase volume may arise, and "caustics" (the envelopes of particle trajectories) may appear, near which the density of the medium sharply increases. In recent decades, the phenomena of clustering and aerodynamic focusing of inertial admixture in gas and liquid flows have attracted increasing attention of researchers. This is due to the importance of taking into account the inhomogeneities in the impurity concentration when describing the transport of aerosol pollutants in the environment, the mechanisms of droplet growth in rain clouds, scattering of radiation by dispersed inclusions, initiation of detonation in two-phase mixtures, as well as when solving problems of two-phase aerodynamics, interpretation of measurements obtained by LDV or PIV methods, and in many other applications. These problems gave an impetus to a significant increase in the number of publications devoted to the processes of accumulation and clustering of inertial particles in gas and liquid flows. Within the framework of classical two-fluid models and standard Eulerian approaches assuming single-valuedness of continuum parameters of the media, it turns out impossible to describe zones of multi-valued velocity fields and density singularities in flows with crossing particle trajectories. One of the alternatives is the full Lagrangian approach proposed by the author earlier. In recent years, this approach has been further developed in combination with averaged Eulerian and Lagrangian (vortex-blob method) methods for describing the dynamics of the carrier phase. Such combined approaches made it possible to study the structure of local zones of accumulation of inertial particles in vortex, transient, and turbulent flows. This article describes the basic ideas of the full Lagrangian approach, provides examples of the most significant results which illustrate the unique capabilities of the method, and gives an overview of the main directions of further development of the method as applied to transient, vortex, and turbulent flows of "gas-particle" media. Some of the ideas discussed and the results presented below are of a more general interest, since they are also applicable to other models of zero-pressure media. [ABSTRACT FROM AUTHOR]

The subject of this work is the development of compact analogs of vortex flows models, which are used in the modeling of vortex structures observed during the flight of an aircraft and the motion of a body in a fluid. In particular, two significant misunderstandings prevailing in this area of science are highlighted. The first misunderstanding is that the stationary motion of fluid parcels in a circle is treated as an inviscid vortex. Therefore, any vortex flow model that does not explicitly contain viscosity is considered to describe inviscid vortex motion. It has been proven that this is not so: the stationary viscous motion of fluid parcels in circular orbits corresponds to the self-balance of one force - the force of viscosity. This conclusion, in an explicit form, was made for the first time. This is very important because it changes our ideas about force balance, where two or more forces of different natures must necessarily be present. Overcoming this misunderstanding opens the way for creating compact analogs of existing models of vortex motions. Along the way, one more - the second general misunderstanding in the field of vortex dynamics was eliminated. Wherever we read it, we can see that the compactness of the vortex flow is associated with the compactness of the vorticity field. This is facilitated by the fact that the equations for vorticity and not for velocity are considered. As a result, except for one or two models of vortices, which correspond to the rotation of the entire space, up to infinity, this violates the fundamental law of physics - the law of conservation and transformation of energy. It is about the fact that, as a second misunderstanding, an error is assumed when calculating the kinetic energy of the vortex flows: the Jacobian in cylindrical (polar) coordinates is not considered. As a result, all the mentioned models of vortex flows, which correspond to the hyperbolic law as their asymptotics in the periphery, have infinite kinetic energy. Certainly, this does not correspond to the formation and evolution of compact vortex structures. Therefore, in this work, based on overcoming the aforementioned misunderstandings, many previously obtained models of compact vortex flows, as well as those obtained for the first time, are presented. In particular, this applies to the turbulent vortex flow during the formation of a vortex sheet, which is a compact analog of the Burgers-Rott vortex - both the classical one corresponding to laminar motion and the one consisting of a laminar flow in the core and a turbulent flow on the periphery of the vortex. Research methods are entirely theoretical. Well-known theorems of theoretical mechanics, mathematical theory of field, and calculus of variations, etc. are used. The obtained solutions are compared with the existing corresponding analogs of non-compact flows. Conclusions. Using the methods of calculus of variation, it was possible to show the possibility of the formation of quasi-solid-like rotational motion in a boundary layer of an incompressible fluid. The very presence of viscosity, or rather its taking into account (boundary layer), indicates a possible transition of the flow from plane-parallel motion to the just-mentioned rotational one due to the Kelvin-Helmholtz instability. In addition, two new models of the Burgers-Rott vortex flow were obtained in this study. The first model uses the general solution obtained by Burgers, but this model corresponds to a combined vortex: although the velocity field is continuous, the vorticity field has a discontinuity - at the point of maximum velocity. It is proved that such an approach is quite possible: the equation of motion is satisfied everywhere, i.e., at every point in space, and the tangential stresses are continuous functions. Since the periphery of the Burgers-Rott vortex is an unstable flow, another model is proposed - with a laminar core and a turbulent periphery. Certainly, the motion of fluid parcels in the peripheral region is described by a velocity distribution other than that of Burgers. Finally, the possible use of known models of compact vortex flows to simulate the von Karman vortex street is considered, with an indication of the advantages of these models.

We analytically derive an amplitude equation for the weakly nonlinear evolution of the linearly most amplified response of a non-normal dynamical system. The development generalizes the method proposed in Ducimetière et al. (J. Fluid Mech., vol. 947, 2022, A43), in that the base flow now arbitrarily depends on time, and the operator exponential formalism for the evolution of the perturbation is not used. Applied to the two-dimensional Lamb-Oseen vortex, the amplitude equation successfully predicts the nonlinearities to weaken or reinforce the transient gain in the weakly nonlinear regime. In particular, the minimum amplitude of the linear optimal initial perturbation required for the amplitude equation to lose a solution, interpreted as the flow experiencing a bypass (subcritical) transition, is found to decay as a power law with the Reynolds number. Although with a different exponent, this is recovered in direct numerical simulations, showing a transition towards a tripolar state. The simplicity of the amplitude equation and the link made with the sensitivity formula permits a physical interpretation of nonlinear effects, in light of existing work on Landau damping and on shear instabilities. The amplitude equation also quantifies the respective contributions of the second harmonic and the spatial mean flow distortion in the nonlinear modification of the gain. [ABSTRACT FROM AUTHOR]

The work considers the results of experimental and numerical study on the hydrodynamic characteristics of a jet vortex reactor, MicroReactor with Intensively Swirled Flows MRISF-1, for which one of the application fields is the synthesis of oxide materials (e.g., perovskite-like material for solar panels). The energy-dissipation rate and micromixing quality are studied (by the iodide–iodate method) for various methods of supplying MRISF-1 and T-shaped millireactors with solutions. Numerical modeling reveals the volumes with the highest energy-dissipation rate. The quality of micromixing in the MRISF-1 is shown to be much higher than in the T-shaped millireactor, due to, among other things, the fact that the zone with the highest energy-dissipation rate is localized near the neck of the MRISF-1. [ABSTRACT FROM AUTHOR]

Study of swirling flows in channels corresponding to the static approximation of flow channels of the heart and major vessels with a longitudinal–radial profile zR2 = const and a concave streamlined surface at the beginning of the longitudinal coordinate has been carried out. A comparative analysis of the flow structure in channel configurations zRN = const, where N = –1, 1, 2, 3, in the absence and presence of a concave surface was carried out. The numerical modeling was compared with the results of hydrodynamic experiments on the flow characteristics and the shape of the flow lines. The numerical model was used to determine the velocity structure, viscous friction losses, and shear stresses. Numerical modeling of steady-state flows for channels without a concave surface showed that in the channel zR2 = const there is a stable vortex flow structure with the lowest viscous friction losses. The presence of a concave surface of sufficient size significantly reduces viscous friction losses and shear stresses in both the steady state and pulsed modes. [ABSTRACT FROM AUTHOR]

Purpose of this article is to study the transport of passive particles in the velocity field of a vortex tripole with a change in the parameter that determines the speed of the configuration movement. A structure consisting of a central vortex and satellite vortices rotating around it with the opposite vorticity is understood as a tripole. We employ a system of three point vortices, the most simple mathematical representation of a vortex tripole, which may be expressed as a system of nonlinear ordinary differential equations with a parameter. Consideration is limited to a particular case of a tripole with zero total vorticity. The influence of the speed values of vortex configuration movement on the processes of passive particle transport has been studied. Methods. The study was carried out numerically using algorithms based on the dynamical systems approaches including the construction of the Poincare map and the analysis of the dynamics of marker particles. Were carried out long ´ times calculations, corresponding to hundreds and thousands of turns around the tripole center. Integrators of high orders of accuracy were used to solve the Cauchy problems, which made it possible to adequacy of the calculation result control. Results. We found that transferring passive particles is fundamentally different depending on the speed of the tripole. A vast zone of chaotic dynamics forms in the neighborhood of the vortices when the velocity is low. This zone slowly shifts along with the tripole. There are subregions of active and slow mixing inside the chaos region. The possible stages of particle dynamics are: transfer from the region to the right of the tripole to the area to the left, vigorous mixing near the vortices, and slowly drifting to the region to the left of the tripole. At a high speed of vortex configuration in the entire chaotic region, the particles are strongly mixed. The vortex tripole removes particles from the vicinity of its initial position over long distances and practically does not capture new particles along its path. In intermediate situations, both processes can be realized at varying degrees. Conclusion. Non-trivial scenarios for the transport of passive particles by a vortex tripole, which can also occur in real vortex configurations of fluids, have been discovered and described.

We study the onset of the three-dimensional mode A instability in the near wake behind a circular cylinder. We show that long-wavelength perturbations organise in a time-shifting pattern such that the in-plane velocity in each streamwise slice corresponds to the base flow solution at shifted times. This observation introduces an additional unifying characteristic for certain mode A type instabilities. We then analyse the mechanisms which control the growth or decay of these perturbations and highlight the crucial role played by the tilting mechanism which operates via non-local interactions in a manner similar to Biot–Savart induction. We characterise its domain of influence using a Green's function-based approach which allows us to rationalise the non-trivial dependence of the growth rate on the spanwise wavenumber. We connect this behaviour to the subtle balance between the local growth of the perturbations as they are swept along by the flow and the feedback on the perturbations that are generated during the next period of the time-periodic base flow. Finally, we discuss generalisations of our findings to other types of flows. [ABSTRACT FROM AUTHOR]

Eddy-viscosity-based turbulence models provide the most commonly used modeling approach for computational fluid dynamics simulations in the aerospace industry. These models are very accurate at a relatively low cost for many cases but lack accuracy in the case of highly rotational leading edge vortex flows for mid to low aspect-ratio wings. An enhanced adaptive turbulence model based on the one-equation Spalart–Allmaras turbulence model is fundamental to this work. This model employs several additional coefficients and source terms, specifically targeting vortex-dominated flow regions, where these coefficients can be calibrated by an optimization procedure based on experimental or high-fidelity numerical data. To extend the usability of the model from single or cluster-wise calibrated cases, this work presents a preconditioning approach of the turbulence model via a neural network. The neural network provides a case-unspecific calibration approach, enabling the use of the model for many known or unknown cases. This extension enables aircraft design teams to perform low-cost Reynolds-averaged Navier–Stokes simulations with increased accuracy instead of complex and costly high-fidelity simulations.

We introduce maps of Cauchy–Green strain tensor eigenvalues to barycentric coordinates to quantify and visualize the full geometry of three-dimensional deformation in stationary and non-stationary fluid flows. As a natural extension of Lagrangian coherent structure diagnostics, which provide separate scalar fields and a one-dimensional quantification of fluid deformation, our barycentric mapping visualizes the role of all three Cauchy–Green eigenvalues (or rates of stretching) in a single plot through a novel stretching coordinate system. The coordinate system is based on the distance from three distinct limiting states of deformation that correspond with the dimension of the underlying invariant manifolds. One-dimensional axisymmetric deformation (sphere to rod deformation) corresponds to one-dimensional unstable manifolds, two-dimensional axisymmetric deformation (sphere to disk deformation) corresponds to two-dimensional unstable manifolds and the rare three-dimensional isometric case (sphere to sphere translation and rotation) corresponds to shear-free elliptic Lagrangian coherent structures (LCSs). We provide methods to visualize the degree to which fluid deformation approximates these limiting states, and tools to quantify differences between flows based on the compositional geometry of invariant manifolds in the flow. We also develop a simple analogue for bilinearly representing and plotting both rates of stretching and rotation as a single vector. As with other LCS techniques, these diagnostics define frame-indifferent material features in the flow. We provide multiple computed examples of LCS and momentum transport barriers, and show advantages over other coherent structure diagnostics. [ABSTRACT FROM AUTHOR]

We derive interface models for three-dimensional Rayleigh–Taylor instability (RTI), making use of a novel asymptotic expansion in the non-locality of the fluid flow. These interface models are derived for the purpose of studying universal features associated with RTI such as the Froude number in single-mode RTI, the predicted quadratic growth of the interface amplitude under multi-mode random perturbations, the optimal (viscous) mixing rates induced by the RTI and the self-similarity of horizontally averaged density profiles and the remarkable stabilization of the mixing layer growth rate which arises for the three-fluid two-interface heavy–light–heavy configuration, in which the addition of a third fluid bulk slows the growth of the mixing layer to a linear rate. Our interface models can capture the formation of small-scale structures induced by severe interface roll-up, reproduce experimental data in a number of different regimes and study the effects of multiple interface interactions even as the interface separation distance becomes exceedingly small. Compared with traditional numerical schemes used to study such phenomena, our models provide a computational speed-up of at least two orders of magnitude. [ABSTRACT FROM AUTHOR]

It is shown that a superposition of an arbitrary number of multipolar spherical and cylindrical oscillations in a cylindrical rigid flow with swirl is an exact solution to the time-dependent nonlinear vorticity equation. The oscillations are normal modes whose fundamental frequency and radial wavenumber are given by the angular speed and scaled inverse pitch, respectively, of the rigid flow. [ABSTRACT FROM AUTHOR]

We carry out a weakly nonlinear analysis of the centrifugal instability for a columnar vortex in a rotating fluid, and compare the results to those of the semi-linear model derived empirically by Yim et al. (J. Fluid Mech. , vol. 897, 2020, A34). The asymptotic analysis assumes that the Reynolds number is close to the instability threshold so that the perturbation is only marginally unstable. This leads to two coupled equations that govern the evolutions of the amplitude of the perturbation and of the mean flow under the effect of the Reynolds stresses due to the perturbation. These equations differ from the Stuart–Landau amplitude equation or coupled amplitude equations involving a mean field that have been derived previously. In particular, the amplitude does not saturate to a constant as in the supercritical Stuart–Landau equation, but decays afterwards reflecting the instability disappearance when the mean flow tends toward a neutrally stable profile in the direct numerical simulations (DNS). These equations resemble those of the semi-linear model except that the perturbation in the weakly nonlinear model keeps at leading order the structure of the eigenmode of the unperturbed base flow. The predictions of the weakly nonlinear equations are compared to those of the semi-linear model and to DNS for the Rossby number $Ro=-4$ and various Reynolds numbers and wavenumbers. They are in good agreement with the DNS when the growth rate is sufficiently small. However, the agreement deteriorates and becomes only qualitative for parameters away from the marginal values, whereas the semi-linear model continues to be in better agreement with the DNS. [ABSTRACT FROM AUTHOR]

Vortex flows, related to solar convective turbulent dynamics at granular scales and their interplay with magnetic fields within intergranular lanes, occur abundantly on the solar surface and in the atmosphere above. Their presence is revealed in high-resolution and high-cadence solar observations from the ground and from space and with state-of-the-art magnetoconvection simulations. Vortical flows exhibit complex characteristics and dynamics, excite a wide range of different waves, and couple different layers of the solar atmosphere, which facilitates the channeling and transfer of mass, momentum and energy from the solar surface up to the low corona. Here we provide a comprehensive review of documented research and new developments in theory, observations, and modelling of vortices over the past couple of decades after their observational discovery, including recent observations in H α , innovative detection techniques, diverse hydrostatic modelling of waves and forefront magnetohydrodynamic simulations incorporating effects of a non-ideal plasma. It is the first systematic overview of solar vortex flows at granular scales, a field with a plethora of names for phenomena that exhibit similarities and differences and often interconnect and rely on the same physics. With the advent of the 4-m Daniel K. Inouye Solar Telescope and the forthcoming European Solar Telescope, the ongoing Solar Orbiter mission, and the development of cutting-edge simulations, this review timely addresses the state-of-the-art on vortex flows and outlines both theoretical and observational future research directions. [ABSTRACT FROM AUTHOR]

We investigate the motion of a thin vortex filament in the presence of buoyancy. The asymptotic model of Moore & Saffman (Phil. Trans. R. Soc. Lond.A, vol. 272, 1972, pp. 403–429) is extended to take account of buoyancy forces in the force balance on a vortex element. The motion of a buoyant vortex is given by the transverse component of force balance, while the tangential component governs the dynamics of the structure in the core. We show that the local acceleration of axial flow is generated by the external pressure gradient due to gravity. The equations are then solved for vortex rings. An analytic solution for a buoyant vortex ring at a small initial inclination is obtained and asymptotically agrees with the literature.

This paper sets out to investigate the vortex flow of spinnaker yacht sails, which are low-aspect-ratio highly cambered wings used to sail downwind. We tested three model-scale sails with the same sections but different twists over a range of angles of attack in a water tunnel at a Reynolds number of 21 000. We measured the forces with a balance and the velocity field with particle image velocimetry. The sails experience massively separated threedimensional flow and leading-edge vortices convect at half of the free-stream velocity in a turbulent shear layer. Despite the massive flow separation, the twist of the sail does not change the lift curve slope, in agreement with strip theory. As the angle of attack and the twist vary, flow reattachment might occur in the time-average sense, but this does not necessarily result in a higher lift to drag ratio as the vorticity field is marginally affected. Finally, we investigated the effect of secondary vorticity, vortex stretching and diffusion on the vorticity fluxes. Overall, these results provide new insights into the vortex flow and associated force generation mechanism of wings with massively separated flow. [ABSTRACT FROM AUTHOR]

This paper sets out to investigate the vortex flow of spinnaker yacht sails, which are low-aspect-ratio highly cambered wings used to sail downwind. We tested three model-scale sails with the same sections but different twists over a range of angles of attack in a water tunnel at a Reynolds number of 21 000. We measured the forces with a balance and the velocity field with particle image velocimetry. The sails experience massively separated three-dimensional flow and leading-edge vortices convect at half of the free-stream velocity in a turbulent shear layer. Despite the massive flow separation, the twist of the sail does not change the lift curve slope, in agreement with strip theory. As the angle of attack and the twist vary, flow reattachment might occur in the time-average sense, but this does not necessarily result in a higher lift to drag ratio as the vorticity field is marginally affected. Finally, we investigated the effect of secondary vorticity, vortex stretching and diffusion on the vorticity fluxes. Overall, these results provide new insights into the vortex flow and associated force generation mechanism of wings with massively separated flow.

Linear modal instabilities of flow over untapered wings with aspect ratios AR = 4 and 8, based on the NACA 0015 profile, have been investigated numerically over a range of angles of attack, α, and angles of sweep, Λ, at chord Reynolds numbers 100 ≤ Re ≤ 400. Laminar base flows have been generated using direct numerical simulation and selective frequency damping, as appropriate. Several families of unstable three-dimensional linear global (TriGlobal) eigenmodes have been identified and their dependence on geometric parameters has been examined in detail at Re = 400. The leading global mode A is associated with the peak recirculation in the three-dimensional laminar separation bubble formed on the wing and becomes unstable when recirculation reaches O(10%). On unswept wings, this mode peaks in the midspan region of the wake and moves towards the wing tip with increasing Λ, following the displacement of peak recirculation; its linear amplification leads to wake unsteadiness. Additional amplified modes exist at nearly the same and higher frequencies compared to mode A. The critical Re has been identified and it is shown that amplification increases with increasing sweep, up to Λ ≈ 10°. At higher Λ, all global modes become less amplified and are ultimately stable at Λ = 30°. An increase in amplification of the leading mode with sweep was not observed over the AR = 4 wing, where tip vortex effects were shown to dominate. [ABSTRACT FROM AUTHOR]

The review presents the main works of Professor A.A. Borisov. The material is presented in several sections written by his students and colleagues. The subjects discussed include detonations in gaseous reactive systems and systems with inhomogeneous heat release are considered. The expediency of using detonation modes in aircraft and rocket engines is also considered. In addition, the results of mathematical modeling of shock waves in air are presented and questions of chemical kinetics are discussed. Based on the experimental study of vortex flows, an approach to the analysis of the formation of hot spots in real fuel combustion devices is formulated. A separate part is devoted to the kinetics of chemical transformations and their role in studying and predicting combustion processes. [ABSTRACT FROM AUTHOR]

The relevance of the research is caused by the lack of effective methods and means of combating atmospheric pollution with particles less than 2,5 microns in size. The ultrasonic effect used for these purposes does not allow ensuring the degree of coarsening of dispersed particles sufficient for their sedimentation or capture by the existing gas cleaning equipment. Experimental studies show that even at the maximum sound pressure level (above which the reverse process – the dispersion of drops or the destruction of particle agglomerates – is initiated), the efficiency of ultrasonic coagulation is insufficient, especially at a low counting concentration of particles. This necessitates the identification of new physical effects and the development of new methods of ultrasonic exposure, providing an increase in the efficiency of coagulation of fine particles. The main aim: development of a method for increasing the efficiency of ultrasonic coagulation of particles less than 2,5 microns in size due to emerging vortex acoustic flows in a thin air gap between the emitter and the reflector and a device for its implementation. Results. The authors have proposed a new method and device for cleaning gases from dispersed particles less than 2,5 microns in size by increasing the time of ultrasonic action on each particle and creating zones of local increase in the concentration of fine and submicron particles. This is provided by the formation of vortex flows between the emitting (in the form of a flexural-vibrating disk) and the reflecting surfaces. A local zone of increased concentration of particles is formed in the peripheral region of the vortex, due to the drift of particles under the action of centrifugal particles from the central region of the vortex to its periphery. The proposed method provides the increase in efficiency from 13 to 50 %, depending on the initial concentration of dispersed particles.

The point vortex is the simplest model of a two-dimensional vortex with non-zero circulation. The limitations introduced by its lack of core structure have been remedied by using desingularizations such as vortex patches and vortex sheets. We investigate steady states of the Sadovskii vortex in strain, a canonical model for a vortex in a general flow. The Sadovskii vortex is a uniform patch of vorticity surrounded by a vortex sheet. We recover previously known limiting cases of the vortex patch and hollow vortex, and examine the bifurcations away from these families. The result is a solution manifold spanned by two parameters. The addition of the vortex sheet to the vortex patch solutions immediately leads to splits in the solution manifold at certain bifurcation points. The more circular elliptical family remains attached to the family with a single pinch-off, and this family extends all the way to the simpler solution branch for the pure vortex sheet solutions. More elongated families below this one also split at bifurcation points, but these families do not exist in the vortex sheet limit.

The paper is devoted to numerical simulation of heat transfer enhancement processes in forced convective cooling systems based on split fins. The choice of the k–ω-SST turbulence model is substantiated, the numerical model is verified on the basis of experimental data, the optimal parameters for the depth and number of cuts of the fin edge are determined, and the analysis of the modernization of the working section geometry is carried out. [ABSTRACT FROM AUTHOR]

This review is devoted to the universal algebraic and geometric properties of the non-relativistic quantum current algebra symmetry and to their representations subject to applications in describing geometrical and analytical properties of quantum and classical integrable Hamiltonian systems of theoretical and mathematical physics. The Fock space, the non-relativistic quantum current algebra symmetry and its cyclic representations on separable Hilbert spaces are reviewed and described in detail. The unitary current algebra family of operators and generating functional equations are described. A generating functional method to constructing irreducible current algebra representations is reviewed, and the ergodicity of the corresponding representation Hilbert space measure is mentioned. The algebraic properties of the so called coherent states are also reviewed, generated by cyclic representations of the Heisenberg algebra on Hilbert spaces. Unbelievable and impressive applications of coherent states to the theory of nonlinear dynamical systems on Hilbert spaces are described, along with their linearization and integrability. Moreover, we present a further development of these results within the modern Lie-algebraic approach to nonlinear dynamical systems on Poissonian functional manifolds, which proved to be both unexpected and important for the classification of integrable Hamiltonian flows on Hilbert spaces. The quantum current Lie algebra symmetry properties and their functional representations, interpreted as a universal algebraic structure of symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics on functional manifolds, are analyzed in detail. Based on the current algebra symmetry structure and their functional representations, an effective integrability criterion is formulated for a wide class of completely integrable Hamiltonian systems on functional manifolds. The related algebraic structure of the Poissonian operators and an effective algorithm of their analytical construction are described. The current algebra representations in separable Hilbert spaces and the factorized structure of quantum integrable many-particle Hamiltonian systems are reviewed. The related current algebra-based Hamiltonian reconstruction of the many-particle oscillatory and Calogero–Moser–Sutherland quantum models are reviewed and discussed in detail. The related quasi-classical quantum current algebra density representations and the collective variable approach in equilibrium statistical physics are reviewed. In addition, the classical Wigner type current algebra representation and its application to non-equilibrium classical statistical mechanics are described, and the construction of the Lie–Poisson structure on the phase space of the infinite hierarchy of distribution functions is presented. The related Boltzmann–Bogolubov type kinetic equation for the generating functional of many-particle distribution functions is constructed, and the invariant reduction scheme, compatible with imposed correlation functions constraints, is suggested and analyzed in detail. We also review current algebra functional representations and their geometric structure subject to the analytical description of quasi-stationary hydrodynamic flows and their magneto-hydrodynamic generalizations. A unified geometric description of the ideal idiabatic liquid dynamics is presented, and its Hamiltonian structure is analyzed. A special chapter of the review is devoted to recent results on the description of modified current Lie algebra symmetries on torus and their Lie-algebraic structures, related to integrable so-called heavenly type spatially many-dimensional dynamical systems on functional manifolds. [ABSTRACT FROM AUTHOR]

An analytical method for determining the shape of hollow vortices in shear flows is presented in detail. In a non-dimensional formulation, it is shown that the problem has one degree of freedom represented by the free choice of the non-dimensionalized speed $\unicode[STIX]{x1D705}$ at the boundary of the vortex. The solutions form two families of shapes corresponding to vortex circulation and shear-flow vorticity having the opposite or same sign. When the signs are opposite, the shape family resembles that described by Llewellyn Smith & Crowdy (J. Fluid Mech., vol. 691, 2012, pp. 178–200) for hollow vortices in a potential flow with strain. As for that flow, there is a minimum value of $\unicode[STIX]{x1D705}$ below which there is no solution as the boundary of the vortex self-intersects, while, when the signs are the same, solutions exist for $0

The aerodynamics of a stationary wing in a turbulent wake are investigated. Force and velocity measurements are used to describe the unsteady flow. Various wakes are studied with different dominant frequencies and length scales. In contrast to the pre-stall angles of attack, the time-averaged lift increases substantially at post-stall angles of attack as the wing interacts with the von Kármán vortex street and experiences temporal variations of the effective angle of attack. At an optimal offset distance from the wake centreline, the time-averaged lift becomes maximum despite of small amplitude oscillations in the effective angle of attack. The stall angle of attack can reach 20° and the maximum lift coefficient can reach 64% higher than that in the freestream. Whereas large velocity fluctuations at the wake centreline cause excursions into the fully attached and separated flows during the cycle, small-amplitude oscillations at the optimal location result in periodic shedding of leading edge vortices. These vortices may produce large separation bubbles with reattachment near the trailing-edge. Vorticity roll-up, strength and size of the vortices increase with increasing wavelength and period of the von Kármán vortex street, which also coincides with an increase in the spanwise length scale of the incident wake, and all contribute to the remarkable increase in lift. [ABSTRACT FROM AUTHOR]

Multipolar spherical solutions to the three-dimensional steady vorticity equation are provided. These solutions are based on the separation of radial and angular contributions in terms of the spherical Bessel functions and vector spherical harmonics, respectively. In this set of multipolar vortex solutions, the Hicks–Moffatt swirling vortex is categorized as a vortex of degree = 1 and therefore as a vortex dipole. This swirling vortex is the three-dimensional dipole in spherical geometry equivalent to the two-dimensional Lamb–Chaplygin dipole in polar geometry. The three-dimensional dipole solution admits two linearly superposable solutions. The first one is a Trkalian flow and the second one is a cylindrical solid-body rotation with swirl. The higher > 1 multipolar vortices found are either vanishing-helicity vortices or Trkalian flow vortices. The multipolar Trkalian flows admit two circular polarizations given by the sign of the wavenumber k. It is also found that piecewise vortex solutions, consisting of interior rotational and exterior potential flow domains, satisfying velocity continuity conditions at the vortex boundary, are possible in the general multipolar Trkalian spherical vortex. A particular polarized dipole solution in three-dimensional cylindrical geometry, consisting as well in the superposition of a Trkalian flow and a rigid motion, is also analysed. This swirling vortex may be interpreted as the three-dimensional dipole in cylindrical geometry equivalent to the two-dimensional Lamb–Chaplygin dipole in polar geometry. [ABSTRACT FROM AUTHOR]

A plane non-parallel vortex flow in a square fluid domain is examined. The energy dissipation of the flow is dominated by viscosity and linear friction effect of a Hartmann layer. This is a traditional Navier–Stokes flow when the linear friction effect is not involved, whereas it is a magnetohydrodynamic flow when the energy dissipation is fundamentally dominated by the friction. It is proved that linear critical values of a spectral problem are nonlinear thresholds leading to the onset of secondary steady-state flows, the nonlinear phenomenon observed in laboratory experiments. [ABSTRACT FROM AUTHOR]

Abstract—Results of a numerical study of the flow structure occurring between the descent module and landing surface during the braking maneuver of the propulsion system are presented. Data on the force and thermal effect of the emerging flow on the descent module are given, depending on its distance and orientation relative to the landing surface and amount of the braking engine thrust. The pictures of the arising unsteady vortex motion of the medium are presented. [ABSTRACT FROM AUTHOR]

The problem of swirling flow in an axisymmetric channel with solid walls is considered. The complete system of the Navier-Stokes equations in variables of stream function and vorticity was used to describe the hydrodynamics of the flow. The finite-difference relaxation method was used to calculate the main flow. The Poisson equation was solved by the method of incomplete reduction. The transfer equations were solved by the block iteration method. Calculation results are presented as streamlines. The main attention was paid to studying the formation of reverse flow zones in the axial region. The stability of the obtained calculated profiles was investigated by the method of small perturbations. The system of six differential equations was solved for complex amplitude functions by the Runge-Kutta method numerically. The stability of the calculated flows is studied. Growth rates and oscillation frequency of unstable perturbations are obtained. The calculation results show a significant effect of swirling on the stability of the flow. The areas ahead of the recirculation zones tend to be the most unstable. This fact shows the connection between the hydrodynamic instability of the flow and the phenomenon of vortex breakdown.

In this work, Joukowski's rotor wake model is considered for a two-blade rotor of radius $R_b$ rotating at the angular velocity $\varOmega _R$ in a normal incident velocity $V_{\infty }$. This model is based on a description of the wake by a limited number of vortices of core size $a$ : a tip vortex of constant circulation $\varGamma$ for each blade and a root vortex of circulation $-2\varGamma$ on the rotation axis. Using a free-vortex method, we obtain solutions matching uniform interlaced helices in the far field that are steady in the frame rotating with the rotor for a large range of tip-speed ratios $\lambda = R_b \Omega _R/V_{\infty }$ and vortex strengths $\eta = \varGamma /(R_b^{2} \Omega _R)$. Solutions are provided for a two-bladed rotor for both helicopters and wind turbines. Particular attention is brought to the study of the solutions describing steep-descent helicopter flight regimes and large tip-ratio wind turbine regimes, for which the vortex structure is strongly deformed in the near wake and crosses the rotor plane. Both the geometry of the structure and its induced velocity field are analysed in detail. The thrust and the power coefficient of the solutions are also provided and compared to the momentum theory. The stability of the solutions is studied by monitoring the linear spatio-temporal development of a localized perturbation placed at different locations. Good agreements with the theoretical predictions for uniform helices and for point vortex arrays are demonstrated for the stability properties in the far wake. However, a more complex evolution is observed for the more deformed solutions when the perturbation is placed close to the rotor. [ABSTRACT FROM AUTHOR]

We employ reconnection-capable, vortex filament methods and finite-volume, Navier–Stokes flow solvers to investigate the topological and helicity dynamics of vortex links for medium and high Reynolds numbers. Our vortex-dynamical model is based on discretization of vortex tubes into bundles of numerical analogues of vortex lines. Due to their nearly singular nature, the numerical vortex lines have topological writhe but not twist. By means of our reconnecting vortex tube model, it is shown that the helicity of a vortex link is conserved during the unknotting process. The dynamics of linking and writhe topological measures indicate that most of the initial linking becomes writhe during the post-reconnection evolution. The helicity spectra of the vortex link present alternating-sign helicity fluctuations at all (potential flow) scales up to the vortex core. At pre-reconnection times, these fluctuations are damped by Biot–Savart vortex stretching and helicity becomes single signed. The post-reconnection spectra indicate an inverse helicity cascade corresponding to the creation of a homogenized vortex blob, a process reminiscent of coherent structure formation in turbulence. An accompanying Navier–Stokes calculation of vortex link dynamics at Reynolds numbers $Re=1500$ confirms the post-reconnection transformation of linking into different topological measures, the pre-reconnection damping of helicity spectra fluctuations and the spectral shift to low wavenumbers at post-reconnection times. Due to viscous dissipation action, however, this shift is accompanied by progressive reduction of helicity peak values. [ABSTRACT FROM AUTHOR]

The method of purification from mechanical pollution by oil, oil products, other materials of surface and bottom surfaces of water bodies with the use of vortex equipment: swirlers, vortex tubes, separatorsconfusers, cyclones is described-confusors, as well as floating vehicles, overpasses, storage tanks, which consists in a consistent separation of the surface layers of polluted water reservoir, de-buoyancy of the bottom layers and, subsequent separation formed, at the same time, the mechanical mixture to the required concentration and combination therein, components, simultaneous enrichment of the resulting semi-finished products and their separation into specific, used in practice materials and substances, transportation of these materials and substances to the packaging for further sale or environmentally friendly disposal. The problem is solved by using the properties of vortex flows of mechanical mixtures, the system application of separators-confusers, cyclones-confusers and creating a new method of complex purification of impurities from surfaces and bottom layers of water bodies by forming counter main flow, swirling flows of mechanical mixtures and managing them in space. The technical result is achieved by improving the technological process of separation of mechanical mixtures, its depth, integrated use of equipment and improve the efficiency of processes. The analysis of literary sources confirms the conclusion that the proposed method has no analogues in the world practice

Exploration of confined swirled flows in the former USSR and present-day Russia has a long history and is presented by numerous publications, mostly written in Russian. The obtained results have been put to practical use in different areas of chemical, energy, and processing industries. In view of the process intensification concept, such characteristics of confined swirled flows may be considered unique: high centrifugal gravity, elongation of trajectories, the presence of internal separation zones, energy separation phenomena, and efficient mass/heat transfer in the absence of any moving parts. For instance, high gravity provides an excellent opportunity for multiphase flow stabilization, preventing the appearance of nonuniformities and stability loss, while enhancement of various driving forces acting on the reaction medium takes place. This review is devoted to outlining the main research trends and to discuss the most essential practical implementations in the subject matter done up until now. It is not foreseen to embrace the whole area of swirled flow investigations in the world, but only covers most of the significant ideas and applications contributed in by former Soviet and Russian scientists and engineers. Shortcomings and difficulties of using swirled flows are also briefly discussed. [ABSTRACT FROM AUTHOR]

This study presents a class of steadily translating two-dimensional approximately circular vortices. The proposed solutions take the form of a superposition of two nearly concentric vorticity patches with zero net vorticity. Exact quasi-monopolar solutions of this type are found for propagation speeds that are much less than typical azimuthal velocities. While all V-states obtained are shown to be formally unstable, a large subset of configurations is characterized by very low growth rates. Fully nonlinear simulations reveal that such nearly stable eddies can propagate large distances from the point of origin while maintaining their structure and intensity. Therefore, the proposed solutions can serve as models of geophysical vortices that are known to drift relative to the ambient fluid, often exhibiting remarkable longevity and resilience to external perturbations. [ABSTRACT FROM AUTHOR]

The development of a wing-tip vortex of a rectangular, square-tipped wing having a NACA 0012 airfoil at a chord Reynolds number Recw = 2 × 105, under the effect of synthetic jet actuation, was experimentally studied. Five control configurations were considered: case C1 with momentum coefficient Cμ = 0.001 and actuation frequency F+ = 0.075; case C2 with Cμ = 0.001 and F+ = 0.15; case C3 with Cμ = 0.001 and F+ = 0.3; case C4 with Cμ = 0.001 and F+ = 0.6; and case C5 with Cμ = 0.001 and F+ = 1.2. Under the most effective configuration, case C3, the vortex was stretched and appeared to be diffuse with a nearly 40 % decrease in the peak circumferential velocity and 50 % decrease in the core axial vorticity. The vortex core radius largely broadened suggesting that the lower-frequency control configuration allowed the synthetic jet to travel larger distances into the vortex bringing turbulent structures within its core resulting in increased mixing and subsequently a more diffuse vortex. [ABSTRACT FROM AUTHOR]

A focused laser can cause local optical breakdown of a gas, which leads to rapid deposition of energy into a high-temperature plasma kernel that expands and induces a complex flow. For some conditions, hot gas is rapidly ejected along the laser axis up to distances several times the kernel size, with a particularly curious feature: relatively small changes in, for example, initial pressure can cause the direction of this ejection to reverse. Detailed axisymmetric simulations of a model energy kernel in an inert gas provide a hydrodynamic description of this phenomenon, reproducing key observations in corresponding experiments, including the vortex-ring-like features that constitute the ejection. These simulations are analysed to show how changes in the early-time kernel can lead to ejection or its reversal via alteration in the relative strength and position of the vorticity produced. A corresponding semi-infinite geometry is used to isolate two mechanisms: vorticity production by the generated shock and by baroclinic torque at the kernel boundary. Dependence on the initial kernel asymmetry is quantified, as it ultimately determines whether the vorticity, upon its subsequent evolution, develops into the ring-like structure that ejects. Even simple elongation of the energy kernel alone can reverse the direction. [ABSTRACT FROM AUTHOR]

• Lab-scale vortex study with constant heat flux and 30° and 60° swirl vanes. • PIV for time-averaged velocity profiles at different heights. • Identification of one-cell and two-cell vortex structures. • Investigation of vortex wandering effects and turbulence statistics within the vortex. • Identification of vortex flow regimes at various radial positions. Measurements were conducted within the flow field of a buoyancy-induced vortex at laboratory scale with a constant heat flux as input at the ground with swirl vanes set at 30° and 60° to the radial. Time-averaged velocity data were obtained using two-dimensional Particle Image Velocimetry (PIV). The velocity profiles in both cross-sectional and vertical planes were measured at heights of 0.3 m, 0.45 m, and 0.6 m above the ground level, and the time-averaged tangential, radial and vertical velocity components were derived. Two types of the vortex structures are identified based on the core swirl ratio, showing one-cell and two-cell type vortex structures with 30° and 60° swirl vane angles, respectively. Vortex wandering effects have also been investigated, including the centre distributions for different types of flow structures, and its impact on flow strength and vortex core sizes have also been quantified. Detailed turbulence statistics have been measured after removing the wandering effect, which show high level of turbulence intensities within the vortex core. [ABSTRACT FROM AUTHOR]

This paper describes the studies conducted in order to identify the limits of ultrasonic exposure’s effect on the fine particle coagulation process. It has been established as a result of the studies that ultrasonic exposure with a sound pressure level of 160 dB is capable of ensuring coagulation of particles sized 2.5 µm with efficiency δ = 83%. An increase of the coagulation up to 13% is induced with generation of swirling flows. The suggested approach to increasing the coagulation efficiency owing to vortex-type flows between the radiating and reflecting surfaces ensures efficiency of coagulation δ = 96 %. The implementation of this approach has shown that with generation of vortex-type acoustic flows, it makes the most sense for a concentration of particles of 18×10−3 g/m3. Incremental efficiency at such concentrations amounts to 50%.

The “Lighthill conjecture” regarding passive forces created in a group of self-propelled objects moving in an inviscid fluid is examined. We show that pressure gradients are produced in the wakes of anterior members of the group, which both indicate and assist rear members to stay in advantageous positions, for saving energy.