Initial Vortex Research Articles

Interactions between vortex and magnetic rings at high kinetic and magnetic Reynolds numbers

Interactions between magnetic and vortex rings are studied over a wide interval of interaction parameter values ranging from negligible magnetic effects on vorticity structure, to very strong effects. The employed interaction parameter measures the strength of the Lorentz force in units of the inertial force. At small interaction parameters, the vortex ring shapes part of the magnetic ring into a dissipative, curved, magnetic sheet structure. At high interaction parameters, the Lorentz force acts as an agent of proliferation of vortex rings, since it generates two vortex rings adjacent to the original magnetic structure, one of which is pulled (together with the advected magnetic field) into the wake of the original vortex ring, while the other escapes, ready to interact with another magnetic ring. Once within the initial vortex ring wake, both magnetic and vorticity structures are stretched into spirals, whilst the Lorentz force continuously generates new, intense vorticity at high magnetic field sites.

A numerical and experimental study of local hydrodynamics due to interactions between a solitary wave and an impervious structure

A series of experiments and numerical simulations on the interactions between a solitary wave and an impervious structure of square cross-section (block) in relatively shallow water were conducted to shed light on the physical processes of origination and evolution of coherent structures induced during such events. The block was placed at two different positions in a laboratory flume and was exposed to a solitary wave. The flow fields around the block were measured spatially and temporally for the validation of a three-dimensional (3D) computational fluid dynamics (CFD) numerical model results. The numerical model results were, then, used to further understand the generation and propagation of turbulent coherent structures around the block. The results show that two-dimensional (2D) spanwise vortices attributed to surface wave can evolve into coupled 3D turbulent coherent structures that penetrate into the water column at the sharp corners of the block. As the incident wave approaches the block, flow accelerates resulting in positive pressure gradients near the leading and trailing edges of the block. This leads to flow separation and, thus, the formation of vortices near the sharp corners. The vortices are extended through the water column, from the surface to the bottom. This is accompanied by a streamwise return flow that has a velocity of 25–50% of the incident flow velocity at the block. This flow carries the vortex tubes away from the block in the upwave direction. The one-dimensional power spectral density of the streamwise velocity demonstrates the production range and inertial subrange, following slopes of −1 and −5/3, respectively. The production range indicates the production of turbulence kinetic energy as a result of low frequency coherent structures. The inertial subrange marks the transfer of energy from the low to high frequency coherent structures, which correspond to high and low energy eddies, respectively. It is noted that the number of the initial vortices formed at the block corresponds to the number of sharp corners exposed to the incident wave.

On the Growth of the Support of Positive Vorticity for 2D Euler Equation in an Infinite Cylinder

We consider the incompressible 2D Euler equation in an infinite cylinder $\mathbb{R}\times \mathbb{T}$ in the case when the initial vorticity is non-negative, bounded, and compactly supported. We study $d(t)$, the diameter of the support of vorticity, and prove that it allows the following bound: $d(t)\leq Ct^{1/3}\log^2 t$ when $t\rightarrow\infty$.

Subseasonal Week 3–5 Surface Air Temperature Prediction During Boreal Wintertime in a GFDL Model

AbstractWith a Geophysical Fluid Dynamics Laboratory (GFDL) coupled model, the subseasonal prediction of wintertime (December–February) surface air temperature (SAT) is investigated through the analysis of 11‐year hindcasts. Significant subseasonal week 3–5 correlation skill exists over a large portion of the global land domain, and the predictability originates primarily from the eight most predictable SAT modes. The first three modes, identified as the El Niño‐Southern Oscillation mode, the North Atlantic Oscillation mode, and the Eurasia Meridional Dipole mode, can be skillfully predicted more than 5 weeks in advance. The North Atlantic Oscillation and Eurasia Meridional Dipole modes are strongly correlated with the initial stratospheric polar vortex strength, highlighting the role of stratosphere in subseasonal prediction. Interestingly, the Madden‐Julian Oscillation is not essential for the subseasonal land SAT prediction in the Northern Hemisphere extratropics. The spatial correlation skill exhibits considerable intraseasonal and interannual fluctuations, indicative of the importance to identify the time window of opportunity for subseasonal prediction.

Impact of Vortex Initialization in Prediction of Tropical Cyclones over Bay of Bengal with NCUM Model

The present study evaluates the impact of vortex initialization (VI) scheme within the NCMRWF Global Unified model (NCUM-G) for prediction of tropical cyclones (TCs) formed over Bay of Bengal (BoB). For this purpose, two numerical experiments such as control simulation (CNTL) without using VI scheme and VOTX simulation using the VI scheme in the NCUM-G are performed by considering four landfalling TCs formed over BoB basin during the year 2016–17. The results suggest that even though TCs are large synoptic systems, the introduction of VI scheme has a positive impact on the prediction of the location, movement, intensity and development of rain bands associated with the TCs. The initial vortex position and landfall position errors are reduced by ∼64% and ∼39% in VOTX simulations over CNTL, respectively. The mean track errors of all the four TCs are reasonably improved by ∼58% in VOTX over CNTL. The equitable threat score (ETS) and frequency bias are significantly improved in the VOTX for all the TC cases as compared to CNTL. Study results provide a positive proof of concept that the VI scheme within the NCUM-G can help to improve the simulation of track and intensity of TCs over BoB.

Dependence of Tropical Cyclone Intensification on the Coriolis Parameter

ABSTRACT The dependence of tropical cyclone (TC) intensification on the Coriolis parameter was investigated in an idealized hurricane model. By specifying an initial balanced vortex on an f-plane, we observed faster TC development under lower planetary vorticity environment than under higher planetary vorticity environment. The diagnosis of the model outputs indicates that the distinctive evolution characteristics arise from the extent to which the boundary layer imbalance is formed and maintained in the presence of surface friction. Under lower planetary vorticity environment, stronger and deeper subgradient inflow develops due to Ekman pumping effect, which leads to greater boundary layer moisture convergence and condensational heating. The strengthened heating further accelerates the inflow by lowing central pressure further. This positive feedback loop eventually leads to distinctive evolution characteristics. The outer size (represented by the radius of gale-force wind) and the eye of the final TC state also depend on the Coriolis parameter. The TC tends to have larger (smaller) outer size and eye under higher (lower) planetary vorticity environment. Whereas the radius of maximum wind or the eye size in the current setting is primarily determined by inertial stability, the TC outer size is mainly controlled by environmental absolute angular momentum.

Uniqueness of axisymmetric viscous flows originating from circular vortex filaments

The incompressible Navier-Stokes equations in R^3 are shown to admit a unique axisymmetric solution without swirl if the initial vorticity is a circular vortex filament with arbitrarily large circulation Reynolds number. The emphasis is on uniqueness, as existence has already been established in [10]. The main difficulty which has to be overcome is that the nonlinear regime for such flows is outside of applicability of standard perturbation theory, even for short times. The solutions we consider are archetypal examples of viscous vortex rings, and can be thought of as axisymmetric analogues of the self-similar Lamb-Oseen vortices in two-dimensional flows. Our method provides the leading term in a fixed-viscosity short-time asymptotic expansion of the solution, and may in principle be extended so as to give a rigorous justification, in the axisymmetric situation, of higher-order formal asymptotic expansions that can be found in the literature [7].

On the well-posedness of the inviscid multi-layer quasi-geostrophic equations

The inviscid multi-layer quasi-geostrophic equations are considered over an arbitrary bounded domain. The no-flux but non-homogeneous boundary conditions are imposed to accommodate the free fluctuations of the top and layer interfaces. Using the barotropic and baroclinic modes in the vertical direction, the elliptic system governing the streamfunctions and the potential vorticity is decomposed into a sequence of scalar elliptic boundary value problems, where the regularity theories from the two-dimensional case can be applied. With the initial potential vorticity being essentially bounded, the multi-layer quasi-equations are then shown to be globally well-posed, and the initial and boundary conditions are satisfied in the classical sense.

Control of jet using burst modulation by coaxial type DBD plasma actuator (Changes in jet diffusion process by applied voltage and burst frequency)

This study demonstrated jet control through the generation of an intermittently induced flow via burst-modulation from a coaxial type, axisymmetric nozzle shape DBD plasma actuator (DBD-PA). Here, a lock-in phenomenon occurred and was characterized by synchronization of the burst-frequency (frequency of burst-modulation) and the jet-generated vortex within a specific burst-frequency range, which aimed to clarify the change in the development process of the jet by the driving condition of the DBD-PA where the applied voltage and burst-frequency were varied. In the main text of this study the Reynolds number that is based on mean velocity and nozzle diameter of the jet was set at 5000. The applied voltages for DBD-PA were Vp-p = 16 kV, 14 kV, and 12 kV, while the burst-frequency was fburst = 0.2–2.0fn ( fn: frequency of occurrence of the initial vortex of free jet is 716 Hz). Results of the control demonstration showed that the lock-in phenomenon occurred at 0.9–1.4fn for all applied voltages. In the downstream, when the driving condition was Vp-p = 14 kV and fburst = 0.7fn, diffusion was dominant in all driving conditions due to fast collapse of the developed vortex ring. Moreover, such collapse was gradual with higher applied voltage. At the end of the burst-frequency of the lock-in phenomenon range, where the driving conditions was Vp-p = 16 kV and fburst = 1.4fn, diffusion became more suppressed as compared to the free jet, as the vortex ring near the nozzle collapsed due to vortices pairing, and did not develop. This work emphasizes that changing the applied voltage and the burst-frequency of DBD-PA potentially promotes and suppresses the diffusion of the jet.

Study on the gas–liquid annular vortex flow for liquid unloading of gas well

Vortex tool is a new technique for the liquid unloading in gas wells. But it lacks a mathematical model to describe and predict the effect of vortex tools. In the present work, according to the axial, radial and circumferential momentum balance of the gas phase and liquid phase, the governing equations of vortex flow model have been established. Then thickness of liquid film and gas and liquid vortex flow intensity as well as the pressure drop gradient can be calculated. The calculation results and the previous experiments indicate that the pressure drop of the gas–liquid flow can be reduced by 5% ~ 25% with the vortex tool, and the vortex flow model has an average relative difference of 6.01%. The model results show that there are two mechanisms for reducing the pressure drop under the vortex flow condition. In addition, the research results show that vortex tools with bigger helical angle will lead to higher vortex flow intensity. The decay rate of vortex flow intensity decreases along the pipe as liquid velocity increases and the vortex flow working distance can be calculated by the vortex intensity gradient and initial vortex flow intensity.

Towards a finite-time singularity of the Navier–Stokes equations Part 1. Derivation and analysis of dynamical system

The evolution towards a finite-time singularity of the Navier–Stokes equations for flow of an incompressible fluid of kinematic viscosity$\unicode[STIX]{x1D708}$is studied, starting from a finite-energy configuration of two vortex rings of circulation$\pm \unicode[STIX]{x1D6E4}$and radius$R$, symmetrically placed on two planes at angles$\pm \unicode[STIX]{x1D6FC}$to a plane of symmetry$x=0$. The minimum separation of the vortices,$2s$, and the scale of the core cross-section,$\unicode[STIX]{x1D6FF}$, are supposed to satisfy the initial inequalities$\unicode[STIX]{x1D6FF}\ll s\ll R$, and the vortex Reynolds number$R_{\unicode[STIX]{x1D6E4}}=\unicode[STIX]{x1D6E4}/\unicode[STIX]{x1D708}$is supposed very large. It is argued that in the subsequent evolution, the behaviour near the points of closest approach of the vortices (the ‘tipping points’) is determined solely by the curvature$\unicode[STIX]{x1D705}(\unicode[STIX]{x1D70F})$at the tipping points and by$s(\unicode[STIX]{x1D70F})$and$\unicode[STIX]{x1D6FF}(\unicode[STIX]{x1D70F})$, where$\unicode[STIX]{x1D70F}=(\unicode[STIX]{x1D6E4}/R^{2})t$is a dimensionless time variable. The Biot–Savart law is used to obtain analytical expressions for the rate of change of these three variables, and a nonlinear dynamical system relating them is thereby obtained. The solution shows a finite-time singularity, but the Biot–Savart law breaks down just before this singularity is realised, when$\unicode[STIX]{x1D705}s$and$\unicode[STIX]{x1D6FF}/\!s$become of order unity. The dynamical system admits ‘partial Leray scaling’ of just$s$and$\unicode[STIX]{x1D705}$, and ultimately full Leray scaling of$s,\unicode[STIX]{x1D705}$and$\unicode[STIX]{x1D6FF}$, conditions for which are obtained. The tipping point trajectories are determined; these meet at the singularity point at a finite angle. An alternative model is briefly considered, in which the initial vortices are ovoidal in shape, approximately hyperbolic near the tipping points, for which there is no restriction on the initial value of the parameter$\unicode[STIX]{x1D705}$; however, it is still the circles of curvature at the tipping points that determine the local evolution, so the same dynamical system is obtained, with breakdown again of the Biot–Savart approach just before the incipient singularity is realised. The Euler flow situation ($\unicode[STIX]{x1D708}=0$) is considered, and it is conjectured on the basis of the above dynamical system that a finite-time singularity can indeed occur in this case.

Anisotropic minimum-dissipation (AMD) subgrid-scale model implemented in OpenFOAM: Verification and assessment in single-phase and multi-phase flows

Minimum-dissipation sub-grid models represent simple alternatives to the Smagorinsky-type approaches to the implementation of sub-grid scales’ (SGS) effects in the large-eddy simulation (LES) approach. Recently, the anisotropic minimum-dissipation (AMD) model has been introduced, which is a static type of eddy-viscosity SGS model and is a new addition to this family. This model is easy to implement; furthermore, not only can it consider the effect of various directions in computing sub-grid stress, it can also operate transitional flows from laminar to turbulent. For the first time, we implemented AMD in the open source package OpenFOAM. Foremost, we verified the OpenFOAM implementation of the AMD model for the prediction of isotropic decaying turbulence, a temporal mixing layer and an internal channel flow. To achieve this, decaying turbulence was considered for the isotropic turbulence produced by a grid with a mesh size of 5.08 × 10–2 m in a flow of mean velocity of 10 m/s. The temporal mixing layer was simulated at a Reynolds number based on half the initial vorticity thickness of 105. Channel flow was investigated at the three frictional Reynolds numbers of 180, 395 and 590. The verification results revealed that the implemented AMD model in OpenFOAM offered satisfactory accuracy to capture decaying turbulence and temporal mixing layer and calculate boundary layer velocity profiles and first and second-order turbulent parameters in the channel flow on anisotropic grids. Following this, for the first time, we evaluated AMD's performance in predicting external non-cavitating and cavitating flows over a 3D sphere. Non-cavitating and cavitating flow over the sphere were considered at Re = 2 × 104 and Re = 1.5 × 106, respectively. The AMD results were then compared with the direct numerical simulation (DNS) data and the numerical results obtained from the established SGS models such as dynamic Smagorinsky (DS), one equation eddy viscosity model (OEEVM), detached eddy simulation (DES), and delayed detached eddy simulation (DDES), where applicable. In treating sphere flow, in spite of the use of a coarse grid rather than the alternative SGS models, the AMD model predicted accurate results for pressure coefficient, shear stress, and separation point location over the sphere as well as the velocity profile in the wake region. It was detected that the simulation time of the AMD model was lower than that of DS in all the considered test cases by approximately 10–16%.

Experimental Investigations on the Interaction of the Single/Co-Rotating Vortex with the Ground

Experiments on the interactions between a single vortex/co-rotating vortices and the ground were conducted in a water channel using particle image velocimetry (PIV) measurements. Both the single vortex (SNV) and co-rotating vortex pair (CVP) were generated by using NACA0012 vortex generators to simulate the main flow features behind one side of the wings at the farfield and near field. The ground effect was achieved by allocating a flat plate downstream of the vortex generators. It has been found that the lower initial vortex height led to greater vortex rebound and lateral drift in both the SNV and CVP cases, whereas the development of a secondary vortex was also promoted with lower initial vortex height. In the CVP cases, the mutual rotation of the primary vortices led to variation of the close-to-wall velocity distribution. This effect added the disturbances to the formation and evolution of the secondary vortical structure, which eventually affected the height of the secondary vorticity and the rebound of the primary vortices.

Sensitivity of Tropical Cyclone Intensification to Axisymmetric Heat Sources: The Role of Low-Level Heating and Cooling from Different Microphysical Processes

Abstract Latent heat release from condensational heating has been recognized as one of the dominating energy sources of a tropical cyclone. Here we argue that other microphysical processes may also play an important role. From an analysis of a real-case simulation of Hurricane Katrina (2005), it was found that cooling from evaporation and melting of some frozen hydrometeors radially outside the eyewall region can have similar magnitudes as condensational heating. Based on this finding, idealized thermally forced experiments were performed. The specified heating and cooling functions mimic those found in the Hurricane Katrina run. The results indicated that the addition of cooling enhances the lower-level inward radial winds, which in turn increases the acceleration of the lower-level tangential winds through an enhanced transport of absolute vorticity. Sensitivity experiments on varying the structure of the cooling functions and the background state of the vortex demonstrate that the lower-level tangential wind acceleration is more sensitive to changes in the vertical structure and location of the cooling than the radial characteristics. In addition, the lower-level acceleration is sensitive to variations in the inertial and static stabilities rather than the vertical tangential wind shear of the initial vortex and its environment.

On annihilation of the relativistic electron vortex pair in collisionless plasmas

In contrast to hydrodynamic vortices, vortices in a plasma contain an electric current circulating around the centre of the vortex, which generates a magnetic field localized inside. Using computer simulations, we demonstrate that the magnetic field associated with the vortex gives rise to a mechanism of dissipation of the vortex pair in a collisionless plasma, leading to fast annihilation of the magnetic field with its energy transforming into the energy of fast electrons, secondary vortices and plasma waves. Two major contributors to the energy damping of a double vortex system, namely, magnetic field annihilation and secondary vortex formation, are regulated by the size of the vortex with respect to the electron skin depth, which scales with the electron$\unicode[STIX]{x1D6FE}$factor,$\unicode[STIX]{x1D6FE}_{e}$, as$R/d_{e}\propto \unicode[STIX]{x1D6FE}_{e}^{1/2}$. Magnetic field annihilation appears to be dominant in mildly relativistic vortices, while for the ultrarelativistic case, secondary vortex formation is the main channel for damping of the initial double vortex system.

Dynamic Stall Flow Structure and Forces on Symmetrical Airfoils at High Angles of Attack and Rotation Rates

This article describes a direct comparison between two symmetrical airfoils undergoing dynamic stall at high, unsteady reduced frequencies under otherwise identical conditions. Particle image velocimetry (PIV) was performed to distinguish the differences in flow structure between a NACA 0021 and a NACA 0012 airfoil undergoing dynamic stall. In addition, surface pressure measurements were performed to evaluate aerodynamic load and investigate the effect of laminar separation bubbles and vortex structures on the pressure fields surrounding the airfoils. Airfoil geometry is shown to have a significant effect on flow structure development and boundary layer separation, with separation occurring earlier for thinner airfoil sections undergoing constant pitch-rate motion. Inertial forces were identified to have a considerable impact on the overall force generation with increasing rotation rate. Force oscillation was observed to correlate with multiple vortex structures shedding at the trailing-edge during high rotation rates. The presence of laminar separation bubbles on the upper and lower surfaces was shown to dramatically influence the steady-state lift of both airfoils. Poststall characteristics are shown to be independent of airfoil geometry such that periodic vortex shedding was observed for all cases. However, the onset of deep stall is delayed with increased nondimensional pitch rate due to the delay in initial dynamic-stall vortex.

Global solvability for two-dimensional filtered Euler equations with measure valued initial vorticity

We study the filtered Euler equations that are the regularized Euler equations derived by filtering the velocity field. The filtered Euler equations are a generalization of two well-known regularizations of incompressible inviscid flows, the Euler-$\alpha$ equations and the vortex blob method. We show the global existence of a unique weak solution for the two-dimensional (2D) filtered Euler equations with initial vorticity in the space of Radon measure that includes point vortices and vortex sheets. Moreover, a sufficient condition for the global well-posedness is described in terms of the filter and thus our result is applicable to various filtered models. We also show that weak solutions of the 2D filtered Euler equations converge to those of the 2D Euler equations in the limit of the regularization parameter provided that initial vorticity belongs to the space of bounded functions.

Self-Similar Multimode Bubble-Front Evolution of the Ablative Rayleigh-Taylor Instability in Two and Three Dimensions.

The self-similar nonlinear evolution of the multimode ablative Rayleigh-Taylor instability (ARTI) is studied numerically in both two and three dimensions. It is shown that the nonlinear multimode bubble-front penetration follows the α_{b}A_{T}(∫sqrt[g]dt)^{2} scaling law with α_{b} dependent on the initial conditions and ablation velocity. The value of α_{b} is determined by the bubble competition theory, indicating that mass ablation reduces α_{b} with respect to the classical value for the same initial perturbation amplitude. It is also shown that ablation-driven vorticity accelerates the bubble velocity and prevents the transition from the bubble competition to the bubble merger regime at large initial amplitudes leading to higher α_{b} than in the classical case. Because of the dependence of α_{b} on initial perturbation and vorticity generation, ablative stabilization of the nonlinear ARTI is not as effective as previously anticipated for large initial perturbations.

Impact of hydrodynamics on clay particle deposition and biofilm development in a labyrinth-channel dripper

To better understand the physical and biological clogging in drip-irrigation, a study was conducted on the impacts of hydrodynamic conditions on clay particle deposition and biofilm development in drippers using an optical method. A transparent milli-fluidic system composed of labyrinth channels was used to identify areas most susceptible to particle clogging using two different types of clay suspensions: sodium bentonite and kaolin. The impact of salt addition [(NaCl) = 200 mg L− 1] on the clay deposition was also analyzed. Biofilm development was studied using the same methodology using a nutritive solution (chemical oxygen demand, COD = 200 mg L−1). In addition, fluid dynamics simulations were performed along the labyrinth channel to understand the effect of flow behaviour on the fouling. Computational fluid dynamics results show two types of flow topology: high velocity in the main flow (around 1 m s− 1) and low velocity in the vortex zones (less than 0.2 m s− 1) found in the channel corners. Using an optical method, kaolin deposition and biofilm growth in the dripper were observed to occur mainly in the inlet channel and initial vortex zones, which are characterized by lower mean velocity and turbulent kinetic energy values. This part of the dripper can be considered as a bottleneck that amplifies the fouling phenomena and which should be optimized. With the addition of NaCl, kaolin particles tend to form bigger flocs. Therefore, more significant particle deposition is observed, but this is not the case of bentonite for which no fouling is observed along the dripper.

Metastability of Kolmogorov Flows and Inviscid Damping of Shear Flows

First, we consider Kolmogorov flow (a shear flow with a sinusoidal velocity profile) for 2D Navier-Stokes equation on a torus. Such flows, also called bar states, have been numerically observed as one type of metastable states in the study of 2D turbulence. For both rectangular and square tori, we prove that the non-shear part of perturbations near Kolmogorov flow decays in a time scale much shorter than the viscous time scale. The results are obtained for both the linearized NS equations with any initial vorticity in L^2, and the nonlinear NS equation with initial L^2 norm of vorticity of the size of viscosity. In the proof, we use the Hamiltonian structure of the linearized Euler equation and RAGE theorem to control the low frequency part of the perturbation. Second, we consider two classes of shear flows for which a sharp stability criterion is known. We show the inviscid damping in a time average sense for non-shear perturbations with initial vorticity in L^2. For the unstable case, the inviscid damping is proved on the center space. Our proof again uses the Hamiltonian structure of the linearized Euler equation and an instability index theory recently developed by Lin and Zeng for Hamiltonian PDEs.