Vortex Instability Research Articles

Quantum vortex instability and black hole superradiance

Vortices and black holes set the scene for many interesting dynamical processes in physics. Here, we study the dynamical instability of quantized vortices and rotational superradiance around rotating black holes, illustrating in the process that the same physics is at play in these two seemingly disparate phenomena. We also compare the instability of the vortex to the black hole bomb instability, which occurs for massive scalar fields in the Kerr spacetime. Taking inspiration from the analogy between black hole bomb modes and the hydrogen spectrum, the vortex instability is compared with nuclear resonances involved in $\ensuremath{\alpha}$ decay.

Closely spaced co-rotating helical vortices: long-wave instability

We consider as base flow the stationary vortex filament solution obtained by Castillo-Castellanos et al. (Phys. Rev. Fluids, vol. 6, 2021, 114701) in the far wake of a rotor with tip-splitting blades. The cases of a single blade and of two blades with a hub vortex are studied. In these solutions, each blade generates two closely spaced co-rotating tip vortices that form a braided helical pattern in the far wake. The long-wave stability of these solutions is analysed using the same vortex filament framework. Both the linear spectrum and the linear impulse response are considered. We demonstrate the existence of different types of instability modes. A first type corresponds to the local pairing of consecutive turns of the helical pattern, which is well described by the instability of a uniform helical vortex with a core size given by the mean separation distance of the vortices in the pair. A second type corresponds to the pairing of consecutive turns of the vortex pair and is observed only for densely braided patterns, which is well described by the instability of two interlaced helical vortices by straightening out the baseline helix. A third type of unstable modes modifies the separation distance between the vortices in each pair and amplifies specific (linear) wavelengths. These unstable modes also spread spatially with a weaker rate.

Numerical dissipation control of a hybrid large-particle method in vortex instability problems

Current trends in the development of numerical schemes are associated with a decrease in dissipative and dispersion errors, as well as an improvement in the grid convergence of the solution. Achieving the computational properties is not an easy problem since a decrease in scheme viscosity is often associated with an increase in the oscillations of gas dynamic parameters. The paper presents a study of the issues of numerical dissipation control in gas dynamics problems in order to increase the resolution in numerical reproduction of vortex instability at contact boundaries. To solve this problem, a hybrid large-particle method of the second order of approximation in space and time on smooth solutions is used. The method is constructed with splitting by physical processes in two stages: gradient acceleration and deformation of the finite volume of the medium; convective transfer of the medium through its facets. An increase in the order of approximation in time is achieved by a time correction step. The regularization of the numerical solution of problems at the first stage of the method consists in the nonlinear correction of artificial viscosity which, regardless of the grid resolution, tends to zero in the areas of smoothness of the solution. At the stage of convective transport, the reconstruction of fluxes was carried out by an additive combination of central and upwind approximations. A mechanism for regulating the numerical dissipation of the method based on a new parametric limiter of artificial viscosity is proposed. The optimal adjustment of the method by the ratio of dissipative and dispersive properties of the numerical solution is achieved by setting the parameter of the limiting function. The efficiency of the method was tested on two-dimensional demonstrative problems. In one of them, the contact surfaces are twisted into a spiral on which the Kelvin-Helmholtz vortex instability develops. Another task is the classic problem with a double Mach reflection of a strong shock wave. Comparison with modern numerical schemes has shown that the proposed variant of the hybrid large-particle method has a high competitiveness. For example, in the problem with double Mach reflection, the considered version of the method surpasses in terms of vortex resolution the popular WENO (Weighted Essentially Non-Oscillatory) scheme of the fifth order and is comparable to the numerical solution of WENO of the ninth order of approximation. The proposed method can be the basis of a convective block of a numerical scheme when constructing a computational technology for modeling turbulence.

Depth effects on the cavity induced transition at hypersonic speed by DNS

Cavity-induced transition (CIT) in a hypersonic boundary layer was simulated by employing direct numerical simulation (DNS). The upwind Roe scheme was discretized by high-order minimum dispersion and controllable dissipation (MDCD) reconstruction based on high-quality multi-block structured grids. The grid scale and time step are determined after evaluating the grid scale and nondimensional time step and comparing with the available measurements. Four depths, 1.0, 1.5, 2.0, and 2.5, multiplied by the baseline depth (D), are evaluated to determine their effects on the CIT on the wall after the cavity. The baseline is a typically “closed” cavity and the width of turbulent region at one cavity length downstream cavity (x = 2L) is 67 mm, caused by the strong adverse pressure gradient and horseshoe vortex instability. Typically, the other three are “open” cavities with no transition for the 1.5D cavity, a turbulent region width of 26 mm for the 2.0D cavity, and 45 mm for the 2.5D cavity at x = 2L were obtained after the cavity. Moreover, the relationship between the flow structures and a typical high heat flux region is explored. Reattachment supplies heat to the wall, and separation removes heat from the wall.

Lagrangian Identification of Coherent Structures and Mass Transport in a Buoyant Jet Diffusion Flame

ABSTRACT Using Lagrangian coherent structures (LCSs), the mass transport process of large-scale coherent structures in a buoyant jet diffusion flame is studied numerically to gain a key understanding of combustion instability. First, the reacting flow fields of the jet diffusion flame are numerically simulated for two cases, a stable case without considering the buoyancy effect and an unstable case that includes the buoyancy effect corresponding to combustion instability. In particular, large-scale Kelvin-Helmholtz instability (KHI) vortex structures outside the flame surface are captured in the unstable case. Then, the ridges in finite-time Lyapunov exponent (FTLE) fields that sketch the distinct regions in the reacting flow field are extracted as LCSs. The mass transport process is studied by comparing the distribution of LCSs with reaction fields. The flame surface is found to coincide with the attracting LCSs, which separate the fuel and air on opposite sides of the flame surface. In contrast, the reaction products, including species and reaction heat, are confined in the boundaries consisting of repelling LCSs on the inner and outer sides of the flame surface. Finally, the evolution of LCSs is tracked to analyze the generation of KHI vortices and species transport in the jet diffusion flame. With the aid of LCSs, it is found that there exist some saddle-type flow features separating the distinct flow structures into several regions, and the jet fuel and airflow enter into the separated regions from different open boundaries. Importantly, the attracting LCSs in the separated regions then bulge outwards, forming KHI vortices as the attracting LCSs further stretch and fold. Furthermore, the vortices continue moving upwards while species flow from repelling LCSs to attracting LCSs, leading to mixing. These results show that attracting and repelling LCSs can act as the flame surface and the mass and energy transport boundary of the reaction products, respectively. In summary, the work presented can provide a new method in combustion controlling to estimate the location of the flame surface and the transport boundaries of species from the velocity field, by using LCSs.

Hybrid RANS/LES study of tip leakage vortex instability and turbulence characteristics of a transonic turbine cascade

To conduct detailed investigations about vortex instability and turbulence characteristics near a transonic turbine tip region, a highly accuracy hybrid Reynolds averaged Navier Stokes (RANS) / large eddy simulation (LES) method, namely detached eddy simulation (DES)-type method, is adopted at the exit isentropic Mach number of 0.95. Validation results show that this hybrid method can provide an accurate prediction against experiments. In contrast with the RANS method, this method can exhibit superiority in capturing detailed small-scale flow structures and more realistic turbulence distribution. Based on various identification methods, two predominant instability patterns of tip leakage vortex (TLV), namely, vortex wandering and breakdown have been recognized successfully in its downstream progression. Due to the supplement of tip leakage flow (TLF), the TLV maintains a concentrated vortex morphology with a monotonically increasing transverse wandering magnitude inside the blade passage. Subsequently, the TLV breakdown phenomenon, which is mainly due to the high adverse pressure gradient aggravated by shock waves, can be observed downstream the trailing edge. Meanwhile, a “spiral-type” vortex breakdown is distinguished firstly in a transonic turbine environment, which cannot be found in the previous RANS literature. To investigate the nature of the vortex instability, we perform an analysis based on the vorticity transport equation, it's found that the convection term due to the velocity gradient dominated the leakage vorticity damping. Combined the triple decomposition with the proper orthogonal decomposition (POD) method, the mechanisms of vortex wandering have been further revealed, which exhibits non-zero perturbations in transverse modes and a helical mode in the streamwise direction. Furthermore, detailed analysis of the turbulence characteristics has been also conducted, which contains distributions of Reynolds stress terms and the turbulent kinetic energy (k) along the TLV core trajectory. It can be recognized that the high adverse pressure gradient by shock waves can result in a sharp increase of Reynolds normal stresses (τii), which can stretch the TLV in different directions and exerts detrimental effects on the vortex breakdown. As a complementary, the turbulent anisotropy is also evaluated by the Lumley triangle method, which exhibits a variation from the one-component anisotropy to a two-component morphology as the TLV migrating downstream, while a isotropic turbulence field may be formed downstream the trailing edge due to the intense mixing. Predicted turbulence characteristics, vortical instabilities, and their flow mechanism can provide guide towards lower loss design and flow control of the turbine blade.

The stability of wakes of floating wind turbines

Floating offshore wind turbines (FOWTs) are subjected to platform motion induced by wind and wave loads. The oscillatory movement trigger vortex instabilities, modifying the wake structure and influencing the flow reaching downstream wind turbines. In this work, the wake of a FOWT is analyzed by means of numerical simulations and a comparison with linear stability theory. Two simplified models based on the stability of vortices are developed for all degrees of freedom of turbine motion. In our numerical simulations, the wind turbine blades are modeled as actuator lines and a spectral-element method with low dispersion and dissipation is employed to study the evolution of the perturbations. The turbine motion excites vortex instability modes predicted by the linear stability of helical vortices. The flow structures that are formed in the non-linear regime are a consequence of the growth of these modes and preserve some of the characteristics that can be explained and predicted by the linear theory. The number of vortices that interact and the growth rate of disturbances are well predicted by a simple stability model of a two-dimensional row of vortices. For all types of motion, the highest growth rate is observed when the frequency of motion is one and a half the frequency of rotation of the turbine that induces the out-of-phase vortex pairing mechanism. For lower frequencies of motion, several vortices coalesce to form large flow structures, which cause the high amplitude of oscillations in the streamwise velocities, which may increase fatigue or induce high amplitude motion on downstream turbines.

On the near-wall instability of oblique flow over a wavy wall

The instability of a shear flow passing over a wavy wall with wave crests not perpendicular to the flow direction is investigated. The friction Reynolds number for the flow is large and the wave amplitude scaled on the wavelength is small compared with the viscous wall layer. The instability takes the form of a streamwise vortex of wavelength comparable to the viscous wall layer in which the basic flow adjusts to the presence of the wall. For a given wall amplitude, the instability considered is the first one to arise as the Reynolds number is increased and modes of wavelength comparable to the viscous layer grow much faster than modes of wavelength comparable to the wall wavelength. The instability is not driven by centrifugal or viscous effects but is a novel kind of cross-flow vortex instability associated with a spatially periodic flow; the existence of the instability is associated with the orientation of the wave crests. The instability is investigated for wavelengths comparable to the depth of the viscous wall layer; the limiting cases of large and small wavelengths are investigated asymptotically. At small wavenumbers and roughness heights the instability connects with disturbances of wavelength comparable to the wall wavelength. At high wavenumbers and roughness heights a new structure emerges and the disturbance moves away from the wall, that structure takes on a self-similar form with progressively faster variations in the streamwise and spanwise directions as the roughness height increases.

Application of the Turbulent Vortex Dynamo Theory for Early Diagnostics of the Tropical Cyclone Genesis

The climate change is becoming more and more obvious, which leads to an increase in the number of intense atmospheric vortices (tropical and quasi-tropical cyclones, polar hurricanes, tornadoes) and an expansion of the geographical and seasonal limits of their occurrence. A recent example was the quasi-tropical cyclone in the Black Sea on August 11–16, 2021. Under these conditions, the accurate diagnosis of cyclogenesis is extremely important and, based on it, the forecast of further evolution and the trajectory of the forming vortex. The main source of energy for tropical, quasi-tropical and polar hurricanes is thermal convection caused by significant temperature differences between the atmospheric layer and the underlying water surface. This allows us to propose a unified approach for the diagnosis of cyclogenesis in all three cases.For the first time, an original approach is proposed for determining the exact time of the onset of tropical cyclogenesis. This approach includes a combined analysis of satellite images of cloudiness and the corresponding data of cloud-resolving numerical modeling for the region of developing vortex disturbance. The theoretical basis is the fundamental hypothesis of a turbulent vortex dynamo. The theory provides quantitative criteria that determine the excitation of large-scale vortex instability in the atmosphere. Atmospheric numerical modeling makes it possible to accurately determine the moment of time at which the necessary conditions for the onset of instability are realized. This moment is interpreted as the beginning of cyclogenesis. The specific configurations of vortical cloud convection found in the work, which correspond to the initial stage of cyclogenesis, can be used in operational meteorological diagnostics when analyzing satellite images of cloudiness. The approach is illustrated by the example of diagnostics of tropical cyclogenesis.

Evolution of double-eye wall hurricanes and emergence of complex tripolar end states in moist-convective rotating shallow water model

A detailed investigation of linear instabilities of double-eyewall hurricane-like vortices with double maxima (“walls”) of azimuthal velocity and vorticity around the central minimum (“eye”) and of their nonlinear saturation is carried out in the framework of the moist-convective rotating shallow water model. It is shown that developing barotropic instability leads to inward displacement and gradual disappearance of the inner wall and to the formation of a nontrivial tripolar quasi-stationary structure, provided the second, outer, wall of the initial vortex is high enough. The effects of moist convection lead to the enhancement of the outer wall. In comparison, under the influence of the same instability, vortices with an inner wall stronger than the outer one evolve toward monopolar single-eyewall structures.

Modal analysis of non-ducted and ducted propeller wake under axis flow

Modal decomposition techniques, flow field, and spectral analysis are employed to investigate the wake dynamics and destabilization mechanisms of a four-bladed marine propeller with or without a nozzle. Numerical simulations are conducted using the delayed detached eddy simulation model for the wake and the arbitrary mesh interface method for the blade rotation. The presence of the nozzle significantly reduces the wake's streamwise velocity, delays the wake destabilization, increases the wake length, and changes the morphologies of wake vortices. In particular, the hub vortex in the ducted propeller wake is broken down into chaotic turbulence by the perturbation of the backflow. Two modal decomposition methods, namely, proper orthogonal decomposition and dynamic mode decomposition, are used to decompose the vorticity magnitude in the rotor wake field. From modal analysis, the spatial scale of flow phenomena decreases with the increase in modal frequency. Underlying destabilization mechanisms in the wake correspond to some characteristic frequencies. The interaction of each sheet vortex with the previously shed tip (leakage) vortices occurs at blade passing frequency (BPF). The pairing of adjacent tip (leakage) vortices occurs at half-BPF. The long-wave instability of the hub vortex and the wake meandering are stochastic processes, each of which occurs at a frequency lower or equal to shaft frequency. These four destabilization mechanisms can approximately reconstruct the large-scale flow phenomena in the wake. Moreover, each sheet vortex's alternating connection and disconnection with the previously shed tip (leakage) vortices cause the short-wave instability of the tip (leakage) vortices and generate the secondary vortices. The radial expansion motion of large-scale helical vortices in the outer slipstream dominates the wake meandering phenomenon.

Recovery in the wake of in-line axial-flow rotors

The flow around the rotor of an axial turbine, operating in the wake of an upstream one, is resolved using large-eddy simulation on a cylindrical grid consisting of 3.8 billion points. Three distances from the upstream rotor are considered, ranging from 6 to 10 diameters. The inflow boundary conditions for the simulation of the downstream rotor were generated by a precursor simulation of the upstream one. The impact on the dynamics of the tip vortices and the statistics at their core is compared across cases. Results demonstrate the strong sensitivity of the tip vortices shed by the downstream rotor to the disturbance produced by the wake of the upstream one. The onset of their instability moves very close to the rotor plane and is almost independent of the distance between the upstream and downstream rotors, at least in the range of simulated distances. This makes the development of the wake of the downstream rotors, driven by the instability of the tip vortices, much faster and very similar across distances from the upstream one. The results explain the phenomena of performance stabilization of downstream turbines in linear arrays, recently reported in the literature.

Size and temperature-dependent stability of polarization vortex in PbTiO3 nanosheet under uniaxial tension or compression

ABSTRACT The stability of polarization vortex is absolutely crucial to the service performance of promising ferroelectric storage devices. Some phase field simulations were conducted on the PbTiO3 nanosheets with an initial polarization vortex under uniaxial tension or compression to investigate the conditions and types of vortex instability as well as the effects of the nanosheet size and temperature on them. The instability of polarization vortex has strong size and temperature dependence. The critical tensile stress decreases with increasing nanosheet size, and only the α-type vortex instability is observed in tensile nanosheets. However, the critical compressive stress first increases and then decreases with increasing nanosheet size, and there exists a peak size. The β-type (including β1 and β2-type) instability occurs when the nanosheet size is less than the peak size, but the α-type instability occurs when the nanosheet size is larger than the peak size. An elevated temperature reduces the critical tensile and compressive stresses, but increases the peak size. These are very important for design of promising nano-ferroelectric devices as high density memories.

Wake oscillator modeling the combined instability of vortex induced vibration and galloping for a 2:1 rectangular cylinder

Reasonable success has been obtained in the literature using Tamura’s nonlinear wake-oscillator model to predict the combined instability arising from the interference of vortex induced vibration and galloping. However, the physical arguments concerning the near-wake behavior, which is a strong point of this model, have never been carefully examined for sharp-edged bluff bodies. This is tackled here, referring to a rectangular cylinder with a side ratio of two, which is known to be very prone to this type of instability, and for which new static and aeroelastic wind tunnel tests are carried out. Therefore, a few physically sound modifications of the equations are proposed and, based on flow measurements, the new version of the model is found to perform considerably better than previous formulations with respect to the local-effect equation, which links the Strouhal number and the characteristic length scales of the wake. Moreover, after a successful attempt to relate the near-wake geometric parameters of the model to specific and measurable wake length scales, a novel method is presented for a direct estimation from wake flow measurements of the key parameter f relating the unsteady force and the wake lamina rotation. This allows the derivation of all the aerodynamic parameters of the model from measurements on the stationary cylinder based on their physical meaning. Nevertheless, f is also calibrated through a set of aeroelastic tests for a high Scruton number. The two approaches provide consistent results, although the calibration procedure yields a somewhat larger value of f, slightly enhancing the prediction capabilities of the model, which are carefully assessed comparing the results with wind tunnel data for a wide range of Scruton numbers. This discrepancy can be explained based on some unconsidered effects in the wake-oscillator model, which are also discussed as a basis for a future development of Tamura’s model.

Sensitivity and downstream influence of the impinging leading-edge vortex instability in a bileaflet mechanical heart valve

Bileaflet mechanical heart valves (BMHV) create unphysiological turbulent flow. Such turbulent flow involves multiple instability mechanisms interacting with one another in a confined geometry. For instance, an impinging leading-edge vortex (ILEV) instability creates disturbances at the leading edge of the valve leaflets, while potentially promoting turbulence downstream of the BMHV (Zolfaghari and Obrist, Phys. Rev. Fluids, vol. 4, 2019). In this article, we use adjoint-based methods to study the structural sensitivity of the ILEV instability in the BMHV, and to quantify the role of this instability in the maximum disturbance energy growth in the wake of the BMHV. We first present a direct numerical simulation to show the effect of the ILEV instability on the turbulent flow in the wake of the valve. Second, we perform a modal linear stability analysis on a two-dimensional subdomain attached to the leading edge of one leaflet. We investigate the sensitivity of the global modes associated with this flow using their adjoints, and then show a passive control scenario using a local feedback source. This results in a partial improvement in the flow oscillations downstream of the leaflets. We finally present a non-modal approach to identify the optimal initial conditions for achieving maximum energy growth at arbitrary locations. We show that, for sufficiently large times, the optimal initial condition for highest energy growth in the wake points at the leading edge, which includes the ILEV instability. Our study illustrates that an improved leading-edge shape can effectively reduce turbulence in the wake of the BMHV.

The dynamics of the tip and hub vortices shed by a propeller: Eulerian and Lagrangian approaches

Large Eddy Simulation on a grid composed of 3.8 billion points is utilized to reproduce the wake of a marine propeller. Results are compared against Particle Imaging Velocimetry experiments. The study is based on a core analysis for the tip and hub vortices, using both Eulerian and Lagrangian methodologies. Results show that the instability of the tip vortices is first triggered by their shear with the wake of the neighboring blades. This promotes short- and long-wave oscillations of the trajectory of the tip vortices and eventually mutual inductance phenomena between them. Then, the process of instability and break-up of the coherence of the tip vortices is accelerated by the interaction with the hub vortex, which is the largest coherent structure shed by the propeller, dominating its wake system and expanding radially as the wake develops downstream. The break-up of the helical structures shed from the tip of the propeller blades results in a substantial increase of turbulence at the wake outer boundary and especially in its diffusion. This process is even enhanced by the energy provided by the hub vortex, associated with its fluctuations at low frequencies. The instability process of the hub vortex is slower than the one experienced by the tip vortices. Although the former develops growing fluctuations around the wake axis, it keeps coherent further downstream, in comparison with the latter. Therefore, within a few diameters from the propeller plane, turbulence at the wake axis keeps decreasing downstream of the onset of the hub vortex.

On the frequency selection mechanism of the low-Re flow around rectangular cylinders

In the flow past elongated rectangular cylinders at moderate Reynolds numbers, vortices shedding from the leading- and trailing-edge corners are frequency locked by the impinging leading-edge vortex instability. The present work investigates how the chord-based Strouhal number varies with the aspect ratio of the cylinder at a Reynolds number (based on the cylinder thickness and the free-stream velocity) of $Re=400$ , i.e. when locking is strong. Several two-dimensional, nonlinear simulations are run for rectangular and D-shaped cylinders, with the aspect ratio ranging from $1$ to $11$ , and a global linear stability analysis of the flow is performed. The shedding frequency observed in the nonlinear simulations is predicted fairly well by the eigenfrequency of the leading eigenmode. The inspection of the structural sensitivity confirms the central role of the trailing-edge vortex shedding in the frequency locking, as already assumed by other authors. Surprisingly, however, the stepwise increase of the Strouhal number with the aspect ratio reported by several previous works is not fully reproduced. Indeed, with increasing aspect ratio, two distinct flow behaviours are observed, associated with two flow configurations where the interaction between the leading- and trailing-edge vortices is different. These two configurations are fully characterised, and the mechanism of selection of the flow configuration is discussed. Lastly, for aspect ratios close to the jump between two consecutive shedding modes, the Strouhal number is found to present hysteresis, implying the existence of multiple stable configurations. Continuing the lower shedding-mode branch by increasing the aspect ratio, we found that the periodic configuration loses stability via a Neimark–Sacker bifurcation leading to different Arnold tongues. This hysteresis can explain, at least partially, the significant scatter of existing experimental and numerical data.

ДИНАМИЧЕСКОЕ ПОВЕДЕНИЕ РАКЕТНОГО ДВИГАТЕЛЯ ТВЕРДОГО ТОПЛИВА В ПРОЦЕССЕ ЭКСПУАТАЦИИ (ОБЗОР)

One of the problems that has been solved for more than 80 years is the dynamic behavior both during the development of a rocket engine and during operation, these are oscillations that occur in the combustion chamber. Gas vibrations and mechanical vibrations of the rocket engine elements can cause vibration loads, which, under certain conditions, leads to resonance phenome-na. This can cause engine failures. An analysis of the behavior of a rocket engine as a dynamic system with an assessment of frequency interactions over the entire time of its operation has not been completely resolved today. Various options for studying the dynamic behavior of a rocket engine, algorithms for determining natural oscillation frequencies are considered. The analysis of existing approaches for solving the problem of determining the dynamic behavior of the rocket engine was carried out. In various works, the mechanical vibrations of the engine housing or its elements, such as a sliding nozzle, are calculated using various methods. In a number of works, the structure is considered as a model of discrete masses, where the elements are connected through the stiffness and viscosity coefficients. In other cases, fluctuations of the gas flow during combustion in the combustion chamber are considered, methods of numerical simulation of the process are developed that take into account the features of vor-tex formation and instability of the gas flow, as well as dependence on the shape of the charge. However, the joint problem has not been solved; in the presented works, the mutual influence of the vibrations of the rocket engine case with the fuel and gas flow during operation is not considered. To get a complete picture of the dynamic loads experienced in a solid propellant rocket engine, this interaction must be taken into account.

Effect of vortex dynamics and instability characteristics on the induced drag of trailing vortices

In this paper, trailing vortices generated by three wingtip configurations, namely the M6 wing and the M6 wing with a blended or split winglet, are experimentally investigated using the Stereo Particle Image Velocimetry (SPIV) technology. Then, linear stability analysis is performed to investigate instability characteristics. Three corresponding trailing vortex patterns, including the isolated trailing vortex without wake (pattern v) and with wake (pattern v-w), co-rotating vortex pair (pattern v-v), are observed in experiments. The strength of trailing vortices, characterized by circulation, is reduced after installing winglets as expected, and the strength of pattern v-v can be further suppressed compared with pattern v-w. Moreover, instability characteristics, such as the eigenvalue spectrum and perturbation mode, are distinctive among these three vortex patterns. The distribution of eigenvalue spectrums indicates that pattern v and pattern v-w are temporally “marginally stable”, while pattern v-v is temporally “unstable.” The primary perturbation mode of pattern v and pattern v-w is the m=-1 helical mode, while |m|>1 for the case of pattern v-v. The effect of vortex dynamics and instability characteristics can be concluded in two aspects. Firstly, the value of induced drag is polluted by about 3% from vortex wandering since vortex wandering affects the tangential velocity and streamwise vorticity of trailing vortices. Secondly, the growth rate and penetration depth perturbation mode affect trailing vortex evolution and further affect induced drag. Specifically, the larger the growth rate and penetration depth are, the more turbulence injects inside the vortex core, thus leading to a quicker and more intense attenuation of trailing vortex, as well as a smaller induced drag. This finding can guide us to manipulate the induced drag in flow control.

Observation and modeling of high-<sup>7</sup>Be concentration events at the surface in northern Europe associated with the instability of the Arctic polar vortex in early 2003

Abstract. Events of very high concentrations of 7Be cosmogenic radionuclide have been recorded at low-elevation surface stations in the subpolar regions of Europe during the cold season. With an aim to investigate the mechanisms responsible for those peak 7Be events, and in particular to verify if they are associated with the fast descent of stratospheric air masses occurring during sudden stratospheric warming (SSW) events, we analyze 7Be observations at six sampling sites in Fennoscandia during January–March 2003 when very high 7Be concentrations were observed and the Arctic vortex was relatively unstable as a consequence of several SSW events. We use the GEOS-Chem chemistry and transport model driven by the MERRA-2 meteorological reanalysis to simulate tropospheric 7Be over northern Europe. We show that the model reasonably reproduces the temporal evolution of surface 7Be concentrations observed at the six sampling sites. Our analysis of model simulations, surface 7Be observations, atmospheric soundings of ozone and temperature and surface ozone measurements indicates that the 7Be peak observed in late February 2003 (between 20 and 28 February 2003) at the six sampling sites in Fennoscandia was associated with downward transport of stratospheric vortex air that originated during an SSW that occurred a few days earlier (between 18 and 21 February 2003).