Coherent Vortical Structures Research Articles

Passive control of vortex-shedding past finite cylinders under the effect of a free surface

Passive technologies for the control of the flow past bluff bodies have been widely studied. Most of these works have focused on high-aspect-ratio, wall-mounted, or infinitely long cylinders, leaving a gap for low-aspect-ratio bodies fully submerged or under the effect of a free water surface. This is the object of the present work. Detached-eddy simulations at a Reynolds number of 1000 have been carried out for infinitely long (case i) and low-aspect-ratio bodies. For the finite case, two configurations were investigated: bodies fully submerged in the flow, away from surface effects (case ii) and that involving a free surface, here represented by a fixed slip-allowing plane (case iii). These computations were conducted for the bare cylinder and the system is comprised of the same main body fitted with eight wake-control rods uniformly distributed around its perimeter. Results showed that the low-aspect-ratio cases relative to infinitely long structures (1) lowered mean drag and root mean square lift, (2) presented a less coherent wake topology, (3) had frontal rods that concentrated most of the hydrodynamic loads, (4) extended the formation length, and (5) although all cases developed larger hydrodynamic loads when the rods were fitted to the main body compared to the plain cylinder, the finite cases produced a lower increase. We show that these results are intrinsically related to end effects and associated with a less correlated wake lacking coherent vortical structures. Furthermore, we analyze the more accentuated streamwise vortices produced by the presence of the free surface in case iii compared with case ii.

Alignment rule and geometric confinement lead to stability of a vortex in active flow.

Vortices are hallmarks of a wide range of nonequilibrium phenomena in fluids at multiple length scales. In this work, we numerically study the whirling motion of self-propelled soft point particles confined in circular domain, and aim at addressing the stability issue of the coherent vortex structure. By the combination of dynamical and statistical analysis at the individual particle level, we reveal the persistence of the whirling motion resulting from the subtle competition of activity and geometric confinement. In the stable whirling motion, the scenario of the coexistence of the irregular microscopic motions of individual particles and the regular global whirling motion is fundamentally different from the motion of a vortex in passive fluid. Possible orientational order coexisting with the whirling are further explored. This work shows the stability mechanism of vortical dynamics in active media under the alignment rule in confined space and may have implications in creating and harnessing macroscale coherent dynamical states by tuning the confining geometry.

Исследование аэродинамических характеристик самолета при попадании в зону турбулентности ясного неба и вопросы безопасности полета

Shear flows in the atmosphere lead to formation of the clear-air turbulence (CAT) zones. These zones are having the characteristic horizontal size of 20 km to 2000 km and may be less than 1000 m thick making it difficult to detect them and create effective systems to find the bypass routes. Intense CAT zones could appear at the altitudes of up to 30 km and higher. The main CAT feature lies in the fact that it occurs not in the clouds, but in the clear sky with good visibility, where meteorological radar is unable to detect it, and the flight crew is unable to get prepared. Every year, about 750 cases of the aircraft entering the CAT zones are registered in the global civil aviation. This work constructs a grid solution that simulates the large-scale atmospheric turbulence based on the atmospheric profiles taken from the experiment within the framework of the boundary value problem for the Reynolds-averaged Navier – Stokes equations. On the basis of the obtained solution and within the frames of the engineering method, coherent vortex structures (CVS) are formed, interaction with which, assuming the hypothesis of the perturbed speed frozen field, makes it possible to evaluate possible increments in the aerodynamic forces and moments and to simulate a situation of the aircraft entering the CAT zones.

Innovative and automated method for vortex identification

Context.As a universally accepted definition of a vortex has not yet been established, the community lacks an unambiguous and rigorous method for identifying vortices in fluid flows. Such a method would be useful for conducting robust statistical studies on vortices in highly dynamical and turbulent systems such as the solar atmosphere.Aims.We aim to develop an innovative and robust automated methodology for the identification of vortices based on local and global characteristics of the flow, while avoiding the use of a threshold that could potentially prevent the detection of weak vortices in the process.Methods.We present a new method that combines the rigor of mathematical criteria with the global perspective of morphological techniques. The core of the method consists of an estimation of the center of rotation for every point of the flow that presents some degree of curvature in its neighborhood. For this purpose, we employed the Rortex criterion and combined it with morphological considerations of the velocity field. We then identified coherent vortical structures based on clusters of estimated centers of rotation.Results.We demonstrate that the Rortex is a more reliable criterion than the swirling strength and the vorticity for the extraction of physical information from vortical flows, because it measures the rigid-body rotational part of the flow alone and is not biased by the presence of pure or intrinsic shears. We show that the method performs well in the context of a simplistic test case composed of two Lamb-Oseen vortices. We combined the proposed method with a state-of-the-art clustering algorithm to build an automated vortex identification algorithm. The algorithm was applied to an artificial flow composed of multiple Lamb–Oseen vortices, with a random noisy background, and to the turbulent flow of a simulated magneto-hydrodynamical Orszag-Tang vortex test. The results demonstrate the reliability and accuracy of the method.Conclusions.The present automated vortex identification method can be considered a new tool for the detection and study of vortices in dynamical and turbulent (magneto)hydrodynamical flows. By applying the implemented algorithm to numerical simulations and observational data, as well as comparing it to existing detection methods, we seek to successively improve the reliability of the detections and, ultimately, our knowledge on swirling motions in the solar, stellar, and planetary atmospheres.

Direct numerical simulation of a transitional, cryogenic cavitating mixing layer of liquefied natural gas behind a flat splitter plate using a homogenous equilibrium mixture cavitation model

A major challenge in the design of liquefied natural gas (LNG) pumps is concerned with the accurate prediction of flow behaviour at off-design conditions where destructive phase change from liquid to vapor - named cavitation - at cryogenic conditions may emerge undesirably and downgrade the machine performance. As a first step of our research towards addressing this challenge, the present study employs a homogenous equilibrium mixture (HEM) –based cryogenic cavitation solver to run direct numerical simulation (DNS) of a fundamental case study of transitional cavitating mixing layer of LNG behind a 3D planar flat plate, which resembles actual conditions of flow behind the vanes of industrial LNG sub-merged pumps. Assessment of the preliminary findings shows that the mixing layer is mainly driven by different modes of the well-known Kelvin-Helmholtz (K–H) instabilities, which develop coherent vortex structures that tend to shed off periodically across the mixing layer. The cavity structures are formed via transient interactions of the shedding vortices, and in the meantime of their pairing processes. The shedding of cavities, which mostly appear as “horse-shoe” and “croissant”-shaped vapor structures, maintains by the unsteady sheet cavity formed on the splitter upper wall and the latent heat exchange mechanisms, beside the dominant K–H instabilities. The presence of three-dimensionality is found to enhance instability of the mixing layer by increasing the frequency of phase change successions.

How sensitive are Lagrangian coherent structures to uncertainties in data?

Lagrangian coherent structures (LCSs) are time-varying entities which capture the most influential transport features of a flow. These can for example identify groups of particles which have greatest stretching, or which maintain a coherent jet or vortical structure. While many different LCS methods have been developed, the impact of the inevitable measurement uncertainty in realistic Eulerian velocity data has not been studied in detail. This article systematically addresses whether LCS methods are self-consistent in their conclusions under such uncertainty for nine different methods: the finite time Lyapunov exponent, hyperbolic variational LCSs, Lagrangian averaged vorticity deviation, Lagrangian descriptors, stochastic sensitivity, the transfer operator, the dynamic Laplacian operator, fuzzy c-means clustering and coherent structure colouring. The investigations are performed for two different realistic data sets: a computational fluid dynamics simulation of a Kelvin–Helmholtz instability, and oceanographic data of the Gulf Stream region. Using statistics gleaned from stochastic simulations, it is shown that the methods which detect full-dimensional coherent flow regions are significantly more robust than methods which detect lower-dimensional flow barriers. Additional insights into which aspects of each method are self-consistent, and which are not, are provided.

Design of Rotary Wings with Passive Mitigation of Coherent Tip Vortex Roll-Up

A rotor blade radial loading profile is presented that aims to passively mitigate the formation of coherent tip vortex structures in the near-field of the rotor wake. The method leverages principles of Helmholtz’s theorems, where the strength of the vortex wake is proportional to radial gradients in the blade loading distribution. By avoiding such radial gradients, the near-field roll-up of the wake vortex can be mitigated. A pair of two-bladed rotor designs configured with the same thrust coefficient was produced using a finite-vortex rotary lifting line framework coupled to a constrained power optimization problem. A baseline rotor was designed based on a power-optimized approach, and a wake-optimized rotor was designed based on a power-optimized approach with an additional blade-root bending moment constraint. Phase-averaged stereoscopic particle image velocimetry data were acquired for each rotor operating in hover. The wake-optimized rotor blade produced a wake characterized by conical vortex sheets of significantly lower peak vorticity than the compact, helical tip vortices produced by the baseline design. The wake-optimized design exhibited increased axial velocities near the root that caused radial distortions of the wake flow structures, which were also found to decay at a faster rate than that for the baseline design.

Unsteady mechanisms in shock wave and boundary layer interactions over a forward-facing step

The flow over a forward-facing step (FFS) at $Ma_\infty =1.7$ and $Re_{\delta _0}=1.3718\times 10^{4}$ is investigated by well-resolved large-eddy simulation. To investigate effects of upstream flow structures and turbulence on the low-frequency dynamics of the shock wave/boundary layer interaction (SWBLI), two cases are considered: one with a laminar inflow and one with a turbulent inflow. The laminar inflow case shows signs of a rapid transition to turbulence upstream of the step, as inferred from the streamwise variation of $\langle C_f \rangle$ and the evolution of the coherent vortical structures. Nevertheless, the separation length is more than twice as large for the laminar inflow case, and the coalescence of compression waves into a separation shock is observed only for the fully turbulent inflow case. The dynamics at low and medium frequencies is characterized by a spectral analysis, where the lower frequency range is related to the unsteady separation region, and the intermediate one is associated with the shedding of shear layer vortices. For the turbulent inflow case, we furthermore use a three-dimensional dynamic mode decomposition to analyse the individual contributions of selected modes to the unsteadiness of the SWBLI. The separation shock and Görtler-like vortices, which are induced by the centrifugal forces in the separation region, are strongly correlated with the low-frequency unsteadiness in the current FFS case. Similarly as observed previously for the backward-facing steps, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode than for SWBLI in flat plate and ramp configurations.

Assessment of turbulence and cavitation models in prediction of vortex induced cavitating flow in fuel injector nozzles

Vortex-induced cavitation develops in high pressure fuel injector equipment in areas where despite the very high surrounding pressures (>100 MPa), the rotational motion of the fluid causes large pressure drops in the core of a well-organized longitudinal vortex structure leading to cavitation with normally string type correspondingly also called string cavitation ; typically, the size of the string cavitation is small compared to the overall dimensions while they develop in a transient mode linked with the local flow turbulence. To address these complex interaction processes, some turbulence models have been tested in a diesel injector nozzle for which quantitative experimental data are available and are utilized to assess the predictive capability of relevant models; the flow has been considered compressible, turbulent and isothermal. The closure models considered include the RNG k−ε, SST k−ω, RSM, WALE LES as well as a developed very-large eddy simulation model (VLES). The employed mass-transfer cavitation models are the Schnerr and Sauer (SS), Zwart-Gerber-Belamri (ZGB), HEM and a modified ZGB model with a self-adaptive adjustment of condensation coefficient. The results indicate that the RNG k−ε model and SST k−ω model fail to predict the string cavitation induced by vortex flow in the nozzle due to the drawback of the isotropic vortex-viscosity hypothesis. The RSM model could capture an acceptable string cavitation morphology. The numerical results utilizing the VLES model and LES model are in considerably good agreement with the experimental data, while the VLES model can provide the predictions of cavitating flow as precise as that using the LES model but on a much coarser mesh. The distributions of tangential velocity are similar to the velocity characteristics of Rankin vortex or Taylor vortex, which can help understand the coherent vortex structures in string cavitating flow. It is also shown that the RSM turbulence model with modified ZGB cavitation model improves the accuracy of prediction in the vortex-induced cavitation compared to the other three cavitation models.

Influence of mass flux ratio on the evolution of coaxial synthetic jet

This paper highlights a direct numerical simulation study on the flow field of a coaxial synthetic jet (CSJ) generated from two independently controlled synthetic jet actuators, which are combined coaxially with 0° orientation angle. The jet is issued into a quiescent environment from inner and annular openings (orifices) with equal hydraulic diameters, employing an oscillating boundary. Seven different mass flux ratios (Mr) such as 0.25, 0.5, 0.75, 1.0, 1.5, 2.0, and 3.0 are considered for the study. The average velocity (Uavg) of inner jet, measured at orifice exit, is kept at 0.7 m/s (Reynolds number, Re=135), and the same is varied for the annular jet to achieve the desired Mr s. The influence of Mr s on the vortex rings, evolved from inner and annular orifices, along with their dynamics, is predicted by furnishing the instantaneous flow field. Also, we examine the effect of Mr s on the mean flow parameters of the CSJ. Moreover, the CSJ flow field is compared with the inner cavity synthetic jet (SJ), and annular cavity SJ under identical conditions, to demonstrate the superior performance of the CSJ over the single cavity SJs. For CSJ, the azimuthal instability of the evolved vortex rings can be triggered by decreasing the Mr, which results in a wide jet. For Mr≥1.0, the CSJ retains its axisymmetric nature, and the interaction of vortex rings emanating from the inner and annular cavities influences the strength and spreading of the CSJ. The modal decomposition of the instantaneous flow field is also performed using proper orthogonal decomposition method to gain insight of the coherent vortical structures present in the modes. The study will be useful for deploying such novel coaxial synthetic jets in various applications.

On coherent vortical structures in wave breaking

The flow generated by the breaking of free-surface waves in a periodic domain is simulated numerically with a gas–liquid Navier–Stokes solver. The solver relies on the volume-of-fluid method to account for different phases, and the interface tracking is carried out by using novel schemes based on a tailored total-variation-diminishing limiter. The numerical solver is proved to be characterized by a low numerical dissipation, thanks to the use of a scheme that guarantees energy conservation in the discrete form. Both two- and three-dimensional simulations have been performed, and the analysis is presented in terms of energy dissipation, air entrainment, bubble fragmentation, statistics and distribution. Particular attention is paid to the analysis of the mechanisms of viscous dissipation. To this purpose, coherent vortical structures, such as vortex tubes and vortex sheets, are identified, and the different behaviours of the vortex sheets and tubes at various Reynolds numbers are highlighted. The correlation between vortical structures and energy dissipation demonstrates clearly their close link both in the mixing zone and in the pure water domain, where the coherent structures propagate as a consequence of the downward transport. Notably, it is found that the dissipation is identified primarily by the vortex sheets, whereas the vortex tubes govern mainly the intermittency.

The evolution of coherent vortical structures in increasingly turbulent stratified shear layers

We study the morphology of Eulerian vortical structures and their interaction with density interfaces in increasingly turbulent stably stratified shear layers. We analyse the three-dimensional, simultaneous velocity and density fields obtained in the stratified inclined duct laboratory experiment (SID). We track, across 15 datasets, the evolution of coherent structures from pre-turbulent Holmboe waves, through intermittent turbulence, to full turbulence and mixing. We use the rortex–shear decomposition of the local vorticity vectors into a rortex vector capturing rigid-body rotation and a shear vector. We describe the morphology of ubiquitous hairpin-like vortical structures (revealed by the rortex), similar to those commonly observed in boundary-layer turbulence. These are born as relatively weak vortices around the strong three-dimensional shearing structures of confined Holmboe waves, and gradually strengthen and deform under increasing turbulence, transforming into pairs of upward- and downward-pointing hairpins propagating in opposite directions on the top and bottom edge of the shear layer. The pair of legs for each hairpin are counter-rotating and entrain fluid laterally and vertically, whereas their arched-up ‘heads’, which are transverse vortices, entrain fluid vertically. We then elucidate how this large-scale vortex morphology stirs and mixes the density field. Essentially, vortices located at the sharp density interface on either edge of the mixing layer (mostly hairpin heads) engulf blobs of unmixed fluid into the mixing layer, whereas vortices inside the mixing layer (mostly hairpin legs) further stir it, generating strong, small-scale shear, enhancing mixing. These findings provide new insights into the role of turbulent coherent structures in shear-driven stratified mixing.

A Combined Numerical and Experimental Investigation of Cycle-to-Cycle Variations in an Optically Accessible Spark-Ignition Engine

A combined numerical and experimental investigation is carried out to analyze the cycle-to-cycle variations (CCV) in an optically accessible spark-ignition engine with port fuel injection. A stable and an unstable operating condition is considered. Well-established turbulence, combustion, and ignition models are employed in the large-eddy simulations (LES). High-speed measurements of the velocity field via particle image velocimetry and flame imaging in the tumble plane are conducted in the experiments. A detailed comparison between LES and experiments is carried out, including the in-cylinder pressure, the flow fields, the spatial flame distribution, and the fields conditioned on fast and slow cycles. Good agreement is achieved for the variables considering all cycles; yet, some discrepancies are observed for the conditionally averaged quantities. A systematic quantitative correlation analysis between the selected influencing variables and the CCV is presented, in which the influencing variables are extracted from different length scales (r = 3 mm, 12 mm, and 43 mm) and the CCV are distinguished between the early flame kernel development and later flame propagation. Even though the most relevant influencing parameters are different for the two operating conditions, the location of the coherent vortex structure is found to be important for the CCV of both cases.

Simultaneous visualization of the velocity and wall temperature fields in impinging swirling jets

Laser-based three-dimensional velocimetry techniques have been recently undergone a fast and significant development enabled by the improvements in both hardware and processing methods. The benefits of this progress are huge especially in the field of the investigation of complex turbulent flows. In this paper, the application of time-resolved tomographic particle image velocimetry (TPIV) to the analysis of submerged impinging swirling jets is presented. Swirling flows recur both in natural phenomena and industrial processes and impinging swirling jets have been extensively investigated for heat transfer applications; however, three-dimensional and time-resolved investigations on the impinging flow fields of swirling jets are rare in the literature. The current study focuses mainly on the effects of the swirl number on the formation and development of the coherent vortex structures arising in this kind of flow. Five values of the swirl number, including the non-swirling case (S=0, 0.23, 0.43, 0.61 and 0.74) are investigated for fixed values of the Reynolds number (Re=5,100) and the impingement distance (equal to two nozzle exit diameters). TPIV measurements are carried out both in the near field (in proximity of the nozzle exit) and in the impingement zone (in proximity of the wall). In the latter case, the water jet is set to a temperature higher than the ambient one and the wall temperature distribution is measured via time-resolved infrared (IR) thermography with the aid of a transparent IR window. The simultaneous velocity and temperature measurements elucidate the role of the vortex structures in both the flow dynamics and transport of internal energy, which is a passive scalar in the present operating conditions. Modal decomposition techniques, in particular the proper orthogonal decomposition, are also applied to identify the most characteristic structures of the turbulent flows.

Computational turbulent flow characteristics in a centrifugal pump

This investigation provides the 3D numerical simulations of a six-blade centrifugal pump that is commonly applied in agriculture and food processing sectors. The simulations were carried out using the unsteady Reynolds averaged Navier–Stokes equations. The k-omega turbulence model was used as a closure for the equations. The velocity and pressure flow fields were used to predict the turbulent flows in the pump under three different operating conditions (part-load 0.8Qd, design 1.0 Qd, and overload 1.2 Qd). The omega vortex identification criterion was further applied to visualize the coherent vortex structures in the impeller and volute at the investigated flow conditions. The impeller eye was characterized with the lowest static pressure fields causing this region to be highly susceptible to cavitation under all flow conditions. At the design point, the velocity vectors were orderly patterned along the blade flow curvature. However, flow separation occurred around the leading edge mainly due to the fact that the flow is non-tangential to the leading edge of the blade as a result of the unsteady effect developed upstream. In conclusion, it can be confirmed that the volute geometry is highly sensitive to the evolution and formation of vortices as revealed by the omega vortex criterion. This work reveals that the design of the volute geometry should be further improved to mitigate unsteady flow losses. Again, this kind of study helps reduce the required experimental measurements for the improvement and design of hydraulic machines.

Canonical scale separation in two-dimensional incompressible hydrodynamics

The rules that govern a two-dimensional inviscid incompressible fluid are simple. Yet, to characterise the long-time behaviour is a knotty problem. The fluid fulfils Euler's equations: a nonlinear Hamiltonian system with an infinite number of conservation laws. In both experiments and numerical simulations, coherent vortex structures emerge after an initial stage. These formations dominate the large-scale dynamics, but small scales also emerge and persist. The resulting scale separation resembles Kraichnan's theory of forward and backward cascades of enstrophy and energy. Previous attempts to model the double cascade use filtering techniques that enforce separation from the outset. Here, we show that Euler's equations possess an intrinsic, canonical splitting of the vorticity function. The splitting is remarkable in four ways: (i) it is defined solely by the Poisson bracket and the Hamiltonian; (ii) it characterises steady flows; (iii) it innately separates scales, enabling the dynamics behind Kraichnan's qualitative description; and (iv) it accounts for ‘broken line’ energy spectra observed in both experiments and numerical simulations. The splitting originates from Zeitlin's truncated model of Euler's equations in combination with a standard quantum tool: the spectral decomposition of Hermitian matrices. In addition to theoretical insight, the scale separation dynamics enables stochastic model reduction, where multiplicative noise models small scales.

Suppression of Vortex-Induced Vibration and Phase-Averaged Analysis of the Wake Generated by a Circular Cylinder Covered with Helical Grooves

The effect of triple helical grooves on the suppression of vortex-induced vibration (VIV) of a circular cylinder was investigated experimentally in a wind tunnel over Reynolds number in the range of 1 × 104 < Re < 4 × 104. It was found that the helical grooves were effective in suppressing VIV with the peak amplitude reduction of approximately 36%. In addition, the lock-on region was also reduced. To explore the mechanism for the suppression of VIV, experiments on flow structures for a stationary grooved cylinder were also conducted in a wind tunnel at a free stream velocity U∞ of 4.37 m/s, corresponding to a Reynolds number based on the bare cylinder diameter of about 3500. The data were then analyzed using the phase-averaged method to evaluate the coherent vortex structures in the wakes. The results for the stationary grooved cylinder showed that the grooves weakened vortex shedding in the near wake. In addition, the grooves also reduced the drag coefficient by 6.6%. These results help explain the reduction of VIV using helical grooves.

Detecting the orbital angular momentum from speckle via convolutional neural network

The inhomogeneity of turbid medium disrupts the coherent vortex structure of the vortex beam and causes the formation of a speckle pattern. Here, we propose a new, flexible approach to measure the orbital angular momentum (OAM) of vortex beams through a turbid medium by a convolutional neural network. The proposed technique directly recognizes the speckle image and obtains the corresponding OAM mode information. The accuracies exceed 99% and 97% in simulations and experiments respectively. In addition, the relationship between the recognition accuracy and environmental noise level, is present. The results show great potential in fiber communication, biomedical imaging and astronomical application, etc.

Robust and efficient identification of optimal mixing perturbations using proxy multiscale measures.

Understanding and optimizing passive scalar mixing in a diffusive fluid flow at finite Péclet number (where and are characteristic velocity and length scales, and is the molecular diffusivisity of the scalar) is a fundamental problem of interest in many environmental and industrial flows. Particularly when , identifying initial perturbations of given energy that optimally and thoroughly mix fluids of initially different properties can be computationally challenging. To address this challenge, we consider the identification of initial perturbations in an idealized two-dimensional flow on a torus that extremize various measures over finite time horizons. We identify such ‘optimal’ initial perturbations using the ‘direct-adjoint looping’ method, thus requiring the evolving flow to satisfy the governing equations and boundary conditions at all points in space and time. We demonstrate that minimizing multiscale measures commonly known as ‘mix-norms’ over short time horizons is a computationally efficient and robust way to identify initial perturbations that thoroughly mix layered scalar distributions over relatively long time horizons, provided the magnitude of the mix-norm’s index is not too large. Minimization of such mix-norms triggers the development of coherent vortical flow structures which effectively mix, with the particular properties of these flow structures depending on and also the time horizon of interest.This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 1)’.

Study of aerodynamic characteristics of an aircraft during approach to landing in a disturbed atmosphere

An approximate method is proposed for determining the aerodynamic effect of coherent vortex structures (CVS) of atmospheric turbulence on an aircraft. As a source of the CVS the vortex wind wakes arising when the atmospheric wind flows around the mountain massif of the Son Tra peninsula, located near the Da Nang airport, and the vortex wake behind the Su-27 type aircraft in the landing configuration are considered. Modeling the formation of a vortex structure is carried out by the grid method within the framework of the boundary value problem for the Reynolds-averaged Navier—Stokes equations. The evolution and stochastics of the far wake are modeled in a two-dimensional approximation by discrete Rankine vortices. The assessment of the increment of forces and moments from the effect of the vortex system on the aircraft was carried out within the framework of the panel method. The situation is considered when a light transport aircraft gets into a vortex wake behind an aircraft with a swept wing and a passenger aircraft of the MS-21 type, approaching for landing at the CVS from a mountainous terrain.