Maximum Vorticity Research Articles

Spiral wind-up of vortex sheets

A model of the spiral wind-up of a vortex sheet by the flow induced by a perpendicular vortex is developed, first in the Euler limit of zero viscosity, then taking account of viscous diffusion. The wind-up of a vortex sheet by a propagating vortex pair is also considered; in this case, the vorticity grows exponentially near the two saddle points of the flow in the moving frame of the vortex pair. Estimates are obtained for the maximum vorticity ω m and maximum enstrophy Ω m attained through this process in terms of the wind-up Reynolds number Re and the initial dimensionless sheet thickness δ 0 . This paper is dedicated to Andrew Soward, whose sustained research in Dynamo Theory and Fluid Mechanics has been brilliantly inspiring for more than 50 years. Happy 80th, Andrew!

Nonlinear transient disturbance growth analysis for the compressible external flow and application to a flow around circular cylinder

The property of nonlinear optimal perturbation (NLOP) analysis for the flow around the circular cylinder was investigated with a comparison with the linear optimal perturbation analysis (LOP). Our analysis revealed that NLOP is highly dependent on the initial disturbance norm and highlighted the limitation of linear prediction in triggering instability in the flow field. This NLOP shows an asymmetric and deformed vortex structure on the cylinder wall, with the angle of the maximum wall vorticity shifting in relation to the initial disturbance norm. We also observed that the circulation and disturbance vorticity at the shear layer in boundary layer efficiently contributed to larger disturbance growth of the separation vortex behind the cylinder compared with the LOP.

Synchronicity of the Gulf Stream path downstream of Cape Hatteras and the region of maximum wind stress curl

The Gulf Stream, a major ocean current in the North Atlantic ocean is a key component in the global redistribution of heat and is important for marine ecosystems. Based on 27 years (1993–2019) of wind reanalysis and satellite altimetry measurements, we present observational evidence that the path of this freely meandering jet after its separation from the continental slope at Cape Hatteras, aligns with the region of maximum cyclonic vorticity of the wind stress field known as the positive vorticity pool. This synchronicity between the wind stress curl maximum region and the Gulf Stream path is observed at multiple time-scales ranging from months to decades, spanning a distance of 1500 km between 70 and 55W. The wind stress curl in the positive vorticity pool is estimated to drive persistent upward vertical velocities ranging from 5 to 17 cm day−1 over its ~ 400,000 km2 area; this upwelling may supply a steady source of deep nutrients to the Slope Sea region, and can explain as much as a quarter of estimated primary productivity there.

Supercell Tornadogenesis: Recent Progress in Our State of Understanding

Abstract Over the last decade, supercell simulations and observations with ever-increasing resolution have provided new insights into the vortex-scale processes of tornado formation. This article incorporates these and other recent findings into the existing three-step model by adding an additional fourth stage. The goal is to provide an updated and clear picture of the physical processes occurring during tornadogenesis. Specifically, we emphasize the importance of the low-level wind shear and mesocyclone for tornado potential, the organization and interaction of relatively small-scale pretornadic vertical vorticity maxima, and the transition to a tornado-characteristic flow. Based on these insights, guiding research questions are formulated for the decade ahead.

Effects of the gap ratio on the flow field structures and the aerodynamic performance of an airfoil with ridge ice

Under SLD icing conditions, the ridge ice may appear on the surface of aircraft, which led to the significant aerodynamic deterioration and affected aircraft flight safety. The present study experimentally investigated the effects of the gap ratio on the flow field structures and aerodynamic performance of an airfoil with ridge ice. Detailed measurements were performed in a low-speed reflux wind tunnel by utilizing the Particle Image Velocimetry (PIV) technique and a high-sensitivity six-component balance. The results showed that the maximum lift coefficient, stall angle, and maximum pitch moment coefficient of the airfoil increased as the gap ratio enlarged. At AOA = 10 deg, the separation bubble length decreased by 77 % when the gap ratio changed from 0 to 0.1. Meanwhile, the separation bubble length decreased by 68 % when the gap ratio changed from 0.1 to 0.3. Besides, as the increase of the gap ratio, the average vorticity, turbulent kinetic energy, and Reynolds shear stress in the selected region above the airfoil decreased, while the average velocity increased. In addition, the gap ratio did not have an apparent effect on the transition onset positions and the maximum spanwise vorticity in the flow field.

Multiscale interaction analysis of Landfall Typhoon Lekima (2019) based on vorticity equation diagnosis

To investigate the multiscale interaction characteristics of Landfall Typhoon Lekima (2019), this study analyzed the characteristics of the different scale vortex structure and interactions among different scales based on vorticity equation diagnosis. The analysis is based on the simulation results of the WRF model which has been thoroughly verified. The main results are as follows: the original vorticity dominated by the meso-α scale vorticity increases with height and then decreases, with maximum vorticity distributed at 900 hPa. The meso-β scale vorticity varies significantly with altitude, while the meso-γ scale vorticity field exhibits obvious positive vorticity below 850 hPa. The meso-α scale vorticity tendency primarily maintains negative, contributing significantly to the overall reduction in the original vorticity field over time. The increase in mid-to-upper-level (above 550 hPa) original vorticity is mainly related to the variations in the meso-β and meso-γ scale vorticity fields. The original vorticity dominated by the meso-α scale vorticity increases with height and then decreases, and the whole layer vorticity decreases over time. The meso-β scale vorticity varies significantly with altitude and time, while the meso-γ scale vorticity field consistently exhibits significant positive vorticity below 850 hPa. The vorticity equation diagnosis revealed that the primary source terms of the vorticity tendencies are the twisting and stretching terms, and the main sink terms being horizontal and vertical vorticity transport terms below 900 hPa. The source terms and sink terms exchange above 850 hPa. Scale separation results show that the primary contributions of all impact factors originate from the meso-α and meso-γ scale fields (accounting for over 80% of the total), with the contribution of the meso-α scale being less than that of the meso-γ scale and a notable contribution over 35.5% of the interactions between different scales.

Stability of Stuart vortices in rotating stratified fluids

The linear stability of the Stuart vortices, which is a model of arrays of vortices often observed in the atmosphere and the oceans, in rotating stratified fluids is investigated by local and modal stability analysis. As in the case of the two-dimensional (2-D) Taylor–Green vortices, five types of instability appear in general: the pure-hyperbolic instability, the strato-hyperbolic instability, the rotational-hyperbolic instability, the centrifugal instability and the elliptic instability. The condition for each instability and the estimate of the growth rate derived by Hattori & Hirota (J. Fluid Mech., vol. 967, 2023, A32) are shown to also be useful for the Stuart vortices, which supports their applicability to general flows. The properties of each instability depend on stratification and rotation in a way similar to the case of the 2-D Taylor–Green vortices. For the Stuart vortices, however, the centrifugal instability and the elliptic instability become more dominant than the three hyperbolic instabilities in comparison to the 2-D Taylor–Green vortices; this is explained by the larger ratios of the maximum vorticity and the strain rate at the elliptic stagnation points to the strain rate at the hyperbolic stagnation points. Direct correspondence between the modal and local stability results is further established by comparing unstable modes to solutions to the local stability equations; this is useful for identifying the types of modes since the mechanism of instability is readily known in the local stability analysis. This helps us to discover the modes of the ring-type elliptic instability, which have been predicted only theoretically.

Vortex-dipole impingement with convex and concave boundaries

The vortex-dipole interactions with convex and concave boundaries in a two-dimensional domain are analyzed using the Bhatnagar–Gross–Krook (BGK) collision-based lattice Boltzmann method (LBM). The formation and detachment of the boundary layers at the flat wall creates new dipoles of non-identical vortices, following cyclic trajectories and exhibiting logarithmic variations in the production of maximum vorticity with Reynolds number (Re). The vortex-dipole interactions with concave boundaries produce a series of secondary dipoles, whose relative strength linearly decreases for the given Re in subsequent vortex-releasing events. Oblique interactions with cavity corners cause secondary dipoles to undergo head-on collisions at the domain center, influencing partner exchange and orthogonal propagation. Conversely, convex boundaries split the primary vortex-dipole upon impingement, intensifying the vorticity production and strain effects. Whereas, the larger ingestion of vorticity at the convex corners of the “T-shaped” cavity forms new dipoles, which deflect, rebound, and follow a parabolic trajectory for the vortex exchange. Normalized enstrophy, Ω(t), and palinstrophy, P(t), show distinct peaks during dipole interactions with boundary walls, influencing enhanced kinetic energy, E(t), decay. Moreover, the evolution of E(t) and Ω(t) satisfies the relation valid for no-slip boundaries. The collision behavior, vorticity production, and vortex rebound are functions of Re. The convex boundaries modify the scaling results of maximum Ω(t) and P(t) to higher exponent values than the dipole interactions with flat and concave boundaries.

An experimental comparison of 3D velocity components around single and twin piers installed in a sharp bend under the influence of upstream implemented vanes

To reduce the trend of scouring, understanding the flow pattern around the bridge piers is necessary. By using hydraulic structures such as submerged vanes, it is possible to alter the flow pattern of water, thus scouring process and sediment transport in riverbeds. Since the scouring mechanism for pier groups differs from single pier, experiments were conducted in a 180° sharp bend channel in the laboratory to investigate the flow pattern around pier group and single pier under the influence of 25% submerged vanes. Furthermore, a comparison was made between the flow patterns in single pier and pier group conditions. Three-dimensional velocities along the bend and different depths were measured using an Acoustic Doppler Velocimeter (ADV(. The results suggest that the maximum vorticity value at the apex position of the bend (location of piers) and the maximum secondary flow value, at the distance between the piers and the vanes, were found to be, 0.15 and 0.89, respectively. In the twin pier experiment, the maximum Reynolds shear stress value τyx\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ au }_{yx}$$\\end{document} decreased by about 36%, and the minimum value decreased by about 49% compared to the single pier experiment. The final results indicated that using submerged vanes obtained the maximum τyx\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ au }_{yx}$$\\end{document} and τzx\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ au }_{zx}$$\\end{document} near the vanes. Near the bed and mid-depth of the water flow, the geometric location of the maximum velocity also occurred around the vanes in both experiments. Therefore, the vanes are important in altering the water flow pattern, diverting the flow from around piers and consequently reducing the bridge pier scouring.

Novel enhanced thermal capabilities of Cu-Al2O3/water hybrid nanofluid in an oblique U-shape cavity: On the molecular behaviour through vorticity analysis

This paper presents the numerical investigation of natural convection heat transfer of copper-alumina/pure water hybrid nanofluid in an oblique U-shaped enclosure. The dimensionless governing equation is formed in the stream function-vorticity formulation using dimensionless variables. The Galerkin weighted residual finite element method with the damped Newton-Raphson iteration method is applied to the problem. The heat transfer performance for the system is investigated by varying the Rayleigh numbers, nanoparticle volume fractions and their ratios, and the oblique angles of the enclosure. The fluid flow, heat transfer, and vorticity analysis are conducted extensively for the Rayleigh number up to 106. It was found that the oblique enclosure dwindled the overall heat transfer performance. Correspondingly, the maximum vorticity is at the lowest with zero obliquenesses. The results are used to gain a deeper understanding of the fluid flow and thermal behaviour of the system to achieve more sustainable and greener energy management.

Shear-Relative Asymmetric Kinematic Characteristics of Intensifying Hurricanes as Observed by Airborne Doppler Radar

Abstract While recent observational studies of intensifying (IN) versus steady-state (SS) hurricanes have noted several differences in their axisymmetric and asymmetric structures, there remain gaps in the characterization of these differences in a fully three-dimensional framework. To address these limitations, this study investigates differences in the shear-relative asymmetric structure between IN and SS hurricanes using airborne Doppler radar data from a dataset covering an extended period of time. Statistics from individual cases show that IN cases are characterized by peak wavenumber-1 ascent concentrated in the upshear-left (USL) quadrant at ∼12-km height, consistent with previous studies. Moderate updrafts (2–6 m s−1) occur more frequently in the downshear eyewall for IN cases than for SS cases, likely leading to a higher frequency of moderate to strong updrafts USL above 9-km height. Composites of IN cases show that low-level outflow from the eye region associated with maximum wavenumber-1 vorticity inside the radius of maximum wind (RMW) in the downshear-left quadrant converges with low-level inflow outside the RMW, forming a stronger local secondary circulation in the downshear eyewall than SS cases. The vigorous eyewall convection of IN cases produces a net vertical mass flux increasing with height up to ∼5 km and then is almost constant up to 10 km, whereas the net vertical mass flux of SS cases decreases with height above 4 km. Strong USL upper-level ascent provides greater potential for the vertical development of the hurricane vortex, which is argued to be favorable for continued intensification in shear environments.

Numerical simulation of biomagnetic pulsatile flow through a channel

The study of biological fluids in the presence of a magnetic field is known as biomagnetic fluid dynamics (BFD). The research work in BFD has been rapidly growing due to its applications in developing magnetic devices used for cell separation, targeted drug delivery and cancer tumor treatment. This study aims to examine the biomagnetic fluid flow with pulsatile conditions through a channel when subjected to a magnetic field that varies in space. The nondimensional continuity and momentum equations are solved with the effect of the magnetic field added as a body force. A two-dimensional computational model is developed using the finite volume method and is implemented on a staggered grid system with the help of the semi-implicit fractional step method. The code is written using MATLAB. Numerical simulations are performed by varying the Magnetic, Reynolds and Womersley numbers. Pulsatile flow results indicate the periodic growth and decay of vortices near the source of the magnetic field. With an increase in the magnetic number from 100 to 150, 250 and 500, the maximum vorticity increases by 48.04%, 149.84% and 402.68%. A similar relation is found when varying the Reynolds number, while almost no change is found when varying the Womersley number.

Rotational effect of a cylinder on hydro-thermal characteristics in a partially heated square enclosure using CNT-water nanofluid

Rotating cylinder movement in a cavity flow is an exciting field of study in heat transfer. Considerable research has been carried out on rotating cylinders under MHD mixed convection in various types of enclosures. However, considering partially heated square enclosure and magnetic field using CNT-water nanofluid is very limited. This study's goal is to assess the hydrothermal phenomena in a square enclosure with a rotating cylinder. Simulation has been conducted for different rotational speeds (Ω) and dimensionless times (τ) to observe the thermal and fluid flow behaviour. The Galerkin Residual based finite element method has been used to conduct numerical calculations. The results are shown as isotherms, streamlines, and average Nusselt number at the cylinder wall. Moreover, the drag force at the moving wall, and the fluid properties such as the root mean square (rms) of velocity, the temperature, the vorticity functions, and the average fluid temperature are also presented. The heat transfer rate, drag force, rms velocity, and temperature increase with the rise of rotational speed and dimensionless time rise. Maximum vorticity occurs at Ω = 8 and τ = 1. The maximum vorticity function increases 12 times with the increasing rotational speed. Higher rotational speed leads to increased average fluid temperature. The case of Ω = 8, τ = 1 shows the most temperature variance, while Ω = 1, τ = 0.1 has the least. Increasing rotational speed results in higher drag force on the cylinder's surface. At Ω = 4, the drag force is 2.8 times greater than at Ω = 2. Overall, the fluid flow and thermal performance boost up while the rotating speed of the cylinder is higher.

Subvortices within a Numerically Simulated Tornado: The Role of Unstable Vortex Rossby Waves

Abstract Multiple subvortices corresponding to suction vortices in observations are obtained within a simulated tornado for the EF4 tornado case of Funing, China, on 23 June 2016. Within the simulation, the tornado evolves from a one-cell structure with vorticity maximum at its center to a two-cell structure with a ring of vorticity maximum. Five well-defined subvortices develop along the ring. The radial profile of tangential wind across the vorticity ring satisfies the necessary condition of barotropic instability associated with phase-locked, counterpropagating vortex Rossby waves (VRWs) along the ring edges. The phased-locked waves revolve around the parent vortex at a speed less than the maximum azimuthal-mean tangential velocity, agreeing with theoretically predicted VRW phase speed. The radii within which the wave activities are confined are also correctly predicted by the VRW theory where radial group velocity approaches zero. Several other characteristics related to the simulated subvortices agree with VRW theories also. The most unstable azimuthal wavenumber depends on the width and the relative magnitude of vorticity of the vortex ring. Their values estimated from the simulation prior to subvortex formation correctly predict wavenumber 5 as the most unstable. The largest contribution to wave kinetic energy is diagnosed to be from the radial shear of azimuthal wind term, consistent with barotropic instability. Vorticity diagnostics show that vertical vorticity stretching is the primary vorticity source for the intensification and maintenance of the simulated subvortices. Significance Statement Multiple subvortices or suction vortices in tornadoes can produce extreme damage but their cause is not well understood. An intense tornado from China that developed five strong subvortices, along a vorticity ring a distance from the tornado vortex center, was successfully simulated. By examining the propagation and other characteristics of these subvortices and comparing them with theoretical models of vortex Rossby waves (VRWs) that have been studied mostly in the context of typhoons/hurricanes, it is believed that nonlinear growth of unstable VRWs associated with barotropic instability is the primary reason for the development of subvortices within the tornado. The conclusion is further supported by analyses of the primary source of wave growth energy. Vertical vorticity stretching is the main vorticity source for intensifying and maintaining the subvortices at their development and mature stages. The unstable growth of VRWs as the cause of tornado suction vortices has not been analyzed in detail for realistic tornadoes until now.

Vortex effects on aerodynamic performance of multi-stage continuous-resistance trim under high pressure gradient

The multi-stage continuous-resistance trim (MSCRT) is widely utilized in gas turbine combined-cycles (GTCC), acting as an indispensable throttling component used for regulating fluid pressure, flow rate and temperature. However, under harsh operating conditions, the flow in MSCRT becomes unstable, leading to disrupted aerodynamic performance and increased energy consumption. Despite its significance, the underlying vortex dynamics and its correlation with aerodynamic performance remain elusive. To address this, a comprehensive investigation into the unsteady flow of MSCRT is proposed, combining experimental and numerical methods. The vortex dynamics mechanism is revealed, and then, the vortex effects on pressure pulsation and aerodynamic performance are investigated. Results show that the novel design allows the pressure gradient to be dissipated between the layers and succeeds in achieving effective control of noise and energy consumption. Based on the aerodynamic design, the mutual correspondence between the vortical structure and the flow field results is verified. Furthermore, the relationship between the instantaneous total vorticity and the pressure pulsation is established, as well as the relationship between the vortex parameters and the maximum sound pressure level. Notably, a linear correlation between the maximum sound pressure level and the maximum instantaneous total vorticity is determined. This study provides support for improving the aerodynamic performance of related throttling components.

Use of threshold parameter variation for tropical cyclone tracking

Abstract. Assessing the capacity of numerical models to produce viable tropical cyclones, as well as assessing the climatological behavior of simulated tropical cyclones, requires an objective tracking method. These make use of parameter thresholds to determine whether a detected feature, such as a vorticity maximum or a warm core, is strong enough to indicate a tropical cyclone. The choice of parameter thresholds is generally subjective. This study proposes and assesses the parallel use of many threshold parameter combinations, combining a number of weaker and stronger values. The tracking algorithm succeeds in tracking tropical cyclones within the model data, beginning at their aggregation stage or shortly thereafter and ending when they interact strongly with extratropical flow and transition into extratropical cyclones or when their warm core decays. The sensitivity of accumulated cyclone energy to tracking errors is assessed. Tracking errors include the faulty initial detection and termination of valid tropical cyclones and systems falsely identified as tropical cyclones. They are found to not significantly impact the accumulated cyclone energy. Thus, the tracking algorithm produces an adequate estimate of the accumulated cyclone energy within the underlying data.

A phytoplankton bloom caused by the super cyclonic storm Amphan in the central Bay of Bengal

Abstract. The super cyclonic storm Amphan originated in the central Bay of Bengal (BoB) in May 2020, and a phytoplankton bloom occurred in the upper ocean that was devoid of background nutrients. The dynamic mechanism of the chlorophyll a (Chl a) bloom was researched based on reanalysis data, remote sensing and Argo float data. During the passage of Amphan, an inertial oscillation with a 2 d period appeared in the thermocline and lasted for approximately 2 weeks. After the passage of Amphan, a cyclonic eddy with a maximum vorticity of approximately 0.36 s−1 formed in the study area (Box A). Additionally, horizontal transport of Chl a also occurred when the maximum inlet fluxes through the western and northern sides of Box A were 0.304 and −0.199 mg m−2 s−1, respectively. With the weakened thermocline and thinner barrier layer thickness (BLT), nitrate and Chl a were uplifted to the upper ocean by upwelling. Then, with the high photosynthetically available radiation (PAR) in the upper ocean, a phytoplankton bloom occurred. This study provides new insights into the biological responses in the BoB during the passage of tropical cyclones (TCs).

Towards a finite-time singularity of the Navier–Stokes equations. Part 3. Maximal vorticity amplification

An exact analytical solution is obtained for the dynamical system derived in Part 1 of this series (Moffatt & Kimura, J. Fluid Mech, vol. 861, 2019a, pp. 930–967), which describes the approach of two initially circular vortices of finite but small cross-section symmetrically located on inclined planes. This exact solution, applicable in the inviscid limit, allows determination of the amplification $\mathcal {A}_{\omega }$ of the axial vorticity within the finite time $T$ during which the basic assumptions of the model continue to apply. It is first shown that, for arbitrarily prescribed $\mathcal {A}_{\omega }$ , it is possible to specify smooth initial conditions of finite energy such that, in the inviscid limit, this amplification is achieved within the time $T$ . When viscosity is included, an estimate is provided for the minimum vortex Reynolds number that is sufficient for the same result to hold. The predictions are broadly compatible with results from direct numerical simulations at moderate Reynolds numbers. Moreover, it is shown that one may come arbitrarily close to a finite-time singularity of the Navier–Stokes equation by appropriate choice of an initial, smooth, finite-energy velocity field; however, this approach to a singularity is ultimately thwarted through breach of the assumptions on which the dynamical system is based. Thus we make no claim here concerning realisation of a Navier–Stokes singularity. Moreover, we find that the conditions required to attain a large amplification $\mathcal {A}_{\omega }\gg 1$ during the time $T$ are far beyond those that can be realised in either experiment or direct numerical simulation.

Numerical Modeling of Nearshore Wave Transformation and Breaking Processes in the Yellow River Delta with FUNWAVE-TVD Wave Model

The presence of wave coherence, which contributes to the inhomogeneity of wave characteristics and significantly affects wave processes over nearshore regions of the Yellow River Delta (YRD), was simulated and analyzed in this study. A phase-resolving Boussinesq-type wave model, FUNWAVE-TVD, was used to simulate waves with desirable coherency effects. Bathymetry and topography data were obtained from the Chinese nautical chart and E.U. Copernicus Marine Service Information. After the model configuration, spatial distributions of the root mean square and significant wave heights, and the maximum cross-shore current velocity and vorticity over the domain with respect to different degrees of wave coherence and energy spectrum discretization were investigated. The results indicate that the complexity of the spatial distribution and magnitude of longshore variations in wave statistics are proportional to the degree of coherence. Waves with higher coherency exhibit more complex variabilities and stronger fluctuations along the longshore direction. The influence of morphological changes on wave height in the YRD was discernible by comparing the results with and without coherency effects. The cross-shore current velocity decreased as the waves moved toward the surf zone, while the vorticity accelerated, indicating a higher shear wave magnitude. The simulated wave dissipates more than 60% (80%) of its energy when it reaches water depths of less than 5 m (2 m) and completely dissipates when it breaks at the shore.

Unsteady evolution of distributed roughness-induced vortices under re-entry conditions

AbstractThis study investigates a re-entry scenario of an Apollo-like space capsule with Direct Numerical Simulations (DNS). The simulation includes the chemical equilibrium gas model. Cross-flow-like vortices are induced through random distributed roughness patches on the capsule surface. Two different machine learning methods are used to predict the maximum vorticity magnitude downstream of a pseudo-random roughness patch, the wall-normal location of the vortex core and spanwise and wall-normal gradient maxima of u. A large DNS database is formed for training and testing of the neural networks. In order to understand the influence of the vorticity magnitude on the transition process, local one-dimensional inviscid (LODI) relations are used to describe perturbations at the inflow. The disturbance evolution in the streamwise direction is analysed with a two-dimensional Fourier transformation in time and space. We show how the vorticity magnitudes of the cross-flow-like vortices, spanwise and wall-normal derivatives of the streamwise velocity influence the transition location.