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Vortex

A vortex is a flow configuration in fluid dynamics where fluid elements exhibit rotational motion around a central axis or line, characterized by concentrated regions of vorticity—the curl of the velocity field that measures the local angular velocity of the fluid.^[1] This rotational structure arises from the interaction of velocity gradients and is ubiquitous in both natural and engineered systems, distinguishing itself from irrotational flow by the presence of non-zero vorticity that can persist and evolve over time.^[2] Vortices are defined mathematically through concepts like vortex lines, which are curves tangent to the vorticity vector at every point, and vortex tubes, which are bundles of such lines forming closed surfaces where vorticity is conserved in inviscid, barotropic flows.^[3] Common types include point vortices in two-dimensional flows, representing idealized singularities of infinite circulation; vortex rings, toroidal structures seen in phenomena like smoke rings or jet propulsion in squid; and line vortices, such as straight or curved filaments approximating tip vortices from aircraft wings.^[1] These structures interact dynamically, leading to processes like vortex merging, stretching, and reconnection, which amplify or dissipate energy in turbulent flows.^[4] In natural contexts, vortices manifest as large-scale features like hurricanes, tornadoes, and ocean eddies, where rotational motion drives energy transfer and mixing across scales, while in engineering, they influence aerodynamics—such as lift generation via wingtip vortices—and propulsion systems, including swirl in rocket engines or turbines.^[5] The study of vortex dynamics, rooted in the Navier-Stokes equations, reveals their role as building blocks of complex fluid motion, with applications spanning meteorology, oceanography, and biomechanics, such as blood flow in arteries. Advances in computational fluid dynamics have enabled detailed simulations of vortex evolution, aiding designs that mitigate unwanted effects like drag or enhance control in vehicles.^[6]

Fundamentals

Definition and Characteristics

A vortex is a region in a fluid where the flow revolves around an axis line, exhibiting rotational motion characterized by the swirling of fluid elements.^[7] This organized pattern arises in various fluid media, including liquids and gases, and is fundamental to many natural and engineered flows.^[1] Key characteristics of a vortex include its swirling motion, where fluid particles follow curved trajectories around the central axis, often accompanied by a low-pressure core at the center due to centrifugal effects from the rotation.^[8] The flow typically features radial velocity components directed toward or away from the axis and tangential velocity components that drive the circumferential motion, contributing to the overall rotational structure.^[9] Unlike turbulence, which represents chaotic and disordered motion with random fluctuations, vortices form coherent, persistent structures that maintain their rotational organization amid surrounding flows.^[10] Intuitive examples of vortices abound in everyday phenomena, such as whirlpools in draining water, tornadoes twisting through the atmosphere, and smoke rings propelled through air, each illustrating the visible manifestation of rotational fluid motion.^[11] Vorticity provides a measure of the local rotation within these structures, quantifying the spin of fluid elements (detailed in the Vorticity and Circulation section).^[2]

Historical Development

The study of vortices traces back to ancient natural philosophy, where Aristotle, in his Meteorologica (circa 340 BCE), described whirlwinds and tornadoes as phenomena arising from wind trapped within clouds that rotates in a circular motion, likening them to a kind of atmospheric "conflagration" that colors the air.^[12] These early observations framed vortices as natural occurrences driven by elemental interactions, influencing subsequent philosophical inquiries into fluid motion without quantitative analysis.^[12] In the 19th century, foundational mathematical treatments emerged with Hermann von Helmholtz's 1858 paper "On the Integrals of the Hydrodynamical Equations Which Express Vortex-Motion," which introduced theorems on the conservation and motion of vortex lines in inviscid fluids, establishing the concept of vorticity as a measure of local rotation.^[13] This work, translated into English in 1867, laid the groundwork for modern vortex dynamics.^[13] Concurrently, William Thomson (later Lord Kelvin) proposed the vortex atom theory in 1867, hypothesizing that atoms could be modeled as stable vortex rings in an ideal fluid ether, emphasizing the topological invariance of vortex structures.^[14] The vorticity concept emerged directly from Helmholtz's theorems on these conserved vortex elements.^[13] The 20th century saw significant progress through Ludwig Prandtl's 1904 introduction of boundary layer theory, which explained how viscous effects near surfaces lead to flow separation in real-fluid flows.^[15] This framework revolutionized the analysis of real-fluid flows by isolating frictional influences near boundaries.^[15] By the 1970s and 1980s, the rise of computational fluid dynamics introduced vortex methods for simulating incompressible flows, with key reviews highlighting their efficiency in tracking vorticity transport without fixed grids.^[16] Recent advancements have integrated vortex dynamics with chaos theory, particularly in climate modeling, where nonlinear interactions amplify small perturbations in polar vortex structures, improving forecasts of stratospheric sudden warmings and their surface impacts.^[17] This includes 2025 studies using theoretical and numerical models to explore perturbations and rapid reconfigurations in annular-like stratospheric polar vortices, potentially triggering sudden stratospheric warmings.^[18] Post-2000 numerical simulations have advanced high-resolution modeling of vortex evolution in turbulent and geophysical flows, addressing limitations in earlier analytical approaches through ensemble predictions that account for chaotic sensitivities.^[17]

Mathematical Foundations

Vorticity and Circulation

In fluid dynamics, vorticity is a vector field defined as the curl of the velocity field, \vec{\omega} = \nabla \times \vec{v}, quantifying the local rotation of fluid elements.^[19] This definition, introduced by Hermann von Helmholtz in his seminal 1858 work on vortex motions, captures the infinitesimal rotation within the fluid.^[19] The magnitude of vorticity has units of radians per second (rad/s), reflecting its role as a measure of rotational rate. Physically, the vorticity vector at a point represents twice the angular velocity of the fluid element centered there, distinguishing pure rotation from deformation or strain in the flow.^[20] Circulation provides an integral measure of vortex strength, defined as the line integral of the velocity field around a closed curve C:

\Gamma = \oint_C \vec{v} \cdot d\vec{l}.

This quantity, with units of velocity times length (m²/s), represents the net "flow" around the contour and is central to understanding large-scale rotational motion.^[21] William Thomson (Lord Kelvin) established in his 1869 paper that, for an inviscid, barotropic fluid under conservative body forces, the circulation around any material contour (one that moves with the fluid) remains constant over time—a result known as Kelvin's circulation theorem.^[21] This conservation law implies that in ideal flows, vortex circulation is preserved, influencing phenomena like vortex stretching and reconnection. The connection between circulation and vorticity is given by Stokes' theorem, which equates the circulation around a closed curve to the flux of vorticity through any surface S bounded by that curve:

\Gamma = \iint_S \vec{\omega} \cdot d\vec{A}.

Formulated by George Gabriel Stokes in the mid-19th century and applied to fluid contexts, this relation shows that circulation arises from the total vorticity enclosed by the contour, providing a bridge between local (vorticity) and global (circulation) descriptions of rotation.^[22] In practice, for two-dimensional flows, the circulation simplifies to the area integral of the scalar vorticity component normal to the plane. To measure these quantities experimentally, particle image velocimetry (PIV) is widely used, seeding the flow with tracer particles illuminated by laser sheets to capture instantaneous velocity fields via cross-correlation of image pairs.^[23] From the resulting velocity data, vorticity is computed as the spatial derivatives of velocity components (e.g., via finite differences or least-squares fitting), enabling direct mapping of \vec{\omega} and subsequent estimation of circulation around contours.^[23] PIV's non-intrusive nature makes it ideal for quantifying vorticity in complex flows, such as those in wind tunnels or water channels, with resolutions down to sub-millimeter scales. These metrics are essential for distinguishing irrotational vortices, where \vec{\omega} = 0 but nonzero circulation may persist due to singularities, from rotational ones with distributed vorticity.

Governing Equations

The governing equations for vortex dynamics in fluid flows are derived from fundamental principles of conservation of mass, momentum, and energy, primarily through the Navier-Stokes equations, which describe the motion of viscous fluids. For a Newtonian fluid with constant density ρ and dynamic viscosity μ, the incompressible Navier-Stokes momentum equation is given by

\rho \left( \frac{\partial \mathbf{v}}{\partial t} + (\mathbf{v} \cdot \nabla) \mathbf{v} \right) = -\nabla p + \mu \nabla^2 \mathbf{v} + \mathbf{f},

where \mathbf{v} is the velocity field, p is the pressure, and \mathbf{f} represents body forces per unit volume. This equation captures the inertial forces on the left-hand side, balanced by pressure gradients, viscous diffusion, and external forces.^[24]^[25] In the limit of inviscid flows, where μ approaches zero, the equation simplifies to the Euler equations:

\rho \left( \frac{\partial \mathbf{v}}{\partial t} + (\mathbf{v} \cdot \nabla) \mathbf{v} \right) = -\nabla p + \mathbf{f},

which omit viscous effects and are applicable to ideal fluids where friction is negligible, such as in high-Reynolds-number vortex cores.^[26]^[27] Taking the curl of the Navier-Stokes equations yields the vorticity transport equation, which directly governs the evolution of vorticity \boldsymbol{\omega} = \nabla \times \mathbf{v} in three-dimensional flows. For incompressible viscous fluids, it takes the form

\frac{D \boldsymbol{\omega}}{Dt} = (\boldsymbol{\omega} \cdot \nabla) \mathbf{v} + \nu \nabla^2 \boldsymbol{\omega},

where \nu = \mu / \rho is the kinematic viscosity and D/Dt is the material derivative. The term (\boldsymbol{\omega} \cdot \nabla) \mathbf{v} represents vortex stretching and tilting, which amplify vorticity in three dimensions by aligning and elongating vortex lines along principal strain directions, while \nu \nabla^2 \boldsymbol{\omega} accounts for diffusive spreading of vorticity due to viscosity. In inviscid cases, the diffusion term vanishes, leaving only advective and stretching effects.^[28]^[29]^[30] The Helmholtz decomposition provides a framework for separating the velocity field into components relevant to vortex identification, expressing \mathbf{v} as the sum of an irrotational (curl-free) part \mathbf{v}_i = \nabla \phi and a solenoidal (divergence-free) part \mathbf{v}_s such that \nabla \cdot \mathbf{v}_s = 0 and \nabla \times \mathbf{v}_s = \boldsymbol{\omega}. This decomposition isolates the rotational contribution to the flow, which is essential for quantifying vortex strength independent of potential flow effects.^[31]^[32] These equations rely on key assumptions about the flow regime. Incompressible flows assume constant density (\nabla \cdot \mathbf{v} = 0), valid for low-Mach-number conditions (typically Ma < 0.3) where pressure changes do not significantly alter density, simplifying vortex analyses in liquids or subsonic gases. Compressible flows, in contrast, incorporate density variations via an equation of state, allowing for baroclinic torque terms in the vorticity equation that generate vorticity from misaligned density and pressure gradients, as seen in supersonic vortices. However, in turbulent regimes, the Navier-Stokes equations face limitations due to the nonlinear advection terms producing chaotic, multiscale structures that require immense computational resources for direct numerical simulation, often necessitating turbulence models like Reynolds-averaged Navier-Stokes to approximate unresolved scales.^[33]^[34]^[35]^[36]

Classification

Irrotational Vortices

Irrotational vortices, also known as potential vortices, are idealized flow configurations in which the vorticity \boldsymbol{\omega} = \nabla \times \mathbf{v} = \mathbf{0} everywhere except possibly at isolated singularities, allowing the velocity field \mathbf{v} to be expressed as the gradient of a scalar velocity potential \phi, such that \mathbf{v} = \nabla \phi.^[37]^[38] This irrotational condition implies that fluid elements translate and deform without rotating about their own axes, enabling the use of Laplace's equation \nabla^2 \phi = 0 to govern the flow in incompressible cases.^[9] Such models approximate inviscid, incompressible fluids and form the basis for analyzing many aerodynamic phenomena under ideal conditions. A canonical example is the free vortex model, which describes a purely circulatory flow with azimuthal symmetry around a central axis. In this model, the tangential velocity component v_\theta varies inversely with the radial distance r from the axis, given by

v_\theta = \frac{\Gamma}{2\pi r},

where \Gamma is the constant circulation strength, defined as the line integral of velocity around a closed contour enclosing the singularity.^[37] The radial velocity v_r = 0, and the velocity potential is \phi = -\frac{\Gamma}{2\pi} \theta, confirming the irrotational nature outside the origin where v_\theta becomes singular. This inverse radial dependence results in higher speeds near the center, capturing the rotational-like appearance of the flow despite zero vorticity in the domain.^[37] Specific realizations include the point vortex in two-dimensional flows, representing a singularity at a point in the plane where circulation \Gamma induces circulatory motion, and the line vortex in three dimensions, modeled as an infinite straight vortex filament with uniform strength along its length, producing the same $1/r velocity profile in perpendicular planes.^[38] These models are applied in ideal aerodynamics, such as approximating wingtip vortices trailing from finite wings in Prandtl's lifting-line theory, where the trailing line vortices account for induced drag and downwash without viscous diffusion.^[39] While powerful for theoretical analysis, irrotational vortex models neglect viscous effects, leading to unphysical singularities and failing to capture real-fluid dissipation or boundary layer interactions.^[40] For more complex configurations involving multiple singularities, such as arrays of point vortices, the velocity potential can be expanded using multipole series solutions to Laplace's equation, representing the far-field behavior through monopole, dipole, and higher-order terms to efficiently compute interactions in potential flow theory.^[40] In contrast to rotational vortices, which exhibit distributed non-zero vorticity, irrotational types concentrate all "rotation" at singularities within otherwise potential flows.^[38]

Rotational Vortices

Rotational vortices are characterized by non-zero vorticity distributed throughout a finite core region, distinguishing them from irrotational flows where vorticity is confined to singular lines. In these structures, fluid elements within the core undergo actual rotation, leading to shear and viscous effects that are prominent in real-world, viscous flows. This distributed vorticity arises from mechanisms such as boundary layer separation or initial momentum imbalances, resulting in a velocity field that transitions from solid-body-like rotation in the core to potential flow decay farther out.^[41] A canonical model for rotational vortices is the Rankine vortex, which approximates the flow as a forced vortex inside a cylindrical core of radius a and an irrotational free vortex outside. Within the core (r < a), the tangential velocity follows solid-body rotation: v_\theta = \omega r, where \omega is the constant angular velocity, yielding uniform vorticity \zeta = 2\omega. Beyond the core (r > a), the flow becomes irrotational with v_\theta = \frac{\Gamma}{2\pi r}, where \Gamma = 2\pi \omega a^2 is the circulation, ensuring a smooth maximum velocity at the core edge. This piecewise model, while idealized, captures the essential features of concentrated rotational cores in applications like cyclone separators and atmospheric tornadoes.^[42] Rotational vortices can be classified as forced or free based on their sustaining mechanisms. Forced vortices are maintained by continuous external torque, such as in a mechanically stirred tank, where the entire fluid rotates as a rigid body with linear velocity increase (v_\theta \propto r) and constant non-zero vorticity. In contrast, free vortices form from initial conditions without ongoing external forcing, like trailing vortices behind aircraft wings, where vorticity diffuses over time under viscous effects. A representative example is the Lamb-Oseen vortex, an exact solution to the Navier-Stokes equations for a viscous line vortex with initial Gaussian vorticity distribution. Its tangential velocity profile is v_\theta = \frac{\Gamma_0}{2\pi r} \left[1 - \exp\left(-\frac{r^2}{r_c^2}\right)\right], where \Gamma_0 is the initial circulation and r_c scales the core radius, which grows diffusively as \sqrt{4\nu t} with kinematic viscosity \nu and time t. This model is particularly relevant for simulating aircraft wake vortices, predicting peak velocities and decay rates that inform air traffic safety protocols.^[43] In three dimensions, rotational vortices often manifest as filamentary structures, slender tubes of concentrated vorticity that can stretch, reconnect, and interact to drive complex flow evolution. These vortex filaments, approximated as line elements with localized circulation, exhibit dynamics governed by self-induction and mutual interactions, leading to phenomena like Crow instability in pairs of filaments. Such 3D configurations are crucial for understanding turbulence and superfluid flows, where filaments form lattices or knots that persist over long times.

Formation and Structure

Mechanisms of Formation

Vortices form in fluids through various instability-driven processes that concentrate vorticity, often initiated by velocity gradients or external forces. One primary mechanism is the roll-up of shear layers, where parallel streams of differing velocities interact, leading to the Kelvin-Helmholtz instability. This instability amplifies small perturbations, causing the interface between the streams to deform and roll into discrete vortices, which may pair and merge in free shear flows such as jets or wakes.^[45]^[46] Another key process occurs at boundaries, where adverse pressure gradients decelerate the flow, promoting boundary layer separation and subsequent vortex shedding. In this scenario, the detached shear layer becomes unstable, generating alternating vortices in a periodic pattern, as exemplified by the von Kármán vortex street behind bluff bodies like cylinders. This shedding arises from the imbalance between inertial and pressure forces, detaching recirculating flow regions that roll up into coherent structures.^[47]^[48]^[49] In rotating flows, centrifugal forces drive radial outflow, balanced by axial inflow toward a central drain, forming axisymmetric vortices like the bathtub vortex in a rotating container. The Coriolis effect in the rotating frame further influences the azimuthal velocity profile, stabilizing the vortex core and enhancing circulation. Vorticity amplification plays a role here by concentrating angular momentum near the axis.^[50] (Note: Direct link to JFM 2006 paper via DTU archive) Additional triggers include buoyancy-driven instabilities in thermal convection, where density gradients from heating lead to rising plumes that organize into vortical structures, as seen in Rayleigh-Bénard convection. In compressible flows, shock wave interactions with shear layers or boundaries generate baroclinic vorticity through rapid pressure changes, producing counter-rotating vortex pairs. Multiphase systems, such as air-water interfaces, exhibit vortex formation via interfacial instabilities, though detailed mechanisms remain less explored compared to single-phase cases.^[51]^[52]^[53]^[54]

Geometric Configurations

Vortices manifest in diverse geometric forms that define their spatial organization and interaction within fluid flows. These configurations range from simple idealized structures to complex three-dimensional topologies, providing essential models for analyzing vortical motion. Line vortices, vortex rings, vortex sheets, and arrays represent fundamental archetypes, while more intricate 3D arrangements like tubes and dipoles illustrate topological variations. Understanding these geometries is crucial for applications in aerodynamics and oceanography, where vortex topology influences flow stability and energy transfer.^[55] A line vortex, or vortex filament, is an idealized representation of a vortex as an infinitely long, straight thread of concentrated vorticity, commonly used to model two-dimensional flows. This configuration assumes uniform circulation Γ along the filament, inducing a circumferential velocity field that decays inversely with distance from the axis, akin to a potential vortex in irrotational flow outside the core. Such models simplify the study of vortex interactions in unbounded fluids, as seen in approximations for aircraft trailing vortices.^[56] Vortex rings consist of closed, toroidal loops of vorticity, propagating through fluids via self-induced motion. These structures, exemplified by smoke rings, maintain their topology under ideal conditions, with propagation speed governed by Helmholtz's laws of vortex motion, which dictate that vortex strength remains constant and lines move with the local fluid velocity. In three dimensions, the ring's velocity arises from the Biot-Savart integration over its contour, leading to axial translation while expanding radially over time. Experimental visualizations confirm that vortex rings in viscous fluids exhibit core deformation but preserve linkage until dissipation intervenes. Vortex sheets represent continuous distributions of vorticity across a surface, often modeling shear layers or wakes where velocity discontinuities occur. These planar or curved arrays of infinitesimal vortex elements induce velocities via the Biot-Savart law, expressed as

\mathbf{v}(\mathbf{x}) = \frac{\Gamma}{4\pi} \int \frac{d\mathbf{l} \times (\mathbf{x} - \mathbf{x}')}{|\mathbf{x} - \mathbf{x}'|^3},

where the integral sums contributions from sheet elements, enabling computation of induced flows in vortex lattice methods. Vortex arrays extend this to discrete lattices, such as those in rotor wakes, where periodic arrangements approximate infinite sheets for efficient numerical simulation. These configurations capture collective effects like mutual induction in trailing vortex systems.^[57]^[58] In three-dimensional flows, vortices form extended tubes—slender cores of concentrated vorticity—and dipoles, pairs of oppositely signed vortices that translate perpendicular to their line connecting them. Vortex tubes model elongated structures like tornadoes, with topology preserved until interactions alter connectivity. Dipoles, in contrast, exhibit self-propulsion due to mutual induction, serving as building blocks for more complex arrays. A key topological process in these 3D structures is vortex reconnection, where intersecting tubes exchange segments, fundamentally changing the linking of vortex lines and enabling cascade of enstrophy in turbulent flows. This event, first numerically demonstrated in classical fluids, involves bridging and rapid separation post-contact, conserving overall helicity while altering local geometry. Irrotational profiles dominate outside these cores, contrasting with rotational interiors.^[59]^[60]

Dynamics

Pressure and Velocity Profiles

In a vortex, the velocity field is typically dominated by the tangential component v_\theta(r), which varies radially from the core outward, while the radial velocity v_r is approximately zero in steady-state conditions due to the absence of net inflow or outflow in the absence of external forcing.^[61] The axial velocity v_z may be present in three-dimensional vortices, such as those with swirl, but often remains secondary to the azimuthal motion in idealized models.^[62] For example, in the Rankine vortex model, the tangential velocity increases linearly with radius r within the core (v_\theta = \omega r) and decays inversely outside (v_\theta = \Gamma / (2\pi r)), providing a smooth transition from rotational to irrotational flow.^[63] The pressure distribution within a vortex arises from the radial momentum balance in the Euler equations, where the centrifugal force due to rotation is countered by the radial pressure gradient, known as cyclostrophic balance.^[64] This yields the relation

\frac{\partial p}{\partial r} = \rho \frac{v_\theta^2}{r},

which integrates to a pressure decrease toward the core, often resulting in a low-pressure region that can drive secondary flows or instabilities if perturbed.^[65] In strong vortices, this core pressure deficit can approach vacuum levels relative to the ambient, enhancing the vortex's intensity.^[66] The core structure significantly influences these profiles: irrotational vortices exhibit a singular velocity at the center due to infinite vorticity concentration, whereas rotational vortices feature a filled core with distributed vorticity, avoiding singularities.^[67] A representative example is the Burgers vortex, where vorticity decays Gaussianly (\omega \propto e^{-r^2 / a^2}), leading to a smooth tangential velocity profile that peaks near the core and decays exponentially outward.^[68] Experimental measurement of these profiles traditionally employs Pitot tubes for total and static pressure to infer velocities, or hot-wire anemometry and laser Doppler velocimetry (LDV) for direct component resolution in controlled flows.^[69] Modern advancements include LIDAR systems, which provide non-intrusive, remote sensing of radial velocity fields in atmospheric or aeronautical vortices, enabling high-resolution profiling over large distances with minimal flow disturbance.^[70]

Evolution and Instabilities

Vortices evolve over time through processes dominated by viscous diffusion, which spreads vorticity according to the transport equation's viscous term \nu \nabla^2 \boldsymbol{\omega}, where \nu is the kinematic viscosity and \boldsymbol{\omega} is the vorticity vector; this diffusion causes the vortex core to expand radially, reducing the peak vorticity and circulation strength. In the case of an idealized line vortex, the peak azimuthal velocity decays as u_\theta \propto t^{-1/2} as vorticity diffuses outward, leading to a gradual dissipation of the coherent structure. At high Reynolds numbers (Re), this viscous decay is suppressed, allowing vortices to maintain coherence for extended periods; the characteristic decay timescale scales positively with Re, often as \tau \sim \mathrm{Re} for the overall lifespan in confined or impulsively generated flows, enabling persistent structures in turbulent environments.^[30]^[71]^[72] Instabilities further drive vortex evolution by amplifying perturbations that lead to deformation, reconnection, or breakdown. The Crow instability in counter-rotating vortex pairs arises from the mutual induction that excites long-wavelength sinusoidal modes, causing the vortices to crowd together, link, and descend, with maximum growth rates occurring for wavelengths around seven times the initial separation. Vortex ring reconnection, observed in head-on collisions, involves the filaments stretching, approaching, and topologically reconnecting, dissipating energy through viscous annihilation of opposing vorticity layers and forming new ring configurations; this process is particularly efficient at moderate Re, where reconnection times scale between \mathrm{Re}^{-1} and \mathrm{Re}^{-1/2}. In axial swirling flows, such as leading-edge vortices over delta wings at high angles of attack, breakdown occurs when adverse pressure gradients stagnate the core axial velocity, expanding the vortex into a recirculating bubble and transitioning to a wake-like state, often triggered by critical swirl levels around 1.2–1.5.^[73]^[74]^[75] In two-dimensional turbulence, vortex merging and pairing contribute to an inverse energy cascade, where enstrophy dissipates at small scales while energy transfers upscale through the coalescence of same-signed vortices into larger entities, following Kraichnan's dual-cascade theory; numerical studies show that merging events align with spectral slopes of -5/3 in the inverse range, enhancing large-scale coherence. Viscosity modulates these evolutions by diffusing fine-scale vorticity, which can accelerate decay in isolated vortices but stabilize pairs against short-wave instabilities by damping rapid perturbations. Stratification introduces buoyancy effects that constrain vertical displacements, often inhibiting merger in horizontal planes by generating internal waves that dissipate energy, though moderate stratification can enhance horizontal crowding and short-wavelength instabilities in vortex pairs. In superfluids, quantum vortex dynamics reveal quantized reconnections and Kelvin wave cascades, with post-2010 experiments in atomic Bose-Einstein condensates demonstrating coherent pairing and inverse cascades analogous to classical 2D turbulence, driven by nonlocal interactions in the vortex tangle; as of 2025, a universal law has been discovered governing reconnection in superfluid helium, where post-reconnection separation velocity exceeds the approach velocity, advancing models of quantum turbulence.^[76]^[77]^[78]^[79]^[80]

Phenomena and Applications

Natural Occurrences

Vortices manifest prominently in Earth's atmosphere through intense rotational phenomena driven by convective and shear processes. Tornadoes form as narrow, violently rotating columns of air extending from supercell thunderstorms, often originating from the rotation of a mesocyclone—a large-scale updraft vortex typically 2-6 miles in diameter detected by Doppler radar.^[81] These mesocyclones arise when horizontal vorticity from wind shear is tilted into the vertical by the storm's updrafts, concentrating rotation near the ground to produce the tornado funnel.^[82] Hurricanes feature eyewall vortices, where a ring of intense thunderstorms encircles the calm central eye, with embedded mesovortices and tornado-scale vortices prevalent at the inner edge of the eyewall convection, contributing to the storm's destructive winds exceeding 74 mph.^[83]^[84] Dust devils, smaller-scale atmospheric vortices, emerge in arid regions under clear skies, forming as thermal columns of rising hot air that entrain dust particles into spinning funnels reaching heights of several hundred meters and winds up to 60 mph.^[85] In oceanic environments, vortices play a key role in large-scale circulation and mixing. The Naruto whirlpools in Japan's Naruto Strait arise from tidal currents colliding between the Pacific Ocean and Seto Inland Sea, generating vortices up to 20 meters in diameter with water speeds reaching 20 km/h during spring tides.^[86] Gulf Stream eddies, mesoscale rotational features with diameters of 50-200 km, detach from the western boundary current and transport heat, salt, and nutrients across the North Atlantic, significantly influencing global ocean circulation by modulating the main current's path and enhancing meridional exchanges.^[87]^[88] These eddies contribute to the ocean's role in climate regulation by facilitating the poleward heat flux equivalent to a substantial portion of the atmosphere's transport capacity.^[89] Geophysical processes also produce striking vortex formations beyond Earth. Volcanic eruptions can generate vortex rings in ash plumes when gas bursts from vents create toroidal structures, as observed at Mount Etna where small vents emitted gas puffs forming visible rings up to several meters in diameter amid ongoing activity.^[90] In planetary atmospheres, Jupiter's Great Red Spot stands as a persistent anticyclonic vortex, a high-pressure storm larger than Earth at approximately 10,000 miles wide, persisting for over 350 years and extending deep into the planet's atmosphere up to 200 miles.^[91]^[92] Biological systems exhibit vortices in fluid dynamics critical to organ function. In the human heart, blood flow from the left atrium into the ventricle forms vortex rings during diastole, optimizing ejection efficiency by minimizing energy dissipation and ensuring uniform shear along the flow boundaries, with peak swirl strengths reflecting cardiac health.^[93]^[94] These vortices facilitate the heart's pumping action, reducing dissipation and enhancing propulsion, as deviations in vortex formation correlate with conditions like diastolic dysfunction.^[95] Recent studies from the 2020s highlight vortices' roles in amplifying climate change effects, particularly through disruptions in large-scale atmospheric and oceanic circulations. Arctic amplification, driven by sea ice loss, has intensified fluctuations in the stratospheric polar vortex, leading to weakened vortex events that propagate cold air outbreaks to midlatitudes and exacerbate extreme weather variability.^[96] In the Arctic, anomalous transport during strong polar vortex persistence, as in 2019/2020, altered trace gas distributions and contributed to hemispheric climate feedbacks, with projections indicating increased vortex instability under warming scenarios.^[97] As of November 2025, meteorological forecasts predict a stratospheric warming event disrupting the polar vortex in December, potentially leading to cold outbreaks across North America and Europe.^[98] Oceanic mesoscale eddies, including those in the Gulf Stream, are projected to intensify with climate change, enhancing heat transport and potentially amplifying regional warming by up to 20% in eddy-rich zones.^[99]

Engineering Contexts

In engineering, vortices are leveraged or mitigated across multiple disciplines to optimize performance, ensure safety, and enhance efficiency in fluid systems. In aerospace engineering, the vortex lattice method (VLM) serves as a foundational computational tool for predicting aerodynamic loads on aircraft wings and other lifting surfaces during preliminary design phases, modeling the flow as a distribution of discrete vortices bound to the surface and trailing from edges.^[100] Wake vortices generated by aircraft during takeoff and landing represent a significant hazard to trailing aircraft, prompting the development of dynamic spacing criteria by NASA to minimize separation distances while maintaining air traffic flow.^[101] Tip vortices at wingtips contribute to induced drag but can be managed through winglet designs that reduce vortex strength and improve fuel efficiency by up to 5-6% in commercial jets.^[100] In civil and hydraulic engineering, vortex flow intakes are employed in structures like pump stations and dropshafts to facilitate sediment transport and prevent clogging by drawing solids into the core of a controlled vortex, where the swirl velocity can reach 10-20 times the axial flow velocity. Vortex shedding from cylindrical structures, such as bridge piers or chimneys, induces oscillatory forces that can lead to structural vibrations; for instance, the Strouhal number for vortex shedding frequency in uniform flow typically ranges from 0.18 to 0.22 for circular cylinders, guiding the design of helical strakes to suppress amplitudes by disrupting coherent vortex formation.^[102] In wind engineering, discrete vortex methods simulate unsteady aerodynamics around bridge decks to predict flutter instabilities, enabling adjustments in deck geometry to maintain stability under gusts up to design wind speeds of 100-150 km/h.^[102] Mechanical engineering applications, particularly in turbomachinery, rely on understanding vortex dynamics to boost efficiency and reduce losses. Tip leakage vortices in axial compressors and turbines form due to pressure differences across blade tips, creating low-momentum regions that can reduce stage efficiency by 2-5% if unmanaged; vortex generators placed on endwalls mitigate secondary flows by energizing the boundary layer and redirecting vorticity.^[103] Horseshoe vortices originating at blade leading edges interact with passage vortices, amplifying losses in high-pressure turbine stages where swirl angles exceed 60 degrees, necessitating optimized blade profiling to control vortex migration.^[104] In cyclone separators, the centrifugal forces from a tangential vortex accelerate particle separation in gas-solid flows, achieving collection efficiencies over 90% for particles larger than 10 microns in industrial dust removal systems.^[105] In chemical engineering, engineered vortices enhance mixing and separation processes critical to reactor design and product quality. Vortex-inducing T-junction mixers generate chaotic advection through merging vortices, reducing mixing times by factors of 2-5 compared to conventional impinging jets, particularly beneficial for fast reactions in microreactors handling viscous fluids.^[106] In stirred tanks, surface vortices induced by impellers promote gas entrainment or heat transfer but must be controlled to avoid air ingestion that could degrade product purity; baffles suppress vortex depth to maintain rotational speeds up to 500 rpm without vortex-induced instabilities.^[107] Gas-liquid vortex separators utilize swirl flow to achieve phase disengagement with pressure drops under 10 kPa, enabling compact designs for offshore processing where space constraints limit traditional gravity separators.^[108]

References

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A vortex is rotating fluid around a centerline, defined by vorticity, which measures the rate of local fluid rotation.
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[PDF] Chapter 7 Fundamental Theorems: Vorticity and Circulation
Vorticity is the local rotation of a fluid element, twice the local rate of rotation, and is the local spin of the fluid element.
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A vortex line is a line whose tangent is everywhere parallel to the local vorticity vector. The vortex lines drawn through each point of a closed curve ...
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We describe four different types of vortex interactions in 2d decaying turbulence: two-vortex merger, dipole propagation, vortex scattering, and tripole merger.<|control11|><|separator|>
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A major factor in the development of enhanced maneuverability and reduced drag by aerodynamic means is the use of effective vortex control devices. The key to ...
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A vortex is intuitively recognized as the rotational/swirling motion of a fluid. Vortices are ubiquitous in nature and are viewed as the building blocks, ...
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Computational Fluid Dynamics and Vortex Dynamics - Z. Jane Wang
The interaction between flapping wings and unsteady flows is governed by the Navier-Stokes equation coupled to the dynamic boundaries.
[8]
[PDF] Detection and Visualization of Vortices - cavs.msstate.edu
Surprisingly, the swirling feature in flow fields, commonly refered to as a vortex, is an example of a feature for which a precise definition does not exist.
[9]
[PDF] Evolution and transition mechanisms of internal swirling flows with ...
Jan 16, 2018 · created along the vortex cores, as shown in Fig. 20(c). The low-pressure core on the centerline is caused by the swirl motion of the bulk flow.
[10]
Potential Flow Theory – Introduction to Aerospace Flight Vehicles
Vortex Flow (Irrotational Vortex). A vortex flow represents purely rotational motion around the origin, as shown in the figure below, where the tangential ...
[11]
[PDF] Coherent Motions in the Turbulent Boundary Layer - ChaosBook.org
Given the definition presented in Section 1.1, vortices are among the most coherent of turbulent motions and tend to be persistent in the absence of ...
[12]
A Vortex Bottle - The Wonders of Physics
In the world around us there are many examples of vortices: tornadoes, whirlpools in a sink or tub, swirling vortices in rivers and oceans and, of course, ...Missing: nature | Show results with:nature
[13]
Theories on Tornado and Waterspout Formation in Ancient Greece ...
Oct 1, 2019 · Aristotle believed that tornadoes and waterspouts were associated with the wind trapped inside the cloud and moving in a circular motion.
[14]
[PDF] Historical Development of Fluid Dynamics
Mar 29, 2021 · Vortex atom theory is the new dimension in the history of vortex dynamics, which was done by William Thomson; later it was developed by Lord ...
[15]
[PDF] Ludwig Prandtl's Boundary Layer
In 1904 a little-known physicist revolutionized fluid dynamics with his notion that the effects of friction are experienced only very near an object moving ...
[16]
Vortex Methods for Flow Simulation - NASA ADS
Recent progress in the development of vortex methods and their applications to the numerical simulation of incompressible fluid flows are reviewed.Missing: 1970s | Show results with:1970s<|separator|>
[17]
Polar Vortices in Planetary Atmospheres - Mitchell - AGU Journals
Dec 1, 2021 · In recent years, there have been significant advances in the observation of planetary polar vortices, culminating in the fascinating discovery ...Missing: advancements | Show results with:advancements
[18]
[PDF] Helmholtz (1858)
Helmholtz's paper on vortex motions was first published in 1858 in the. Journal fur die reine and angewandte Mathematik*. It was the first in a series of ...
[19]
[PDF] an introduction to - fluid dynamics
... velocity distribution with specified rate page 84 of expansion and vorticity ... (twice the local angular velocity of the fluid). 1 (OUi OU/) e -. - +- rate-of ...
[20]
[PDF] VI.-On Vortex Motion. By Sir W. THOMSON.
The mathematical work of the present paper has been performed to illus- trate the hypothesis, that space is continuously occupied by an incompressible.Missing: Kelvin | Show results with:Kelvin
[21]
[PDF] Stokes's Fundamental Contributions to Fluid Dynamics
Jul 12, 2019 · It also expresses the fact that the circulation around the closed boundary curve C = ∂A is equal to the flux of vorticity across the surface.
[22]
Particle image velocimetry - Classical operating rules from today's ...
In this work, we provide a detailed review of particle image velocimetry (PIV) for velocity measurements in flows.
[23]
Navier-Stokes Equations
These equations describe how the velocity, pressure, temperature, and density of a moving fluid are related. The equations were derived independently by G.G. ...Euler Equations · Aerodynamics Index · Conservation of Momentum
[24]
[PDF] 3 The Navier-Stokes Equation
... Navier-Stokes equation to find. Dω. Dt= (ω · r)u + ⌫r2ω. (3.13). This is the vorticity equation for a viscous fluid. The term due to viscosity, naturally.
[25]
[PDF] Euler's Equation for Inviscid Fluid Flow
Derivation of Euler's Equation for Inviscid Fluid Flow from Newton's Second Law of Motion: We can derive Euler's equation for inviscid fluid flow using ...
[26]
[PDF] An Introduction to the Incompressible Euler Equations - UC Davis Math
Sep 25, 2006 · We derive the incompressible Euler equations for the flow of an inviscid, incompressible fluid, describe some of their basic mathematical ...
[27]
[PDF] Vorticity Transport Equation
[B] In a three-dimensional, inviscid flow the vorticity transport equation becomes. Dω. Dt. = (ω.∇)u. (Bhi8). Page 2. Therefore, in a flow that originates with ...Missing: 3D | Show results with:3D
[28]
[PDF] The Vorticity equation
For 3D flows, the first term on the RHS in (4) represents vortex stretching: velocity gradients lead to a change in the rate of rotation of material particles.
[29]
[PDF] 3.5 Vorticity Equation
• Diffusion of vorticity is analogous to the heat equation: = K∇. 2. T, where K is the. ∂t heat diffusivity. Numerical example for ν ∼ 1 mm. 2. /s. For ...
[30]
[PDF] Helmholtz Decomposition of Vector Fields
Introduction. The Helmholtz Decomposition Theorem, or the fundamental theorem of vector calculus, states that any well-behaved vector field can be ...
[31]
Helmholtz decomposition coupling rotational to irrotational flow of a ...
Sep 26, 2006 · The decomposition of the velocity into rotational and irrotational parts holds at each and every point and varies from point to point in the flow domain.
[32]
Compressible Flow vs Incompressible Flow in Fluid Mechanics
Aug 11, 2023 · Compressible flow is a flow that changes in density under pressure, whereas incompressible flow does not. A good indicator is Mach Number.
[33]
[PDF] Vortex stretching in incompressible and compressible fluids
remains valid even for non isentropic compressible flows and incompressible flows with nonconstant density. This is the conservation of the potential vorticity.
[34]
Turbulent Flows – Introduction to Aerospace Flight Vehicles
Mathematical models, such as the Navier-Stokes equations, can be used to describe turbulent flows. However, solving these equations accurately for all ...
[35]
[PDF] Lecture 4: The Navier-Stokes Equations: Turbulence
Sep 23, 2015 · To appraise the potential and limitations of the numerical approach to fluid turbulence, it is instructive to revisit some basic facts about the ...Missing: regimes | Show results with:regimes
[36]
[PDF] Potential Flow Theory - MIT
Irrotational Vortex (Free Vortex). A free or potential vortex is a flow with circular paths around a central point such that the velocity distribution still ...
[37]
[PDF] 3 IRROTATIONAL FLOWS, aka POTENTIAL FLOWS - DAMTP
Irrotational flows, also called potential flows, have a velocity field that can be represented as the gradient of a scalar field, and their vorticity is zero.
[38]
Lifting Line Theory – Introduction to Aerospace Flight Vehicles
Prandtl's lifting line theory addressed this need by modeling a finite wing as a bound vortex line with a spanwise circulation distribution.
[39]
[PDF] CHAPTER 10 ELEMENTS OF POTENTIAL FLOW ( )# !2U
Potential flow motions beyond the vortical region do not contribute to the total momentum of the fluid! 10.11 MULTIPOLE EXPANSION OF THE POISSON EQUATION IN THE ...
[40]
Vortex Flow - an overview | ScienceDirect Topics
Vortex flow is a complex, disordered flow with eddies or vortices, which are regions of concentrated rotation, and can be rotational or irrotational.
[41]
[PDF] The Rankine Vortex Model - Moodle@Units
Oct 4, 2006 · The Rankine vortex model is a circular flow in which an inner circular region about the origin is in solid rotation, while the outer region ...
[42]
Vortices
### Definitions and Differences Between Free and Forced Vortices
[43]
[PDF] Review of Idealized Aircraft Wake Vortex Models
The Lamb-Oseen model predicts the highest peak tangential velocity and shows the largest variation in peak tangential velocity as a function of vortex core ...
[44]
The three-dimensional evolution of a plane mixing layer: the Kelvin ...
Apr 26, 2006 · The spanwise vorticity rolls up into a corrugated spanwise roller with vortex stretching creating strong spanwise vorticity in a cup-shaped ...<|separator|>
[45]
Vortex sheet roll-up revisited | Journal of Fluid Mechanics
Sep 18, 2018 · The second is the Kelvin–Helmholtz instability of an infinite vortex sheet. The critical time at which the sheet forms a singularity in ...
[46]
On the Origins of Vortex Shedding in Two-dimensional ...
Results are presented here on the ability to suppress the von Kármán vortex street via mitigation of the VSM, thereby illustrating that the VSM is a necessary ...
[47]
Suppression of the von Kármán vortex street behind a circular ...
Feb 15, 2007 · An advanced moving-wall control strategy to manage the unsteady separated flow over a circular cylinder is developed.
[48]
An Insight into Quasi-Two-Dimensional Flow Features Over Turbine ...
It features the separation of a laminar boundary layer that is induced by an adverse pressure gradient. ... Relationship Between Von Karman Vortex Shedding and ...Transition Modeling · Separated Flow Transition · Streamwise Vorticity...<|separator|>
[49]
Analysis of a stable bathtub vortex in a rotating container
Mar 20, 2023 · The centrifugal force causes the fluid at the bottom to flow radially outward. This flow is balanced by flux from the interior of the fluid.
[50]
Large-scale vortex formation in three-dimensional rotating Rayleigh ...
Jun 14, 2024 · It is confirmed that a large-scale vortex (LSV) with positive vorticity (cyclonic) is formed over a significant part of the region and its horizontal size ...
[51]
Henri Bénard: Thermal convection and vortex shedding
We present in this article the work of Henri Bénard (1874–1939), a French physicist who began the systematic experimental study of two hydrodynamic systems.<|separator|>
[52]
https://www.sciencedirect.com/science/article/pii/S1631072117300980
[53]
Vortex bifurcation and air entrainment mitigation using multi-point ...
Apr 25, 2024 · Vortex formation and air entrainment are integral phenomena during the drainage of water through intakes, particularly at high liquid ...
[54]
Local vortex line topology and geometry in turbulence
Aug 5, 2021 · Topological characterization of the vorticity field provides a useful analytical basis for examining vorticity dynamics in turbulence and other fluid flows.
[55]
[PDF] VORTEX DYNAMICS: THE LEGACY OF HELMHOLTZ AND KELVIN
The fluid dynamical origins of knot theory and topology. The origins of vortex dynamics lie in the seminal work of Hermann von Helmholtz [7], who (i) ...
[56]
Viscous diffusion induced evolution of a vortex ring - AIP Publishing
Mar 23, 2021 · Theoretical works on vortex rings may be traced back to the seminal work of Helmholtz40 and Kelvin.41 Lamb42 obtained an expression for the ...
[57]
[PDF] Biot-Savart law and Helmholtz's theorems, Vortex filament: Infinite and
The two vortex sheets-the one with vortex lines running parallel to y with strength y (per unit length in the x direction) and the other with vortex lines ...
[58]
Bridging in vortex reconnection | Physics of Fluids (PFL)
Oct 1, 1987 · The mechanism of vortex reconnection is investigated by solving the Navier–Stokes equation numerically starting with a closed knotted vortex ...
[59]
Helicity conservation by flow across scales in reconnecting vortex ...
We find that the reassociation of vortex lines through a reconnection enables the transfer of helicity from links and knots to helical coils.
[60]
[PDF] Experimental profiles of velocity components and radial pressure ...
It has been common practice in the study of cyclone separators and other vortex devices to evaluate the radial distribution of the tangential velocities from ...Missing: dynamics | Show results with:dynamics
[61]
A two-cell vortex model | Physics of Fluids - AIP Publishing
Sep 30, 2024 · The derived tangential velocity profile is kept general, allowing for the recovery of the single-cell profile as a special case. The model ...
[62]
Viscous Rankine vortices | Physics of Fluids - AIP Publishing
Jul 7, 2022 · The obvious elementary mathematical vortex in two dimensions is the singular vortex of potential flow theory. It has no length scale, but ...Missing: filled | Show results with:filled
[63]
[PDF] Vortex Flows
» It is convenient to express Euler's equation in cylindrical ... acceleration and we refer to this as cyclostrophic balance. » Cyclostrophic balance is closely ...Missing: distribution | Show results with:distribution
[64]
Mathematical Modeling of Structure and Dynamics of Concentrated ...
The decrease in pressure reflects the so-called cyclostrophic balance, i.e., the mutual counteraction of centrifugal force and radial pressure gradient. Also, ...
[65]
REVIEW Centrifugal Waves in Tornado-Like Vortices - AMS Journals
For the base-state vortex flow V(r) to be a solution of the above equations, a state of cyclostrophic balance is implied. The azimuthal base-state velocity ...
[66]
[PDF] Vorticity - MIT
The fluid which has been affected by viscous forces forms a concentrated vortex. In Fig. 23b, two vortices are made by pulling a plate with sharp edges through ...
[67]
[PDF] a brief introduction to vortex dynamics and turbulence - DAMTP
It is this velocity field that transports the vorticity field, a nonlinear feedback that encapsulates the central difficulty of the dynamics of fluids. If, as ...
[68]
[PDF] An Experimental And Theoretical Study Of The Confined Vortex With ...
The angular velocity (i.e. tangential Reynolds number) was held constant, and the velocity profiles were obtained for a variety of air flow rates (i.e. radial.
[69]
[PDF] Aircraft Wake Vortex Study and Characterization with 1.5 µm Fiber ...
Monitoring of vortices at ranges exceeding a few hundred meters is best carried out using pulsed lidar.
[70]
[PDF] Vorticity diffusion and boundary layers
Let us consider the decay of a line vortex in which the fluid velocity is given in plane polar coordinates (r, θ) by: u = Γ. 2πr eθ. This is an idealised ...
[71]
On the stages of vortex decay in an impulsively stopped, rotating ...
Dec 18, 2019 · The complete decay of the initial SBR is captured by means of direct numerical simulations for a wide range of Reynolds numbers ( $Re$).
[72]
Stability theory for a pair of trailing vortices | AIAA Journal
Stability theory for a pair of trailing vortices. Corrections for this article. Stability theory for a pair of trailing vortices. S. C. CROW ... See PDF for ...
[73]
Reconnection of two vortex rings | Physics of Fluids - AIP Publishing
Apr 1, 1989 · We found two prominent reconnection processes: first, the two vortex rings merge into one by viscous annihilation of opposite vorticity and second, two new ...
[74]
Vortex breakdown: a review - ScienceDirect.com
Although early experimental investigations of vortex breakdown were carried out in flows over delta wings, there was a need for more controlled conditions.
[75]
Vortex merging and spectral cascade in two‐dimensional flows
Sep 1, 1996 · The merging of two identical vortices is studied numerically using a spectral code. It is noted that the enstrophy cascade is most active on ...
[76]
Understanding evolution of vortex rings in viscous fluids
Dec 13, 2017 · The evolution of vortex rings in isodensity and isoviscosity fluid has been studied analytically using a novel mathematical model.
[77]
Effect of density stratification on vortex merger - AIP Publishing
Jan 7, 2013 · We study the effect of density stratification in the plane on the merging of two equal vortices. Direct numerical simulations are performed ...
[78]
Coherent vortex dynamics in a strongly interacting superfluid on a ...
Dec 20, 2019 · Abstract. Quantized vortices are fundamental to the two-dimensional dynamics of superfluids, from quantum turbulence to phase transitions.
[79]
Severe Weather 101: Tornado Detection
When a Doppler radar detects a large rotating updraft that occurs inside a supercell, it is called a mesocyclone. The mesocyclone is usually 2-6 miles in ...
[80]
How tornadoes form – Markowski Research Group
In step 1 of tornadogenesis, the storm acquires large-scale rotation—a midlevel mesocyclone—by tilting the horizontal vorticity in winds entering the storm's ...
[81]
Hurricane Dynamics - NOAA
The clear eye, 15-30 km in radius, contains the axis of vortex rotation and is surrounded by this ring of strong winds. The eye is characterized by the warmest ...
[82]
Prevalence of tornado-scale vortices in the tropical cyclone eyewall
Jul 30, 2018 · Our numerical experiment suggests that tornado-scale vortices are prevalent at the inner edge of the intense eyewall convection.
[83]
https://www.aoml.noaa.gov/hrd/hrd_sub/dynamics.html
[84]
Naruto Whirlpools Seen from Space | 2006
Aug 11, 2006 · The Naruto whirlpool is known as the largest one in the world. Its diameter exceeds 15m, and its current speed, 10 knots (about 20 km per hour).<|separator|>
[85]
Kuroshio Extension and Gulf Stream dominate the Eddy Kinetic ...
Jul 1, 2025 · Abstract. Ocean mesoscale variability, including meanders and eddies, is a crucial component of the global ocean circulation. The Eddy Kinetic ...
[86]
Gulf Stream eddy characteristics in a high‐resolution ocean model
Jul 24, 2013 · A detailed statistical study of the mesoscale eddy activity in the Gulf Stream (GS) region is performed based on a high-resolution multidecadal regional ocean ...
[87]
Ocean Mesoscale Eddies - Geophysical Fluid Dynamics Laboratory
Ocean mesoscale eddies are the “weather” of the ocean, with typical horizontal scales of less than 100 km and timescales on the order of a month.Missing: paper | Show results with:paper
[88]
Smithsonian / USGS Weekly Volcanic Activity Report
Apr 3, 2024 · Ash plumes ... A small vent at Etna's Southeast Crater began emitting unprecedented quantities of volcanic gas puffs that formed vortex rings ...
[89]
Jupiter and the Great Red Spot - NASA Science
Jupiter's trademark Great Red Spot – a swirling anticyclonic storm feature larger than Earth – has shrunken to the smallest size ever measured.
[90]
Jupiter's Great Red Spot: Both Deep and Wide - NASA
Dec 8, 2021 · NASA's Juno spacecraft captured this detailed look at Jupiter's most recognizable feature, the Great Red Spot.
[91]
Vortex ring behavior provides the epigenetic blueprint for the human ...
Feb 26, 2016 · Vortex rings in the heart therefore provide a recurring fluid structure with a consistent amount of shear along its outer boundary, which could ...
[92]
Nature Optimizes the Swirling Flow in the Human Left Ventricle
Sep 2, 2005 · The asymmetry of the blood flow in the human left ventricle is commonly assumed to facilitate the following ejection of blood in the primary circulation.
[93]
Optimal vortex formation as an index of cardiac health - PMC - NIH
In this work, it is demonstrated that major aspects of cardiac function are reflected uniquely and sensitively in the optimization of vortex formation in the ...
[94]
Arctic-associated increased fluctuations of midlatitude winter ...
Mar 27, 2023 · Known as Arctic amplification (AA), this phenomenon is associated with the reduced sea ice and the increased surface air and ocean temperatures ...
[95]
(PDF) Signatures of Anomalous Transport in the 2019/2020 Arctic ...
Oct 3, 2022 · The exceptionally strong and long‐lived Arctic stratospheric polar vortex in 2019/2020 resulted in large transport anomalies throughout the fall ...
[96]
Understanding Energy Pathways in the Gulf Stream in - AMS Journals
Feb 16, 2023 · Abstract The Gulf Stream (GS) is one of the strongest ocean currents on the planet. Eddy-rich resolution models are needed to properly ...
[97]
[PDF] VORTEX-LATTICE - NASA Technical Reports Server
APPLICATIONS OF VORTEX-LATTICE THEORY TO PRELIMINARY. AERObYNAMICDESIGN ... A potential flow computer program has been in use at the Arnold Engineering De-.
[98]
[PDF] A Candidate Wake Vortex Strength Definition for Application to the ...
A significant effort is underway at NASA Langley to develop a system to provide dynamical aircraft wake vortex spacing criteria to Air Traffic Control. (ATC).<|control11|><|separator|>
[99]
[PDF] Development of discrete vortex method for wind engineering ...
Bridge deck designers can use it to study the pattern of shed vortices and quickly make changes in design to satisfy their design criteria. The flow ...
[100]
Efficient Design Method for Applying Vortex Generators in ...
Vortex generators (VGs) offer the potential to attenuate secondary flow when implemented at the endwall of the blade passage.
[101]
Encounters with Vortices in a Turbine Nozzle Passage - 2012
Nov 14, 2012 · Secondary flows and a wide range of vortex types were encountered, including horseshoe vortices, shock-induced passage vortices, and streamwise ...
[102]
Separation Characteristics in a Novel Gas–Liquid Vortex Separator
Sep 10, 2020 · A novel gas–liquid vortex separator (GLVS) was put forward to use in the FT synthesis. GLVS has four symmetry vortex arms set inside the separator body.
[103]
Mixing Performance and Application of a Three-Dimensional ...
Jul 2, 2019 · Mixing Performance and Application of a Three-Dimensional Serpentine Microchannel Reactor with a Periodic Vortex-Inducing Structure. Click to ...
[104]
[PDF] Tackling Difficult Mixing Problems - AIChE
A modest vortex on the surface may help move liquid across the surface. A deep vortex will draw air into the liquid.
[105]
Characteristics of flow and liquid distribution in a gas–liquid vortex ...
A gas–liquid vortex separator with simple structure, low pressure drop and big separation capacity was designed to achieve the efficient separation between gas ...