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fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) a ...
, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings,
whirlpool A whirlpool is a body of rotating water produced by opposing currents or a current running into an obstacle. Small whirlpools form when a bath or a sink is draining. More powerful ones formed in seas or oceans may be called maelstroms ( ). ''Vo ...
s in the wake of a boat, and the winds surrounding a
tropical cyclone A tropical cyclone is a rapidly rotating storm system characterized by a low-pressure center, a closed low-level atmospheric circulation, strong winds, and a spiral arrangement of thunderstorms that produce heavy rain and squalls. Dep ...
,
tornado A tornado is a violently rotating column of air that is in contact with both the surface of the Earth and a cumulonimbus cloud or, in rare cases, the base of a cumulus cloud. It is often referred to as a twister, whirlwind or cyclone, alt ...
or
dust devil A dust devil is a strong, well-formed, and relatively short-lived whirlwind. Its size ranges from small (half a metre wide and a few metres tall) to large (more than 10 m wide and more than 1 km tall). The primary vertical motion is ...
. Vortices are a major component of
turbulent flow In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between t ...
. The distribution of velocity,
vorticity In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along wi ...
(the
curl cURL (pronounced like "curl", UK: , US: ) is a computer software project providing a library (libcurl) and command-line tool (curl) for transferring data using various network protocols. The name stands for "Client URL". History cURL was ...
of the flow velocity), as well as the concept of circulation are used to characterise vortices. In most vortices, the fluid flow velocity is greatest next to its axis and decreases in inverse proportion to the distance from the axis. In the absence of external forces,
viscous friction The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inter ...
within the fluid tends to organise the flow into a collection of irrotational vortices, possibly superimposed to larger-scale flows, including larger-scale vortices. Once formed, vortices can move, stretch, twist, and interact in complex ways. A moving vortex carries some angular and linear momentum, energy, and mass, with it.


Properties


Vorticity

A key concept in the dynamics of vortices is the
vorticity In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along wi ...
, a
vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
that describes the ''local'' rotary motion at a point in the fluid, as would be perceived by an observer that moves along with it. Conceptually, the vorticity could be observed by placing a tiny rough ball at the point in question, free to move with the fluid, and observing how it rotates about its center. The direction of the vorticity vector is defined to be the direction of the axis of rotation of this imaginary ball (according to the
right-hand rule In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation of axes in three-dimensional space. It is also a convenient method for quickly finding the direction of a cross-product of 2 vectors. Most of ...
) while its length is twice the ball's
angular velocity In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object ...
. Mathematically, the vorticity is defined as the curl (or rotational) of the
velocity field In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...
of the fluid, usually denoted by \vec \omega and expressed by the
vector analysis Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subjec ...
formula \nabla \times \vec, where \nabla is the
nabla operator Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a one-dimensional domain, it denotes ...
and \vec is the local flow velocity. The local rotation measured by the vorticity \vec \omega must not be confused with the angular velocity vector of that portion of the fluid with respect to the external environment or to any fixed axis. In a vortex, in particular, \vec \omega may be opposite to the mean angular velocity vector of the fluid relative to the vortex's axis.


Vortex types

In theory, the speed of the particles (and, therefore, the vorticity) in a vortex may vary with the distance from the axis in many ways. There are two important special cases, however: *If the fluid rotates like a rigid body – that is, if the angular rotational velocity is uniform, so that increases proportionally to the distance from the axis – a tiny ball carried by the flow would also rotate about its center as if it were part of that rigid body. In such a flow, the vorticity is the same everywhere: its direction is parallel to the rotation axis, and its magnitude is equal to twice the uniform angular velocity of the fluid around the center of rotation. *:\vec = (0, 0, \Omega) , \quad \vec = (x, y, 0) , *:\vec = \vec \times \vec = (-\Omega y, \Omega x, 0) , *:\vec \omega = \nabla \times \vec = (0, 0, 2\Omega) = 2\vec . *If the particle speed is inversely proportional to the distance from the axis, then the imaginary test ball would not rotate over itself; it would maintain the same orientation while moving in a circle around the vortex axis. In this case the vorticity \vec \omega is zero at any point not on that axis, and the flow is said to be ''irrotational''. *:\vec = (0, 0, \alpha r^) , \quad \vec = (x, y, 0) , *:\vec = \vec \times \vec = (-\alpha y r^, \alpha x r^, 0) , *:\vec = \nabla \times \vec = 0 .


Irrotational vortices

In the absence of external forces, a vortex usually evolves fairly quickly toward the irrotational flow pattern, where the flow velocity is inversely proportional to the distance . Irrotational vortices are also called ''free vortices''. For an irrotational vortex, the circulation is zero along any closed contour that does not enclose the vortex axis; and has a fixed value, , for any contour that does enclose the axis once. The tangential component of the particle velocity is then u_ = \tfrac. The angular momentum per unit mass relative to the vortex axis is therefore constant, r u_ = \tfrac. The ideal irrotational vortex flow in free space is not physically realizable, since it would imply that the particle speed (and hence the force needed to keep particles in their circular paths) would grow without bound as one approaches the vortex axis. Indeed, in real vortices there is always a core region surrounding the axis where the particle velocity stops increasing and then decreases to zero as goes to zero. Within that region, the flow is no longer irrotational: the vorticity \vec \omega becomes non-zero, with direction roughly parallel to the vortex axis. The
Rankine vortex The Rankine vortex is a simple mathematical model of a vortex in a viscous fluid. It is named after its discoverer, William John Macquorn Rankine. The vortices observed in nature are usually modelled with an irrotational (potential or free) vort ...
is a model that assumes a rigid-body rotational flow where is less than a fixed distance 0, and irrotational flow outside that core regions. In a viscous fluid, irrotational flow contains viscous dissipation everywhere, yet there are no net viscous forces, only viscous stresses. Due to the dissipation, this means that sustaining an irrotational viscous vortex requires continuous input of work at the core (for example, by steadily turning a cylinder at the core). In free space there is no energy input at the core, and thus the compact vorticity held in the core will naturally diffuse outwards, converting the core to a gradually-slowing and gradually-growing rigid-body flow, surrounded by the original irrotational flow. Such a decaying irrotational vortex has an exact solution of the viscous
Navier–Stokes equations In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...
, known as a
Lamb–Oseen vortex In fluid dynamics, the Lamb–Oseen vortex models a line vortex that decays due to viscosity. This vortex is named after Horace Lamb and Carl Wilhelm Oseen. Mathematical description Oseen looked for a solution for the Navier–Stokes equation ...
.


Rotational vortices

A rotational vortex – a vortex that rotates in the same way as a rigid body – cannot exist indefinitely in that state except through the application of some extra force, that is not generated by the fluid motion itself. It has non-zero vorticity everywhere outside the core. Rotational vortices are also called rigid-body vortices or forced vortices. For example, if a water bucket is spun at constant angular speed about its vertical axis, the water will eventually rotate in rigid-body fashion. The particles will then move along circles, with velocity equal to . In that case, the free surface of the water will assume a parabolic shape. In this situation, the rigid rotating enclosure provides an extra force, namely an extra pressure
gradient In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gr ...
in the water, directed inwards, that prevents transition of the rigid-body flow to the irrotational state.


Vortex formation on boundaries

Vortex structures are defined by their
vorticity In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along wi ...
'','' the local rotation rate of fluid particles. They can be formed via the phenomenon known as
boundary layer separation In fluid dynamics, flow separation or boundary layer separation is the detachment of a boundary layer from a surface into a wake. A boundary layer exists whenever there is relative movement between a fluid and a solid surface with viscous f ...
which can occur when a fluid moves over a surface and experiences a rapid acceleration from the fluid velocity to zero due to the
no-slip condition In fluid dynamics, the no-slip condition for viscous fluids assumes that at a solid boundary, the fluid will have zero velocity relative to the boundary. The fluid velocity at all fluid–solid boundaries is equal to that of the solid boundary. C ...
. This rapid negative acceleration creates a
boundary layer In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary cond ...
which causes a local rotation of fluid at the wall (i.e.
vorticity In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along wi ...
) which is referred to as the wall shear rate. The thickness of this boundary layer is proportional to \surd(vt) (where v is the free stream fluid velocity and t is time). If the diameter or thickness of the vessel or fluid is less than the boundary layer thickness then the boundary layer will not separate and vortices will not form. However, when the boundary layer does grow beyond this critical boundary layer thickness then separation will occur which will generate vortices. This boundary layer separation can also occur in the presence of combatting
pressure gradients In atmospheric science, the pressure gradient (typically of air but more generally of any fluid) is a physical quantity that describes in which direction and at what rate the pressure increases the most rapidly around a particular location. The pr ...
(i.e. a pressure that develops downstream). This is present in curved surfaces and general geometry changes like a convex surface. A unique example of severe geometric changes is at the
trailing edge The trailing edge of an aerodynamic surface such as a wing is its rear edge, where the airflow separated by the leading edge meets.Crane, Dale: ''Dictionary of Aeronautical Terms, third edition'', page 521. Aviation Supplies & Academics, 199 ...
of a
bluff body In fluid dynamics, the drag coefficient (commonly denoted as: c_\mathrm, c_x or c_) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equ ...
where the fluid flow deceleration, and therefore boundary layer and vortex formation, is located. Another form of vortex formation on a boundary is when fluid flows perpendicularly into a wall and creates a ''splash effect.'' The velocity streamlines are immediately deflected and decelerated so that the boundary layer separates and forms a toroidal vortex ring.


Vortex geometry

In a stationary vortex, the typical streamline (a line that is everywhere tangent to the flow velocity vector) is a closed loop surrounding the axis; and each
vortex line In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along wit ...
(a line that is everywhere tangent to the vorticity vector) is roughly parallel to the axis. A surface that is everywhere tangent to both flow velocity and vorticity is called a vortex tube. In general, vortex tubes are nested around the axis of rotation. The axis itself is one of the vortex lines, a limiting case of a vortex tube with zero diameter. According to Helmholtz's theorems, a vortex line cannot start or end in the fluid – except momentarily, in non-steady flow, while the vortex is forming or dissipating. In general, vortex lines (in particular, the axis line) are either closed loops or end at the boundary of the fluid. A whirlpool is an example of the latter, namely a vortex in a body of water whose axis ends at the free surface. A vortex tube whose vortex lines are all closed will be a closed
torus In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does n ...
-like surface. A newly created vortex will promptly extend and bend so as to eliminate any open-ended vortex lines. For example, when an airplane engine is started, a vortex usually forms ahead of each
propeller A propeller (colloquially often called a screw if on a ship or an airscrew if on an aircraft) is a device with a rotating hub and radiating blades that are set at a pitch to form a helical spiral which, when rotated, exerts linear thrust upon ...
, or the
turbofan The turbofan or fanjet is a type of airbreathing jet engine that is widely used in aircraft engine, aircraft propulsion. The word "turbofan" is a portmanteau of "turbine" and "fan": the ''turbo'' portion refers to a gas turbine engine which ac ...
of each
jet engine A jet engine is a type of reaction engine discharging a fast-moving jet (fluid), jet of heated gas (usually air) that generates thrust by jet propulsion. While this broad definition can include Rocket engine, rocket, Pump-jet, water jet, and ...
. One end of the vortex line is attached to the engine, while the other end usually stretches out and bends until it reaches the ground. When vortices are made visible by smoke or ink trails, they may seem to have spiral pathlines or streamlines. However, this appearance is often an illusion and the fluid particles are moving in closed paths. The spiral streaks that are taken to be streamlines are in fact clouds of the marker fluid that originally spanned several vortex tubes and were stretched into spiral shapes by the non-uniform flow velocity distribution.


Pressure in a vortex

The fluid motion in a vortex creates a dynamic
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
(in addition to any hydrostatic pressure) that is lowest in the core region, closest to the axis, and increases as one moves away from it, in accordance with
Bernoulli's principle In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after the Swiss mathematici ...
. One can say that it is the gradient of this pressure that forces the fluid to follow a curved path around the axis. In a rigid-body vortex flow of a fluid with constant
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
, the dynamic pressure is proportional to the square of the distance from the axis. In a constant
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
field, the
free surface In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. An example of two such homogeneous fluids would be a body of water (liquid) and the air in ...
of the liquid, if present, is a concave
paraboloid In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every plan ...
. In an irrotational vortex flow with constant fluid density and cylindrical symmetry, the dynamic pressure varies as , where is the limiting pressure infinitely far from the axis. This formula provides another constraint for the extent of the core, since the pressure cannot be negative. The free surface (if present) dips sharply near the axis line, with depth inversely proportional to . The shape formed by the free surface is called a
hyperboloid In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by def ...
, or "
Gabriel's Horn Gabriel's horn (also called Torricelli's trumpet) is a particular geometry, geometric figure that has infinite surface area but finite volume. The name refers to the Christian tradition where the archangel Gabriel blows the horn to announce Last ...
" (by
Evangelista Torricelli Evangelista Torricelli ( , also , ; 15 October 160825 October 1647) was an Italian physicist and mathematician, and a student of Galileo. He is best known for his invention of the barometer, but is also known for his advances in optics and wo ...
). The core of a vortex in air is sometimes visible because water vapor
condenses Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor to ...
as the low pressure of the core causes
adiabatic cooling In thermodynamics, an adiabatic process (Greek: ''adiábatos'', "impassable") is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, a ...
; the funnel of a tornado is an example. When a vortex line ends at a boundary surface, the reduced pressure may also draw matter from that surface into the core. For example, a dust devil is a column of dust picked up by the core of an air vortex attached to the ground. A vortex that ends at the free surface of a body of water (like the whirlpool that often forms over a bathtub drain) may draw a column of air down the core. The forward vortex extending from a jet engine of a parked airplane can suck water and small stones into the core and then into the engine.


Evolution

Vortices need not be steady-state features; they can move and change shape. In a moving vortex, the particle paths are not closed, but are open, loopy curves like helices and
cycloid In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another cu ...
s. A vortex flow might also be combined with a radial or axial flow pattern. In that case the streamlines and pathlines are not closed curves but spirals or helices, respectively. This is the case in tornadoes and in drain whirlpools. A vortex with helical streamlines is said to be
solenoidal In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field) is a vector field v with divergence zero at all points in the field: \nabla \cdot \mathbf ...
. As long as the effects of viscosity and diffusion are negligible, the fluid in a moving vortex is carried along with it. In particular, the fluid in the core (and matter trapped by it) tends to remain in the core as the vortex moves about. This is a consequence of
Helmholtz's second theorem In fluid mechanics, Helmholtz's theorems, named after Hermann von Helmholtz, describe the three-dimensional motion of fluid in the vicinity of vortex lines. These theorems apply to inviscid flows and flows where the influence of viscous forces ar ...
. Thus vortices (unlike
surface wave In physics, a surface wave is a mechanical wave that propagates along the interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occur within liquids, at ...
s and pressure waves) can transport mass, energy and momentum over considerable distances compared to their size, with surprisingly little dispersion. This effect is demonstrated by smoke rings and exploited in vortex ring
toys A toy or plaything is an object that is used primarily to provide entertainment. Simple examples include toy blocks, board games, and dolls. Toys are often designed for use by children, although many are designed specifically for adults and pe ...
and
guns A gun is a ranged weapon designed to use a shooting tube (gun barrel) to launch projectiles. The projectiles are typically solid, but can also be pressurized liquid (e.g. in water guns/cannons, spray guns for painting or pressure washing, ...
. Two or more vortices that are approximately parallel and circulating in the same direction will attract and eventually merge to form a single vortex, whose circulation will equal the sum of the circulations of the constituent vortices. For example, an airplane wing that is developing
lift Lift or LIFT may refer to: Physical devices * Elevator, or lift, a device used for raising and lowering people or goods ** Paternoster lift, a type of lift using a continuous chain of cars which do not stop ** Patient lift, or Hoyer lift, mobil ...
will create a sheet of small vortices at its trailing edge. These small vortices merge to form a single wingtip vortex, less than one wing chord downstream of that edge. This phenomenon also occurs with other active
airfoil An airfoil (American English) or aerofoil (British English) is the cross-sectional shape of an object whose motion through a gas is capable of generating significant lift, such as a wing, a sail, or the blades of propeller, rotor, or turbin ...
s, such as
propeller A propeller (colloquially often called a screw if on a ship or an airscrew if on an aircraft) is a device with a rotating hub and radiating blades that are set at a pitch to form a helical spiral which, when rotated, exerts linear thrust upon ...
blades. On the other hand, two parallel vortices with opposite circulations (such as the two wingtip vortices of an airplane) tend to remain separate. Vortices contain substantial energy in the circular motion of the fluid. In an ideal fluid this energy can never be dissipated and the vortex would persist forever. However, real fluids exhibit
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...
and this dissipates energy very slowly from the core of the vortex. It is only through dissipation of a vortex due to viscosity that a vortex line can end in the fluid, rather than at the boundary of the fluid.


Further examples

*In the
hydrodynamic In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) ...
interpretation of the behaviour of
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...
s, the acceleration of electric fluid in a particular direction creates a positive vortex of magnetic fluid. This in turn creates around itself a corresponding negative vortex of electric fluid. Exact solutions to classical nonlinear magnetic equations include the Landau–Lifshitz equation, the continuum Heisenberg model, the
Ishimori equation The Ishimori equation is a partial differential equation proposed by the Japanese mathematician . Its interest is as the first example of a nonlinear spin-one field model in the plane that is integrable . Equation The Ishimori equation has the for ...
, and the
nonlinear Schrödinger equation In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. It is a classical field equation whose principal applications are to the propagation of light in non ...
. *
Vortex ring A vortex ring, also called a toroidal vortex, is a torus-shaped vortex in a fluid; that is, a region where the fluid mostly spins around an imaginary axis line that forms a closed loop. The dominant flow in a vortex ring is said to be toroidal, ...
s are
torus In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does n ...
-shaped vortices where the axis of rotation is a continuous closed curve. Smoke rings and bubble rings are two well-known examples. *The lifting force of
aircraft wings A fixed-wing aircraft is a heavier-than-air flying machine, such as an airplane, which is capable of flight using wings that generate lift caused by the aircraft's forward airspeed and the shape of the wings. Fixed-wing aircraft are distinc ...
,
propeller A propeller (colloquially often called a screw if on a ship or an airscrew if on an aircraft) is a device with a rotating hub and radiating blades that are set at a pitch to form a helical spiral which, when rotated, exerts linear thrust upon ...
blades,
sail A sail is a tensile structure—which is made from fabric or other membrane materials—that uses wind power to propel sailing craft, including sailing ships, sailboats, windsurfers, ice boats, and even sail-powered land vehicles. Sails ma ...
s, and other airfoils can be explained by the creation of a vortex superimposed on the flow of air past the wing. *
Aerodynamic drag In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding ...
can be explained in large part by the formation of vortices in the surrounding fluid that carry away energy from the moving body. *Large whirlpools can be produced by ocean tides in certain
strait A strait is an oceanic landform connecting two seas or two other large areas of water. The surface water generally flows at the same elevation on both sides and through the strait in either direction. Most commonly, it is a narrow ocean chan ...
s or
bay A bay is a recessed, coastal body of water that directly connects to a larger main body of water, such as an ocean, a lake, or another bay. A large bay is usually called a gulf, sea, sound, or bight. A cove is a small, circular bay with a nar ...
s. Examples are
Charybdis Charybdis (; grc, Χάρυβδις, Khárybdis, ; la, Charybdis, ) is a sea monster in Greek mythology. She, with the sea monster Scylla, appears as a challenge to epic characters such as Odysseus, Jason, and Aeneas. Scholarship locates her in ...
of classical
mythology Myth is a folklore genre consisting of narratives that play a fundamental role in a society, such as foundational tales or origin myths. Since "myth" is widely used to imply that a story is not objectively true, the identification of a narra ...
in the Straits of
Messina Messina (, also , ) is a harbour city and the capital of the Italian Metropolitan City of Messina. It is the third largest city on the island of Sicily, and the 13th largest city in Italy, with a population of more than 219,000 inhabitants in t ...
, Italy; the
Naruto whirlpool The are tidal whirlpools in the Naruto Strait, a channel between Naruto in Tokushima and Awaji Island in Hyōgo, Japan. The strait between Naruto and Awaji island has a width of about . The strait is one of the connections between the Pacifi ...
s of Nankaido, Japan; and the
Maelstrom Maelstrom may refer to: * Maelstrom (whirlpool), a powerful whirlpool ** originally the Moskstraumen in English Amusement rides * Maelstrom (ride), a former log flume dark ride attraction in the Epcot theme park at Walt Disney World Resort i ...
at
Lofoten Lofoten () is an archipelago and a traditional district in the county of Nordland, Norway. Lofoten has distinctive scenery with dramatic mountains and peaks, open sea and sheltered bays, beaches and untouched lands. There are two towns, Svolv� ...
, Norway. *Vortices in the
Earth's atmosphere The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing fo ...
are important phenomena for
meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...
. They include
mesocyclone A mesocyclone is a meso-gamma mesoscale (or storm scale) region of rotation (vortex), typically around in diameter, most often noticed on radar within thunderstorms. In the northern hemisphere it is usually located in the right rear flank (back ...
s on the scale of a few miles, tornadoes,
waterspout A waterspout is an intense columnar vortex (usually appearing as a funnel-shaped cloud) that occurs over a body of water. Some are connected to a cumulus congestus cloud, some to a cumuliform cloud and some to a cumulonimbus cloud. In the ...
s, and hurricanes. These vortices are often driven by temperature and humidity variations with altitude. The sense of rotation of hurricanes is influenced by the Earth's rotation. Another example is the
Polar vortex A circumpolar vortex, or simply polar vortex, is a large region of cold, rotating air that encircles both of Earth's polar regions. Polar vortices also exist on other rotating, low-obliquity planetary bodies. The term polar vortex can be used to ...
, a persistent, large-scale cyclone centered near the Earth's poles, in the middle and upper troposphere and the stratosphere. *Vortices are prominent features of the atmospheres of other
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
s. They include the permanent
Great Red Spot The Great Red Spot is a persistent high-pressure region in the atmosphere of Jupiter, producing an anticyclonic storm that is the largest in the Solar System. Located 22 degrees south of Jupiter's equator, it produces wind-speeds up to 432&nb ...
on
Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousand ...
, the intermittent
Great Dark Spot The Great Dark Spot (also known as GDS-89, for Great Dark Spot, 1989) was one of a series of dark spots on Neptune similar in appearance to Jupiter's Great Red Spot. In 1989, GDS-89 was the first Great Dark Spot on Neptune to be observed by NASA' ...
on
Neptune Neptune is the eighth planet from the Sun and the farthest known planet in the Solar System. It is the fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 time ...
, the polar vortices of
Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never f ...
, the
Martian dust devil A dust devil is a strong, well-formed, and relatively short-lived whirlwind. Its size ranges from small (half a metre wide and a few metres tall) to large (more than 10 m wide and more than 1 km tall). The primary vertical motion is ...
s and the North Polar Hexagon of
Saturn Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...
. *
Sunspot Sunspots are phenomena on the Sun's photosphere that appear as temporary spots that are darker than the surrounding areas. They are regions of reduced surface temperature caused by concentrations of magnetic flux that inhibit convection. S ...
s are dark regions on the Sun's visible surface (
photosphere The photosphere is a star's outer shell from which light is radiated. The term itself is derived from Ancient Greek roots, φῶς, φωτός/''phos, photos'' meaning "light" and σφαῖρα/''sphaira'' meaning "sphere", in reference to it ...
) marked by a lower temperature than its surroundings, and intense magnetic activity. *The
accretion disk An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is typically a star. Friction, uneven irradiance, magnetohydrodynamic effects, and other ...
s of
black hole A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can def ...
s and other massive gravitational sources. *
Taylor–Couette flow In fluid dynamics, the Taylor–Couette flow consists of a viscous fluid confined in the gap between two rotating cylinders. For low angular velocities, measured by the Reynolds number ''Re'', the flow is steady and purely azimuthal. This basic s ...
occurs in a fluid between two nested cylinders, one rotating, the other fixed.


Summary

In the dynamics of fluid, a vortex is fluid that revolves around the axis line. This fluid might be curved or straight. Vortices form from stirred fluids: they might be observed in smoke rings,
whirlpools A whirlpool is a body of rotating water produced by opposing currents or a current running into an obstacle. Small whirlpools form when a bath or a sink is draining. More powerful ones formed in seas or oceans may be called maelstroms ( ). ''Vo ...
, in the wake of a boat or the winds around a
tornado A tornado is a violently rotating column of air that is in contact with both the surface of the Earth and a cumulonimbus cloud or, in rare cases, the base of a cumulus cloud. It is often referred to as a twister, whirlwind or cyclone, alt ...
or
dust devil A dust devil is a strong, well-formed, and relatively short-lived whirlwind. Its size ranges from small (half a metre wide and a few metres tall) to large (more than 10 m wide and more than 1 km tall). The primary vertical motion is ...
. Vortices are an important part of
turbulent flow In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between t ...
. Vortices can otherwise be known as a circular motion of a liquid. In the cases of the absence of forces, the liquid settles. This makes the water stay still instead of moving. When they are created, vortices can move, stretch, twist and interact in complicated ways. When a vortex is moving, sometimes, it can affect an angular position. For an example, if a water bucket is rotated or spun constantly, it will rotate around an invisible line called the axis line. The rotation moves around in circles. In this example the rotation of the bucket creates extra force. The reason that the vortices can change shape is the fact that they have open particle paths. This can create a moving vortex. Examples of this fact are the shapes of tornadoes and
drain whirlpools In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...
. When two or more vortices are close together they can merge to make a vortex. Vortices also hold energy in its rotation of the fluid. If the energy is never removed, it would consist of circular motion forever.


See also


References


Notes


Other

* * * * *


External links


Optical VorticesVideo of two water vortex rings colliding
(
MPEG The Moving Picture Experts Group (MPEG) is an alliance of working groups established jointly by ISO and IEC that sets standards for media coding, including compression coding of audio, video, graphics, and genomic data; and transmission and f ...
)
Chapter 3 Rotational Flows: Circulation and Turbulence

Vortical Flow Research Lab
(MIT) – Study of flows found in nature and part of the Department of Ocean Engineering. {{Authority control Rotation Aerodynamics Fluid dynamics