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| | Other people might benefit from a fat reduction supplement. These are people whom have reached a plateau of weight reduction. Supplements are utilized in this case to help drop these stubborn pounds.<br><br><br><br>Utilizing a Shape Mass Index chart is a decent means for you to discover in the event you are at a nourishing body weight or not. Because the selection for standard body weight is substantial for a certain individual of any peak, adult guys plus most girls that falsely are convinced which there is a person "magic number" which they must weigh is reassured by working with the BMI. The calculator and chart are equally uncomplicated to employ and are commonly available web based plus inside health plus health organizations.<br><br>If you certainly want to sort out the issue for calculations of BMI, then you may be suggested to employ the online [http://safedietplans.com/calories-burned-walking calories burned] which will help you calculate the BMI with all the help of the height and fat. It is easy to work this tool in order to calculate the BMI. All we need to insert a weight and height plus it will provide we the actual result of the BMI.<br><br>NLP and hypnotherapy are excellent tools to help stop anorexia nervosa when and for all. They work by altering the patterns of thought from those that are conducive to an anorexic pattern to something less positive for anorexia to take hold. This way is further enhanced by utilizing hypnotherapy together with it in purchase to improve feelings of peace, approval, happy thoughts, plus positive eating behavior.<br><br>Obesity and morbid weight are 2 serious conditions which could frequently be identified from the calories burned walking calculator. Individuals with a body mass index of 35 or high could discuss the option of gastric band surgery to reduce fat.<br><br>This useful service was invented with a Belgian polymath named, Adolphe Quetelet back inside the 1800s. It has initially been called the Quetelet index before being renamed as the BMI. This is very helpful in keeping track of how much weight we are losing and how much fat we require gain to be fit. Combine this with a diet right for the eating habits and cravings plus exercise and sooner or later we will have a magnificently fit plus healthy body, with a BMI range of best wellness.<br><br>Those of we which have an above average magnitude of muscle constituting their body, an exact measurement of fats is achieved finding a like caliper that measures skin folds at certain regions of the body, namely the waist plus below the upper arms. |
| [[File:IrrotationalVortexFlow-anim-frame0.png|thumb|Pathlines of fluid particles around the axis (dashed line) of an ideal irrotational vortex. (See [[commons:File:IrrotationalVortexFlow-anim.gif|animation]]) ]]
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| [[File:Vortex in draining bottle of water.jpg|thumb|Plughole Vortex]]
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| In [[fluid dynamics]], a '''vortex''' is a region within a [[fluid]] where the [[Fluid dynamics|flow]] is mostly a [[rotation|spinning]] motion about an imaginary axis, straight or curved. That motion pattern is called a '''vortical flow'''.<ref>{{cite book |last=Ting |first=L. |title=Viscous vortical flows |series=Lecture notes in physics |publisher=Springer-Verlag |year=1991 |isbn=3-540-53713-9 }}</ref><ref>{{cite conference |last=Kida |first=Shigeo |url=http://www.igf.fuw.edu.pl/IUTAM/ABSTRACTS/Kida.pdf |title=Life, Structure, and Dynamical Role of Vortical Motion in Turbulence |conference=IUTAM Symposium on Tubes, Sheets and Singularities in Fluid Dynamics |year=2001 |location=Zakopane, Poland }}</ref> (The original and most common [[plural]] of "vortex" is '''vortices''',<ref>The Oxford English Dictionary</ref> although '''vortexes''' is often used too.<ref>The Merriam Webster Collegiate Dictionary</ref>)
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| Vortices form in stirred fluids, including [[liquid]]s, [[gas]]es, and [[plasma (physics)|plasma]]s. Some common examples are [[smoke ring]]s, the [[whirlpool]]s often seen in the [[wake]] of [[boat]]s and [[paddle]]s, and the winds surrounding [[tropical cyclone|hurricane]]s, [[tornado]]es and [[dust devil]]s. Vortices form in the wake of [[airplane]]s and are prominent features of [[Atmosphere of Jupiter|Jupiter's atmosphere]].
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| Vortices are a major component of [[turbulence|turbulent flow]]. In the absence of external forces, [[viscosity|viscous friction]] within the fluid tends to organize the flow into a collection of so-called ''irrotational'' vortices. Within such a vortex, the fluid's [[velocity]] is greatest next to the imaginary axis, and decreases in inverse proportion to the distance from it. The [[vorticity]] (the curl of the fluid's velocity) is very high in a core region surrounding the axis, and nearly zero in the rest of the vortex; while the pressure drops sharply as one approaches that region.
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| Once formed, vortices can move, stretch, twist, and interact in complex ways. A moving vortex carries with it some angular and linear momentum, energy, and mass. In a [[steady flow|stationary]] vortex, the [[streamlines, streaklines, and pathlines|streamlines and pathlines]] are closed. In a moving or evolving vortex the streamlines and pathlines are usually [[spiral]]s.
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| ==Properties==
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| [[Image:Crow instability contrail.JPG|[[Crow Instability]] [[contrail]] demonstrates vortex|300px|thumb]]
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| ===Vorticity===
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| A key concept in the dynamics of vortices is the [[vorticity]], a [[vector (geometry)|vector]] 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 would be the direction of the axis of rotation of this imaginary ball (according to the [[right-hand rule]]) while its length would be proportional to the ball's [[angular velocity]]. Mathematically, the vorticity is defined as the curl (or rotational) of the [[velocity field]] of the fluid, usually denoted by <math>\vec \omega</math> and expressed by the [[vector analysis]] formula <math>\nabla \times \vec{\mathit{u}}</math>, where <math>\nabla</math> is the [[nabla operator]].<ref>{{cite book|url=http://www.princeton.edu/~gkv/geoturb/turbch.pdf|page=1|accessdate=2012-09-26|year=1999|first=Geoffrey |last=Vallis|title=Geostrophic Turbulence: The Macroturbulence of the Atmosphere and Ocean Lecture Notes|series=Lecture notes|publisher=[[Princeton University]]}}</ref>
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| The local rotation measured by the vorticity <math>\vec \omega</math> 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, <math>\vec \omega</math> may be opposite to the mean angular velocity vector of the fluid relative to the vortex line.
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| ===Vorticity profiles===
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| The vorticity in a vortex depends on how the speed ''v'' of the particles varies as the distance ''r'' from the axis. There are two important special cases:
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| *If the fluid rotates like a rigid body – that is, if ''v'' increases proportionally to ''r'' – a tiny ball carried by the flow would also rotate about its center as if it were part of that rigid body. In this case, <math>\vec \omega</math> is the same everywhere: its direction is parallel to the spin axis, and its magnitude is twice the angular velocity of the whole fluid.
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| <table border="0"> | |
| <tr>
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| <td>[[File:Rotational vortex.gif]]</td>
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| </tr>
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| <tr>
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| <td style="text-align:center;">Rotational (rigid-body) vortex</td>
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| </tr>
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| <tr>
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| <td style="text-align:center;"><math>\vec \omega_{vorticity}=\frac{v_{\theta}}{r}+\frac{dv_{\theta}}{dr}=2\vec \omega_{ang. velocity}</math></td>
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| </tr>
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| </table>
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| *If the particle speed ''v'' is inversely proportional to the distance ''r'', then the imaginary test ball would not rotate over itself; it would maintain the same orientation while moving in a circle around the vortex line. In this case the vorticity <math>\vec \omega</math> is zero at any point not on that line, and the flow is said to be ''irrotational''.
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| <table border="0">
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| <tr>
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| <td>[[File:Irrotational vortex.gif]]</td>
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| </tr>
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| <tr>
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| <td style="text-align:center;">Irrotational vortex</td>
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| </tr>
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| <tr>
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| <td style="text-align:center;"><math>\vec \omega_{vorticity}=\frac{v_{\theta}}{r}+\frac{dv_{\theta}}{dr}=0</math></td>
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| </tr>
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| </table>
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| ====Irrotational vortices====
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| In the absence of external forces, a vortex usually evolves fairly quickly toward the irrotational flow pattern, where the flow velocity ''v'' is inversely proportional to the distance ''r''. For that reason, irrotational vortices are also called ''free vortices''.
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| For an irrotational vortex, the [[circulation (fluid dynamics)|circulation]] is zero along any closed contour that does not enclose the vortex axis and has a fixed value, <math>\Gamma</math>, for any contour that does enclose the axis once.<ref name=LJC7.5>{{harvnb|Clancy|1975|loc=sub-section 7.5}} </ref> The tangential component of the particle velocity is then <math>v_{\theta} = \Gamma/(2 \pi r)</math>. The angular momentum per unit mass relative to the vortex axis is therefore constant, <math> r v_{\theta} = \Gamma/(2 \pi)</math>.
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| However, the ideal irrotational vortex flow 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 line. 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 ''r'' goes to zero. Within that region, the flow is no longer irrotational: the vorticity <math>\vec \omega</math> becomes non-zero, with direction roughly parallel to the vortex line. The [[Rankine vortex]] is a model that assumes a rigid-body rotational flow where ''r'' is less than a fixed distance ''r''<sub>0</sub> and irrotational flow outside of the rotational core. The [[Lamb-Oseen vortex]] model is an exact solution of the [[Navier-Stokes equations]] governing fluid flows and assumes cylindrical symmetry, for which
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| :<math>v_{\theta} = (1 - e^{-r^2/(4\nu t)})\Gamma/(2 \pi r).</math>
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| In an irrotational vortex, fluid moves at different speed in adjacent streamlines, so there is friction and therefore energy loss throughout the vortex, especially near the core.
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| ====Rotational vortices====
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| A rotational vortex – one which has non-zero vorticity away from the core – can be maintained indefinitely in that state only through the application of some extra force, that is not generated by the fluid motion itself.
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| For example, if a water bucket is spun at constant angular speed ''w'' about its vertical axis, the water will eventually rotate in rigid-body fashion. The particles will then move along circles, with velocity ''v'' equal to ''wr''.<ref name=LJC7.5/> In that case, the free surface of the water will assume a [[paraboloid|parabolic]] shape.
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| In this situation, the rigid rotating enclosure provides an extra force, namely an extra pressure [[gradient]] in the water, directed inwards, that prevents evolution of the rigid-body flow to the irrotational state.
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| ===Vortex geometry===
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| In a stationary vortex, the typical streamline (a line that is everywhere tangent to the velocity vector) is a closed loop surrounding the axis; and each [[vortex line]] (a line that is everywhere tangent to the vorticity vector) is roughly parallel to the axis. A surface that is everywhere tangent to both 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.
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| 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 likewise be a closed [[torus]]-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]], or the [[turbofan]] of each [[jet engine]]. One end of the vortex line is attached to the engine, while the other end usually stretches outs and bends until it reaches the ground.
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| 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 streamlines and were stretched into spiral shapes by the non-uniform velocity distribution. This is the case, for example, of the spiral arms of [[galaxy|galaxies]] and [[hurricane]]s.
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| ===Pressure in a vortex===
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| The fluid motion in a vortex creates a dynamic [[pressure]] (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]]. One can say that it is the gradient of this pressure that forces the fluid to curve around the axis.
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| In a rigid-body vortex flow of a fluid with constant [[density]], the dynamic pressure is proportional to the square of the distance ''r'' from the axis. In a constant [[gravity]] field, the [[free surface]] of the liquid, if present, is a concave [[paraboloid]].
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| In an irrotational vortex flow with constant fluid density and [[cylindrical symmetry]], the dynamic pressure varies like ''P''<sub>∞</sub> − ''K''/''r''<sup>2</sup>, where ''P''<sub>∞</sub> 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 ''r''<sup>2</sup>.
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| The core of a vortex in air is sometimes visible because of a plume of water vapor caused by [[condensation]] in the low pressure and low temperature of the core; the spout of a tornado is a classic example. When a vortex line ends at a boundary surface, the reduced pressure at 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. By the same token, a vortex in a body of water that ends at the free surface (like the whirlpool that often forms over a bathtub drain) may draw a column of air down the core. The forward vortex extending from an engine of a parked airplane can suck water and small stones into the core and then into the engine.
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| ===Evolution===
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| [[Image:Airplane vortex edit.jpg|thumb|250px|Vortex created by the passage of an aircraft wing, revealed by colored smoke]]
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| Vortices need not be steady-state features; they can move about and change their shape.
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| In a moving vortex, the particle paths are no longer closed, but are open loopy curves similar to [[helix|helices]] or [[cycloid]]s.
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| A vortex flow may also be combined with a radial or axial flow pattern. In that case the streamlines and pathlines are not closed curves but spirals or [[helix|helices]], respecively. This is the case in tornadoes and in drain whirlpools. A vortex with helical streamlines is said to be [[solenoidal vector field|solenoidal]].
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| 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 theorems|Helmholtz's second theorem]]. Thus vortices (unlike [[surface wave|surface]] and [[pressure wave]]s) 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 toy]]s and [[vortex ring gun|gun]]s.
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| 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 (fluid dynamics)|circulation]] will equal the sum of the circulations of the constituent vortices. For example, an [[wing|airplane wing]] that is developing [[lift (force)|lift]] will create a sheet of small vortices at its trailing edge. These small vortices merge to form a single [[wingtip vortices|wingtip vortex]], less than one [[chord (aircraft)|wing chord]] downstream of that edge. This phenomenon also occurs with other active [[airfoil]]s, such as [[propeller]] blades. On the other hand, two parallel vortices with opposite circulations (such as the two wingtip vortices of an airplane) tend to remain separate.
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| 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]] 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.
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| ==Two-dimensional modeling==
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| When the particle velocities are constrained to be parallel to a fixed plane, one can ignore the space dimension perpendicular to that plane, and model the flow as a two-dimensional velocity field on that plane. Then the vorticity vector <math>\vec \omega</math> is always perpendicular to that plane, and can be treated as a scalar. This assumption is sometimes made in meteorology, when studying large-scale phenomena like hurricanes.
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| The behavior of vortices in such contexts is qualitatively different in many ways; for example, it does not allow the stretching of vortices that is often seen in three dimensions.
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| ==Further examples==
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| [[File:Saturn north polar vortex 2012-11-27.jpg|thumb|250px|[[Saturn's hexagon]], a cloud vortex at the planet [[Saturn]]'s north pole.]]
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| [[File:C17 Reverse Thrust.JPG|thumb|250px|A visible vortex formed when a [[Boeing C-17 Globemaster III|C-17]] uses high engine power at slow speed on a wet runway.]]
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| *In the [[hydrodynamics|hydrodynamic]] interpretation of the behaviour of [[electromagnetic field]]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 model|Landau-Lifshitz equation]], the continuum [[Heisenberg model (classical)|Heisenberg model]], the [[Ishimori equation]], and the [[nonlinear Schrödinger equation]].
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| *[[Bubble ring]]s are underwater vortex rings whose core traps a ring of bubbles, or a single donut-shaped bubble. They are sometimes created by playful [[dolphin]]s and [[whale]]s.
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| *The [[lift-induced drag|lifting force]] of aircraft wings, propeller blades, [[sail]]s, and other airfoils can be explained by the creation of a vortex superimposed on the flow of air past the wing.
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| *[[Aerodynamic drag]] can be explained in large part by the formation of vortices in the surrounding fluid that carry away energy from the moving body.
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| *Large whirlpools can be produced by ocean tides in certain [[strait]]s or [[bay]]s. Examples are [[Charybdis]] of classical [[mythology]] in the Straits of [[Messina]], [[Italy]]; the [[Naruto whirlpool]]s of [[Nankaido]], [[Japan]]; the [[Maelstrom]] at [[Lofoten]], [[Norway]].
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| *Vortices in the [[Earth's atmosphere]] are important phenomena for [[meteorology]]. They include [[mesocyclone]]s on the scale of a few miles, tornados, [[waterspout]]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 persistent, large-scale cyclone centered near the Earth's poles, in the middle and upper troposphere and the stratosphere.
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| *Vortices are prominent features of the atmospheres of other [[planet]]s. They include the permanent [[Great Red Spot]] on [[Jupiter]] and the intermittent [[Great Dark Spot]] on [[Neptune]], as well as the [[Martian dust devil]]s and the [[Saturn's hexagon|North Polar Hexagon]] of [[Saturn]].
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| *[[Sunspot]]s are dark regions on the [[Sun]]'s visible surface ([[photosphere]]) marked by a lower temperature than its surroundings, and intense magnetic activity.
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| *The [[accretion disk]]s of [[black hole]]s and other massive gravitational sources.
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| ==See also==
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| {{Portal|Physics}}
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| {{columns-list|4|
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| *[[Artificial gravity]]
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| *[[Batchelor vortex]]
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| *[[Biot–Savart law]]
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| *[[Coordinate rotation]]
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| *[[Cyclonic separation]]
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| *[[Eddy (fluid dynamics)|Eddy]]
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| *[[Gyre]]
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| *[[Helmholtz's theorems]]
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| *[[History of fluid mechanics]]
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| *[[Horseshoe vortex]]
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| *[[Hurricane]]
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| *[[Kelvin–Helmholtz instability]]
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| *[[Quantum vortex]]
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| *[[Shower-curtain effect]]
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| *[[Strouhal number]]
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| *[[Vile Vortices]]
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| *[[Von Kármán vortex street]]
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| *[[Vortex engine]]
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| *[[Vortex tube]]
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| *[[Vortex cooler]]
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| *[[Vortex shedding]]
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| *[[Vortex stretching]]
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| *[[Vortex induced vibration]]
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| *[[Vorticity]]
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| *[[Wormhole]]
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| }}
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| ==References==
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| ===Notes===
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| {{reflist}}
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| ===Other===
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| *{{cite report |last=Loper |first=David E. |title=An analysis of confined magnetohydrodynamic vortex flows |location=Washington |publisher=National Aeronautics and Space Administration |date=November 1966 |type=NASA contractor report NASA CR-646 |id={{LCCN|67060315}} |url=http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19670004091_1967004091.pdf }}
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| *{{cite book |author-link=George Batchelor |last=Batchelor |first=G.K. |year=1967 |title=An Introduction to Fluid Dynamics |publisher=Cambridge Univ. Press |isbn=9780521098175 |at=Ch. 7 et seq }}
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| *{{cite book |last=Falkovich |first=G. |title=Fluid Mechanics, a short course for physicists |publisher=Cambridge University Press |year=2011 |isbn=978-1-107-00575-4 }}
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| *{{cite book |last=Clancy |first=L.J. |year=1975 |title=Aerodynamics |publisher=Pitman Publishing Limited |location=London |isbn=0-273-01120-0}}
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| *{{cite doi |10.1046/j.1365-8711.2001.04228.x}}
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| ==External links==
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| {{Commons category|Vortex}}
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| *[http://www.cse.salford.ac.uk/profiles/gsmcdonald/Solitons/Optical_Vortex_Solitons.php Optical Vortices]
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| *[http://www.eng.nus.edu.sg/mpelimtt/collision.mpg Video of two water vortex rings colliding] ([[MPEG]])
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| *[http://maxwell.ucdavis.edu/~cole/phy9b/notes/fluids_ch3.pdf Chapter 3 Rotational Flows: Circulation and Turbulence]
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| * [http://mit.edu/vfrl/www/ Vortical Flow Research Lab] (MIT) – Study of flows found in nature and part of the Department of Ocean Engineering.
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| [[Category:Vortices| ]]
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| [[Category:Aerodynamics]]
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| [[Category:Fluid dynamics]]
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