1956:
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1630:; 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.
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1485:, 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
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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
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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
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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
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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
240:
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
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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
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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
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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
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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
1646:. 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
1107:{\displaystyle {\begin{aligned}{\vec {\Omega }}&=\left(0,0,\alpha r^{-2}\right),\quad {\vec {r}}=(x,y,0),\\{\vec {u}}&={\vec {\Omega }}\times {\vec {r}}=\left(-\alpha yr^{-2},\alpha xr^{-2},0\right),\\{\vec {\omega }}&=\nabla \times {\vec {u}}=0.\end{aligned}}}
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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
1756:, 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
1600:
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
762:{\displaystyle {\begin{aligned}{\vec {\Omega }}&=(0,0,\Omega ),\quad {\vec {r}}=(x,y,0),\\{\vec {u}}&={\vec {\Omega }}\times {\vec {r}}=(-\Omega y,\Omega x,0),\\{\vec {\omega }}&=\nabla \times {\vec {u}}=(0,0,2\Omega )=2{\vec {\Omega }}.\end{aligned}}}
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is demonstrated in this photo, as winds from the west blow onto clouds that have formed over the mountains in the desert. This phenomenon observed from ground level is extremely rare, as most cloud-related Kármán vortex street activity is viewed from
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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.
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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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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.
1873:, 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
1666:) 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
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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
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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
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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
1443:(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
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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
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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
376:
1474:(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
181:. 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.
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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,
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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.
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1478:. 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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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
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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.
99:) 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
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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
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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
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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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about its vertical axis, the water will eventually rotate in rigid-body fashion. The particles will then move along circles, with velocity
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1504:. 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.
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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
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that originally spanned several vortex tubes and were stretched into spiral shapes by the non-uniform flow velocity distribution.
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which can occur when a fluid moves over a surface and experiences a rapid acceleration from the fluid velocity to zero due to the
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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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1877:, a persistent, large-scale cyclone centered near the Earth's poles, in the middle and upper troposphere and the stratosphere.
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pressure) that is lowest in the core region, closest to the axis, and increases as one moves away from it, in accordance with
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2505:"The effect of long-lived vortical circulation on the dynamics of dust particles in the mid-plane of a protoplanetary disc"
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1536:. One can say that it is the gradient of this pressure that forces the fluid to follow a curved path around the axis.
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In an irrotational vortex flow with constant fluid density and cylindrical symmetry, the dynamic pressure varies as
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The velocity streamlines are immediately deflected and decelerated so that the boundary layer separates and forms a
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vorticity vector is defined to be the direction of the axis of rotation of this imaginary ball (according to the
1809:, 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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Another form of vortex formation on a boundary is when fluid flows perpendicularly into a wall and creates a
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visually demonstrates the vortex created in the atmosphere (gas fluid medium) by the passage of the aircraft.
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core region surrounding the axis where the particle velocity stops increasing and then decreases to zero as
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in the water, directed inwards, that prevents transition of the rigid-body flow to the irrotational state.
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2009: – Swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime
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will create a sheet of small vortices at its trailing edge. These small vortices merge to form a single
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1400:) which is referred to as the wall shear rate. The thickness of this boundary layer is proportional to
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where the fluid flow deceleration, and therefore boundary layer and vortex formation, is located.
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In this situation, the rigid rotating enclosure provides an extra force, namely an extra pressure
2430:(NASA contractor report NASA CR-646). Washington: National Aeronautics and Space Administration.
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Pathlines of fluid particles around the axis (dashed line) of an ideal irrotational vortex. (See
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may be opposite to the mean angular velocity vector of the fluid relative to the vortex's axis.
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is zero along any closed contour that does not enclose the vortex axis; and has a fixed value,
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Sirakov, B. T.; Greitzer, E. M.; Tan, C. S. (2005). "A note on irrotational viscous flow".
2270:. IUTAMim Symposium on Tubes, Sheets and Singularities in Fluid Dynamics. Zakopane, Poland.
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the local rotation rate of fluid particles. They can be formed via the phenomenon known as
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of the particles (and, therefore, the vorticity) in a vortex may vary with the distance
2567:(MIT) – Study of flows found in nature and part of the Department of Ocean Engineering.
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Geostrophic
Turbulence: The Macroturbulence of the Atmosphere and Ocean Lecture Notes
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2003: – Method of removing particulates from a fluid stream through vortex separation
1926:) marked by a lower temperature than its surroundings, and intense magnetic activity.
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If the fluid rotates like a rigid body – that is, if the angular rotational velocity
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will equal the sum of the circulations of the constituent vortices. For example, an
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goes to zero. Within that region, the flow is no longer irrotational: the vorticity
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occurs in a fluid between two nested cylinders, one rotating, the other fixed.
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249:. Mathematically, the vorticity is defined as the curl (or rotational) of the
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from the axis in many ways. There are two important special cases, however:
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This boundary layer separation can also occur in the presence of combatting
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becomes non-zero, with direction roughly parallel to the vortex axis. The
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downstream of that edge. This phenomenon also occurs with other active
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2113: – Device for separating compressed gas into hot and cold streams
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The core of a vortex in air is sometimes visible because water vapor
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Life, Structure, and
Dynamical Role of Vortical Motion in Turbulence
2086: – Dimensionless number describing oscillating flow mechanisms
1994: – Motion of a certain space that preserves at least one point
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is zero at any point not on that axis, and the flow is said to be
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For example, if a water bucket is spun at constant angular speed
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2015: – Any large system of circulating ocean surface currents
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2065: – Quantized flux circulation of some physical quantity
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Vortices are prominent features of the atmospheres of other
1358:. In that case, the free surface of the water will assume a
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Large whirlpools can be produced by ocean tides in certain
1432:(where v is the free stream fluid velocity and t is time).
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is a model that assumes a rigid-body rotational flow where
1973: – Use of circular rotational force to mimic gravity
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which causes a local rotation of fluid at the wall (i.e.
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An analysis of confined magnetohydrodynamic vortex flows
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Vortices formed by milk when poured into a cup of coffee
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Pages displaying short descriptions of redirect targets
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Pages displaying short descriptions of redirect targets
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Pages displaying short descriptions of redirect targets
2035: – system present in the flow of air around a wing
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Pages displaying short descriptions of redirect targets
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Pages displaying short descriptions of redirect targets
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Chapter 3 Rotational Flows: Circulation and
Turbulence
1252:{\displaystyle ru_{\theta }={\tfrac {\Gamma }{2\pi }}}
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1202:{\displaystyle u_{\theta }={\tfrac {\Gamma }{2\pi r}}}
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2158: – Hypothetical topological feature of spacetime
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uses high engine power at slow speed on a wet runway.
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In a rigid-body vortex flow of a fluid with constant
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1607:. The shape formed by the free surface is called a
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also called rigid-body vortices or forced vortices.
1311:, and irrotational flow outside that core regions.
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316:{\displaystyle \nabla \times {\vec {\mathit {u}}}}
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2509:Monthly Notices of the Royal Astronomical Society
228:A key concept in the dynamics of vortices is the
138:of the flow velocity), as well as the concept of
2134: – Lengthening of vortices in 3D fluid flow
2104: – Device for various rides and attractions
1922:are dark regions on the Sun's visible surface (
1524:The fluid motion in a vortex creates a dynamic
27:Fluid flow revolving around an axis of rotation
2467:Fluid Mechanics, a short course for physicists
2377:Kheradvar, Arash; Pedrizzetti, Gianni (2012),
2122: – Field experiments that study tornadoes
2071: – Mathematical formula for viscous fluid
2053: – Repeating pattern of swirling vortices
166:, in the wake of a boat or the winds around a
2383:Vortex Formation in the Cardiovascular System
2240:. Lecture notes in physics. Springer-Verlag.
2044: – Type of rapidly rotating storm system
1392:. This rapid negative acceleration creates a
381:The local rotation measured by the vorticity
8:
2024: – 3D motion of fluid near vortex lines
1988: – Important law of classical magnetism
484:of the fluid around the center of rotation.
2503:De La Fuente Marcos, C.; Barge, P. (2001).
2385:, London: Springer London, pp. 17–44,
1725:The visible core of a vortex formed when a
1140:is inversely proportional to the distance
787:is inversely proportional to the distance
2550:Video of two water vortex rings colliding
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2189:. Oxford University Press. Archived from
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1869:on the scale of a few miles, tornadoes,
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1144:. Irrotational vortices are also called
2450:. Cambridge Univ. Press. Ch. 7 et seq.
2174:
1626:as the low pressure of the core causes
1377:Vortex structures are defined by their
245:) while its length is twice the ball's
111:of a boat, and the winds surrounding a
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2488:. London: Pitman Publishing Limited.
2059: – Phenomenon of fluid mechanics
150:momentum, energy, and mass, with it.
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2092: – Alternative to tall chimneys
371:{\displaystyle {\vec {\mathit {u}}}}
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1752:interpretation of the behaviour of
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2448:An Introduction to Fluid Dynamics
2423:Loper, David E. (November 1966).
253:of the fluid, usually denoted by
2530:10.1046/j.1365-8711.2001.04228.x
2187:Oxford Dictionaries Online (ODO)
1954:
1289:{\displaystyle {\vec {\omega }}}
1151:For an irrotational vortex, the
813:{\displaystyle {\vec {\omega }}}
432:{\displaystyle {\vec {\omega }}}
403:{\displaystyle {\vec {\omega }}}
275:{\displaystyle {\vec {\omega }}}
130:. The distribution of velocity,
1979: – fluid dynamics equation
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2469:. Cambridge University Press.
1770:nonlinear Schrödinger equation
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1373:Vortex formation on boundaries
1304:is less than a fixed distance
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1884:. They include the permanent
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2057:Kelvin–Helmholtz instability
1861:are important phenomena for
1790:are two well-known examples.
378:is the local flow velocity.
2391:10.1007/978-1-4471-2288-3_2
2294:. p. 1. Archived from
54:, revealed by colored smoke
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2565:Vortical Flow Research Lab
2152: – Whirling aerophone
2028:History of fluid mechanics
1656:Helmholtz's second theorem
1425:{\displaystyle \surd (vt)}
29:
2281:Vallis, Geoffrey (1999).
1740:formed off the island of
1386:boundary layer separation
2138:Vortex-induced vibration
1900:, the polar vortices of
1758:Landau–Lifshitz equation
1658:. Thus vortices (unlike
31:Not to be confused with
2342:(10): 108102–108102–3.
1317:Navier–Stokes equations
336:{\displaystyle \nabla }
40:Vortex (disambiguation)
2465:Falkovich, G. (2011).
2238:Viscous Vortical Flows
2218:. Merriam-Webster, Inc
2216:Merriam-Webster Online
1754:electromagnetic fields
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1617:Evangelista Torricelli
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2484:Clancy, L.J. (1975).
2261:Kida, Shigeo (2001).
2075:Shower-curtain effect
1738:Kármán vortex streets
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1534:Bernoulli's principle
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2292:Princeton University
2051:Kármán vortex street
2022:Helmholtz's theorems
1528:(in addition to any
1512:Pressure in a vortex
1483:Helmholtz's theorems
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471:is uniform, so that
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38:For other uses, see
2521:2001MNRAS.323..601D
2348:2005PhFl...17j8102S
2193:on February 3, 2013
2001:Cyclonic separation
1992:Coordinate rotation
1941:Taylor–Couette flow
1910:North Polar Hexagon
1906:Martian dust devils
1892:, the intermittent
1685:that is developing
1327:Rotational vortices
462:A rigid-body vortex
236:that describes the
1971:Artificial gravity
1859:Earth's atmosphere
1834:in the Straits of
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1441:pressure gradients
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272:
226:
77:
64:
56:
2495:978-0-273-01120-0
2476:978-1-107-00575-4
2400:978-1-4471-2287-6
2379:"Vortex Dynamics"
2356:10.1063/1.2104550
2336:Physics of Fluids
2324:, sub-section 7.5
2247:978-3-540-53713-7
2236:Ting, L. (1991).
2132:Vortex stretching
1846:, Japan; and the
1840:Naruto whirlpools
1766:Ishimori equation
1628:adiabatic cooling
1520:A plughole vortex
1390:no-slip condition
1321:Lamb–Oseen vortex
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16:(Redirected from
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2033:Horseshoe vortex
2018:
1997:
1982:
1977:Batchelor vortex
1964:
1959:
1958:
1857:Vortices in the
1813:Aerodynamic drag
1762:Heisenberg model
1760:, the continuum
1742:Tristan da Cunha
1717:Further examples
1693:, less than one
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247:angular velocity
218:Crow instability
193:drain whirlpools
147:viscous friction
113:tropical cyclone
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2444:Batchelor, G.K.
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2126:Vortex shedding
2120:VORTEX projects
2114:
2105:
2084:Strouhal number
2078:
2045:
2036:
2016:
1995:
1986:Biot–Savart law
1980:
1960:
1953:
1950:
1931:accretion disks
1894:Great Dark Spot
1865:. They include
1826:. Examples are
1719:
1636:
1602:
1598:
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1582:
1579:
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1489:-like surface.
1468:
1466:Vortex geometry
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284:vector analysis
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243:right-hand rule
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2596:Fluid dynamics
2593:
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2547:
2540:
2539:External links
2537:
2536:
2535:
2515:(3): 601–614.
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2072:
2069:Rankine vortex
2066:
2063:Quantum vortex
2060:
2054:
2048:
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2030:
2025:
2019:
2010:
2004:
1998:
1989:
1983:
1974:
1967:
1966:
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1962:Physics portal
1949:
1946:
1945:
1944:
1938:
1927:
1917:
1886:Great Red Spot
1878:
1855:
1816:
1810:
1799:aircraft wings
1791:
1773:
1718:
1715:
1691:wingtip vortex
1664:pressure waves
1635:
1632:
1613:Gabriel's Horn
1596:
1567:
1513:
1510:
1467:
1464:
1456:splash effect.
1421:
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1394:boundary layer
1374:
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1298:Rankine vortex
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251:velocity field
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179:turbulent flow
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128:turbulent flow
81:fluid dynamics
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2312:
2301:on 2013-12-28
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2111:Vortex cooler
2109:
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2102:Vortex tunnel
2100:
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2090:Vortex engine
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1481:According to
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1462:vortex ring.
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1445:trailing edge
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1319:, known as a
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1146:free vortices
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52:aircraft wing
48:
41:
34:
19:
2591:Aerodynamics
2512:
2508:
2486:Aerodynamics
2485:
2466:
2447:
2404:, retrieved
2382:
2372:
2339:
2335:
2329:
2303:. Retrieved
2296:the original
2283:
2276:
2263:
2256:
2237:
2231:
2220:. Retrieved
2215:
2206:
2195:. Retrieved
2191:the original
2186:
2177:
1875:Polar vortex
1867:mesocyclones
1788:bubble rings
1776:Vortex rings
1750:hydrodynamic
1707:
1676:
1652:
1637:
1621:
1603:
1593:
1583:
1575:
1564:
1561:
1553:free surface
1538:
1523:
1506:
1491:
1480:
1475:
1469:
1455:
1453:
1438:
1434:
1381:
1376:
1364:
1345:
1341:
1313:
1261:
1150:
1145:
1135:
822:irrotational
821:
446:
443:Vortex types
380:
237:
227:
197:
190:
186:
183:
176:
157:
144:
125:
96:
92:
84:
78:
2322:Clancy 1975
2150:Whirly tube
2096:Vortex tube
1935:black holes
1924:photosphere
1871:waterspouts
1863:meteorology
1784:Smoke rings
1679:circulation
1609:hyperboloid
1551:field, the
1530:hydrostatic
1476:vortex tube
1472:vortex line
1436:vortices.
1153:circulation
160:smoke rings
140:circulation
101:smoke rings
2575:Categories
2406:2021-03-16
2305:2012-09-26
2222:2015-08-29
2197:2015-08-29
2164:References
1768:, and the
1701:, such as
1695:wing chord
1648:solenoidal
1557:paraboloid
1502:jet engine
1449:bluff body
203:Properties
172:dust devil
164:whirlpools
121:dust devil
105:whirlpools
2364:1070-6631
2144:Vorticity
2042:Hurricane
1854:, Norway.
1848:Maelstrom
1832:mythology
1828:Charybdis
1803:propeller
1710:viscosity
1703:propeller
1634:Evolution
1624:condenses
1496:, or the
1494:propeller
1408:√
1398:vorticity
1379:vorticity
1360:parabolic
1354:equal to
1281:→
1278:ω
1243:π
1236:Γ
1225:θ
1190:π
1183:Γ
1172:θ
1130:animation
1089:→
1080:×
1077:∇
1064:→
1061:ω
1032:−
1021:α
1010:−
999:α
996:−
982:→
973:×
967:→
964:Ω
948:→
905:→
882:−
874:α
844:→
841:Ω
805:→
802:ω
747:→
744:Ω
729:Ω
702:→
693:×
690:∇
677:→
674:ω
649:Ω
640:Ω
637:−
625:→
616:×
610:→
607:Ω
591:→
548:→
532:Ω
504:→
501:Ω
424:→
421:ω
395:→
392:ω
363:→
331:∇
308:→
297:×
294:∇
267:→
264:ω
230:vorticity
208:Vorticity
132:vorticity
2586:Rotation
2581:Vortices
2446:(1967).
2436:67060315
2212:"vortex"
2183:"vortex"
2156:Wormhole
1948:See also
1920:Sunspots
1908:and the
1844:Nankaido
1805:blades,
1699:airfoils
1644:cycloids
1591:, where
1526:pressure
1500:of each
1498:turbofan
1460:toroidal
1367:gradient
1336:Saturn's
323:, where
286:formula
222:contrail
154:Overview
97:vortexes
93:vortices
18:Vortices
2517:Bibcode
2344:Bibcode
1898:Neptune
1890:Jupiter
1882:planets
1852:Lofoten
1836:Messina
1820:straits
1748:In the
1640:helices
1588:
1572:
1549:gravity
1541:density
1362:shape.
343:is the
168:tornado
117:tornado
107:in the
2492:
2473:
2454:
2434:
2397:
2362:
2244:
1914:Saturn
1904:, the
1764:, the
1615:" (by
1611:, or "
234:vector
85:vortex
33:vertex
2428:(PDF)
2417:Other
2299:(PDF)
2288:(PDF)
2268:(PDF)
2169:Notes
1902:Venus
1807:sails
1780:torus
1487:torus
1447:of a
238:local
134:(the
75:space
2554:MPEG
2490:ISBN
2471:ISBN
2452:ISBN
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