User:Cleon Teunissen/Coriolis effect

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In physics, Coriolis effect is a general name for a range of aspects of dealing with rotation. In ballistics, it refers to the fact that the rotation of Earth needs to be taken into account. In meteorology, it refers to the fact that the physics of wind patterns is dependent on whether the planet is rotating, and how fast it is rotating. The common theme is inertia: to change the velocity of an object, a force is required.

[edit] Ballistics

In firing projectiles over a significant distance, the rotation of the Earth must be taken into account. During its flight, the projectile is in inertial motion, that is: motion in a straight line (not counting effects of gravitation and air resistance for now). The target, co-rotating with the Earth, is a moving target, so the gun must be aimed not directly at the target, but at a point where the projectile and the target will arrive simultaneously.

The blue dot represents an object that is thrown over. During the flight there is no force acting on the object: it moves in a straight line

When the straight path of the projectile is plotted in the rotating coordinate system that is used, then this path appears curvilinear. In accordance with that, adjusting terms for a centrifugal motion with respect to the rotating coordinate system, and a Coriolis motion with respect to the rotating coordinate system are added to the equation of motion. When the appropriate centrifugal and coriolis terms are added to the equation of motion, the predicted path with respect to the rotating coordinate system is curvilinear, corresponding to the actual straight line motion of the projectile.

In the context of a non-rotating coordinate system, the equation of motion has its simplest form:

$\vec{F} = m \vec{a}$

In the context of a rotating coordinate system that equation of motion takes on the following form:

$\vec{F} = m \vec{a}_r + 2 m (\vec{\omega} \times \vec{v}_r) + m(\vec{\omega} \times (\vec{\omega} \times \vec{r}))$

With $\vec{a}_r$ the acceleration with respect to the rotating coordinats system, and $\vec{v}_r$ the velocity with respect to the rotating coordinates system.

[edit] The formula

The term

$\vec{F}_C = -2 m (\vec{\omega} \times \vec{v})$

Is the coriolis term of the equation of motion.

In this formula the arrow above the symbol indicates vector quantities

$\vec{F}_C$ is the Coriolis force
$\vec{\omega}$ is the angular velocity of the rotating system, this vector is parallel to the rotation axis
$\vec{v}$ is the velocity of the moving object with respect to the rotating system
m is the mass of the moving object
$\times$ is the vector cross product

The formula implies that the Coriolis force is perpendicular both to the velocity of the moving mass and to the rotation axis. So in particular:

if the velocity is parallel to the rotation axis, the Coriolis force is zero
if the velocity is straight (perpendicularly) inward to the axis, the force will follow the direction of rotation
if the velocity is following the rotation, the force will be (perpendicularly) outward from the axis

At a given rotation speed, the force will be proportional to the velocity and the sine of the angle between the velocity vector and the axis.

The transformation of the equation of motion to a rotating coordinate system is a mathematical operation, a mathematical regrouping. The Coriolis term in the equation of motion does not describe an effect or a physical force.

A transformation to a rotating coordinate system preserves everything. It preserves all relative positions, it preserves all relative velocities, and it preserves all relative accelerations. Coordinate transformation is a reversible operation.

Transforming to a rotating coordinates system can be visualized by thinking about what video-images taken by a rotating video-camera will look like.

[edit] Rotational dynamics in the atmosphere

The way fluids and gases move around on a planet is to a large extend dependent on how fast or how slow that planet is rotating; Venus rotates slower than Earth, Saturn rotates faster, and thus their atmospheric dynamics is different.

The following section of the article will discuss exclusively the physics part of these differences.

[edit] Consequences of the Earth's rotation

Decomposing the direction of gravitation. The arrow on the outside is the direction of a plumb line.

The Earth is rotating, and as a consequence of that the Earth is an oblate spheroid. For objects resting on the Earth the vector of true gravity can be decomposed in a component perpendicular to the surface and a component perpendicular to the Earth's axis. The component of true gravity that acts perpendicular to the Earth's axis provides the force that keeps objects at the same latitude.

In the hypothetical case of a perfectly spherical rotating celestial body, all water and air would gather at the equator.

Each component of true gravity has a different effect. The effect of the perpendicular to the surface component is that objects remain tightly on Earth. The result of the perpendicular to the Earth's axis component is that all objects that are co-rotating with the Earth remain on the same latitude, instead of sliding towards the equator.

This is an example of Newton's second law: to change the velocity of an object, a force must be exerted. To corotate with the Earth on for example 60 degrees latitude is to be moving in a large circle around the axis of the Earth. That circular motion will only remain that circular motion if the necessary force is provided: a centripetal force, acting in that plane of circular motion.

This decomposition applies exclusively for mass that is resting on the Earth, or that is in any form buoyant. (It can readily be seen that neutral buoyancy is a form of resting on the Earth.) This decomposition does not apply in the case of objects that are in any form of satellite orbit (around Earth). Examples: an airship, (a rigid airship is also called a Zeppelin), is buoyant. On the other hand: the vomit comet is, for the duration of the parabolic flight path, in a form of satellite orbit; not resting on the Earth.

In technical language: because of the rotation-induced oblateness of the geopotential surfaces there is a component of true gravity that acts parallel to the geopotential surfaces, in each hemisphere directed to the pole of that hemisphere.

A geopotential surface is a continuous surface with the property that everywhere a plumb line is perpendicular to it. Given the fact that the Earth is rotating, that surface is (by good approximation) an oblate spheroid in shape. The most obvious example of a geopotential surface is the global sealevel.

[edit] Formation of flow around a low pressure area

Schematic representation of flow around a low-pressure area. Pressure gradient force represented by blue arrows, The deflecting tendency, always perpendicular to the velocity, by red arrows

In the following section a single aspect of rotational dynamics in atmospheric motions is discussed: the flow pattern around a low-pressure area. There are many other aspects. The following is a much-simplified description.

In the atmosphere, there is a continuous system of balanced forces: differences in air pressure between different areas with varying densities and temperatures. In nature, low-pressure areas form gradually; the following description, however, discusses a low-pressure area that has formed instantaneously in the Northern hemisphere. (In the Southern hemisphere the dynamics are a mirror-image of the dynamics of the Northern hemisphere.)

With this low-pressure area formed, air flows toward it from all directions. On a non-rotating planet the air would flow along the straightest possible line, quickly leveling the air pressure. On a rotating planet a particular mechanism comes into action.

To visualize the dynamics that is involved it is necessary to think of the motion of the air mass from a non-rotating point of view. It is necessary to think about the air mass's overall motion, circumnavigating the Earth's axis, together with the Earth as whole.

The pressure gradient force gives the air mass a velocity with respect to the Earth. When that velocity is in south-to-north direction, then that corresponds to the radius of the circumnavigating motion getting tighter. Because of conservation of angular momentum the angular velocity of the air mass will increase (unless another force provides a torque to prevent this). So the air mass tends to not move parallel to the longitudes to the north, instead it tends to deflect to the right of the original south-to north direction. The amount of force that would be required to prevent that deflection is proportional to the velocity with respect to the Earth (See the section Derivations in angular mechanics for the mathematics.)

When the pressure gradient force is giving air mass a velocity in north-to-south direction, then the circumnavitating motion is getting wider, so the angular velocity will decrease, and the air mass will not move along a longitude line, but it deflects to the right of the original north-to-south direction.

When the pressure gradient force is giving air mass a velocity in west-to-east direction, then this air is in the same sort of situation as cars on a banked race circuit. The faster a car goes into the curve, the higher up the bank it will climb. When air is moving from west to east with respect to the Earth it is in a sense "speeding", and it will tend to slide to the equator. The larger the deviation from co-rotating with Earth, the stronger the additional force that would be required to prevent that deflection. (See the section Derivations in angular mechanics for the mathematics.)

When the pressure gradient force is giving air mass a velocity in east-to-west direction, then there is a surplus of gravity pulling on this air, like a car tends to slide towards the bottom of a banked curve if its speed is too low for the slope of the curve. So air mass with a east-to-west velocity will deflect to the right of its original direction of flow.

The exact mechanism is different for every direction of flow. In the end the strength of the tendency to deflect is comparable for all directions of flow.

For a more comprehensive discussion of the dynamics involved, see the section: Rotational dynamics in the atmosphere

Hurricane Isabel east of the Bahamas on September 15, 2003.

A system of equilibrium can then establish itself creating circular movement, or a cyclonic flow. There is a pressure gradient force towards the low-pressure area drawing air toward it, but there is also the tendency to deflect to the right, away from the center of the low pressure. Instead of flowing down the gradient, the air tends to flow perpendicular to the air-pressure gradient and forms a cyclonic flow.

It takes quite some time for the cyclonic flow to dissolve, leveling the air-pressure difference. There is a tendency for the flow to lose velocity because of friction, but contraction of the cyclonic flow is once again a motion towards the center of cyclonic flow, with the rotational dynamics then sustaining the velocity around the center of cyclonic flow. As long as there is a pressure gradient, the flow perpendicular to the gradient tends to be sustained.

This pattern of deflection, and the direction of movement, is called Buys-Ballot's law. The pattern of flow is called a cyclone. In the Northern Hemisphere the direction of movement around a low-pressure area is counterclockwise, as explained above. In the Southern Hemisphere, the direction of movement is clockwise because the rotational dynamics is a mirror image there. Cyclones cannot form on the equator, and they rarely travel towards the equator, because in the equatorial region there is little to no motion with respect to the Earth's axis.

[edit] Draining bathtubs

People often ask whether the Coriolis effect determines the direction in which bathtubs or toilets drain, and whether water always drains in one direction in the Northern Hemisphere, and in the other direction in the Southern Hemisphere. The answer is almost always no. The Coriolis effect is a few orders of magnitude smaller than other random influences on drain direction, such as the geometry of the sink, toilet, or tub; whether it is flat or tilted; and the direction in which water was initially added to it. If one takes great care to create a flat circular pool of water with a small, smooth drain; to wait for eddies caused by filling it to die down; and to remove the drain from below (or otherwise remove it without introducing new eddies into the water) – then it is possible to observe the influence of the Coriolis effect in the direction of the resulting vortex. There is a good deal of misunderstanding on this point, as most people (including many scientists) do not realize how small the Coriolis effect is on small systems.¹

[edit] Coriolis flow meter

A practical application of the Coriolis effect is the mass flow meter, an instrument that measures the mass flow rate of a fluid through a tube. The operating principle was introduced in 1977 by Micro Motion Inc. Simple flow meters measure volume flow rate, which is proportional to mass flow rate only when the density of the fluid is constant. If the fluid has varying density, or contains bubbles, then the volume flow rate multiplied by the density is not an accurate measure of the mass flow rate. The Coriolis mass flow meter operating principle does not actually involve rotation. It works by inducing a vibration of the tube through which the fluid passes, and subsequently monitoring and analysing the inertial effects that occur in response to the combination of the induced vibration and the mass flow.

[edit] History

In 1829 Coriolis published a textbook, Calcul de l'Effet des Machines (Calculation of the Effect of Machines), which presented mechanics in a way that could be readily be applied by industry. In this period the correct expression for kinetic energy, $\frac{1}{2}mv^2$ , and its relation to mechanical work became established.

During the following years Coriolis worked to extend the notion of kinetic energy and work to rotating systems. The first of his papers, Sur le principe des forces vives dans les mouvements relatifs des machines (On the principle of kinetic energy in the relative motion in machines), was read to the Académie des Sciences (Coriolis 1832). Three years later came the paper that would make his name famous, Sur les équations du mouvement relatif des systèmes de corps (On the equations of relative motion of a system of bodies (Coriolis 1835). Coriolis's papers do not deal with the atmosphere or even the rotation of the earth, but with the transfer of energy in rotating systems like waterwheels.

In 1851 Léon Foucault demonstrated that a pendulum is affected by the Earth's rotation. Foucault's demonstration attracted wide scientific and popular attention and, together with reading Newton's and Laplace's works, (but independent of Coriolis's work) inspired William Ferrel in 1856 to conclude that the direction of the wind is parallel to the isobars, its strength dependent on the latitude and the horizontal pressure gradient.

Coriolis's name began to appear in the meteorological literature at the end of the nineteenth century, although the term "Coriolis force" was not used until the beginning of the twentieth century. All major discoveries about the general circulation and the relation between the pressure and wind fields were made without knowledge about Gaspard Gustave Coriolis.

[edit] Rotational dynamics and fluids

Parabolic shape formed by the surface of a liquid under rotation.

To demonstrate the full extent of the rotational dynamics that apply in meteorology, a special type of turntable is used. The turntable has a rim and can be filled with liquid. When the liquid is rotating it assumes a parabolic shape.

[edit] Parabolic turntable

If a liquid that sets after several hours is used, such as a synthetic resin, a permanent shape is obtained.

Disks cut from cylinders of dry ice can be used as pucks, moving around almost frictionless over the surface of the parabolic turntable, allowing dynamic phenomena to show themselves. To also get a view of the motions as seen from a rotating point of view, a video-camera is attached to the turntable in such a way that the camera is co-rotating with the turntable. This type of setup, with a parabolic turntable, at the center about a centimeter deeper than the rim, is used at Massachusetts Institute of Technology (MIT) for teaching purposes. ²

First to consider is the situation when the turntable is not rotating.

Schematic representation of harmonic oscillation on parabolic surface. The concavity is exaggerated.

When the puck is released from the rim, without giving it any push, the puck will commence an oscillating motion, back and forth across the turntable. Because of the specific shape of the cross section, the oscillation will be a harmonic oscillation. The period of this oscillation will be the same as the period of rotation of the parabolic turntable as it was being manufactured.

The puck can also be set in a concentric circular motion, and again: due to the parabolic shape of the surface, all concentric circular motions of the puck will have the same period, independent of the distance to the center of rotation. (Just as the resin, after redistributing itself to a form with a parabolic surface had the same period of rotation at every distance to the center or rotation.)

[edit] Comparison with the shape of the Earth

The parabolic shape of the turntable models the dynamic equilibrium of the shape of the Earth. If the Earth were exactly spherical, there would not be a centripetal force that would keep the water of the oceans and the air of the atmosphere from flowing towards the equator. However, since the shape of the solid Earth is governed by the same tendency towards a dynamic equilibrium, the solid Earth is somewhat flattened; at the equator the surface of the Earth is about 21 kilometers further away from the Earth's center than the poles are. Given this difference in height, flowing towards the equator is effectively flowing uphill.

[edit] Unconstrained motion

Schematic representation of a puck moving over a parabolic surface.

An elliptical trajectory as seen by a video camera that is co-rotating with the turntable.

When the puck is moving around on the parabolic turntable the only force influencing its motion is the centripetal force in correspondence to the inclination of the surface. Other than that, motion parallel to the surface is unconstrained.

Let the puck be floating above the parabolic turntable surface, following a circular concentric trajectory around the center of rotation of the parabolic turntable. Next the puck is given a jolt, a small push. The trajectory of the puck will then change from a circular shape to an elliptical shape. In the field of view of a video camera that is co-rotating with the turntable only the eccentricity of the orbit will be directly visible. For every complete elliptical orbit, the object goes through two cycles of the eccentricity of the elliptical orbit.

When the puck is in the areas marked with the letter A, the puck is moving slower than the velocity of a concentric circular orbit at that distance to the center, so there is a surplus of centripetal force acting on the puck there, and the puck is being accelerated towards the center of rotation. In the areas marked B the puck is sliding down the incline, so it is picking up speed; the puck is "catching up" in that section. The centripetal force is doing mechanical work, increasing the rotational kinetic energy of the puck. In the areas marked C the puck is moving faster than the velocity of a concentric circular orbit at that distance to the center, so the centripetal force there is not strong enough to hold it at a constant radial distance and after C the puck is once again moving away from the center of rotation. In the areas marked D the puck is climbing up the incline, losing velocity, the rotational kinetic energy decreases.

This dynamics of energy conversions of the elliptical orbit looks as seen by a co-rotating video camera like smooth motion along a circular trajectory with a small diameter. As seen by a co-rotating video camera it looks as if there is a single "coriolis force" causing the puck to follow that small circular trajectory.

In actual fact the apparent circular trajectory is an oscillation in the overall orbit that is governed by the force directed towards the axis of rotation of the turntable. In this particular example that centripetal force is provided by the Earth's gravity, redirected by the slope of the parabolic turntable. The expression "coriolis force" must in this context be understood as physics shorthand: abbreviating a lot of dynamics into a single expression.

[edit] Comparison with moving masses of air

Schematic representation. Inertial circles of fast moving air mass in the absence of other forces.

Inertial oscillation as seen from a non-rotating point of view. The eccentricity is the oscillation.

If an air parcel is has a velocity with respect to the Earth then the rotational dynamcis will lead to an approximately circular motion with respect to the Earth called 'inertial circle's.

The frequency of these oscillations is given by f, the coriolis parameter; and their amplitude by [1]:

v / f

where v is the velocity of the air mass. A typical mid-latitude value for f is 10^-4; hence for a typical atmospheric speed of 10 m/s the radius is 100 km, with a period of about 14 hours.

Closer to the equator the component of the velocity towards or away from the Earth's axis is smaller, this component varies as $s i n (l a t i t u d e)$ , and this is taken into account in the form of including the parameter f. For a given velocity the oscillations are smallest at the poles as shown by the picture and would increase indefinitely at the equator, except the dynamics ceases to apply close to the equator. On a rotating planet the oscillations are only approximately circular [2] and do not form closed loops as indicated in the drastically simplified picture.

These inertial circles are proof that the component of true gravity that acts perpendicular to the Earth's axis (parallel to the latitude lines) is a key factor in influencing the direction of large scale winds. Air mass that is not co-rotating with the Earth as a whole, but has a lower velocity instead, will be pulled to the north. The inertial oscillations are like oscillations of a weight suspended on a spring, bobbing south and north, remaining in a particular latitudal band.

The animation on the right represents the motion of a weather balloon, being swept along with inertial wind. Inertial wind is an example of an inertial oscillation. A full cycle of the animation represents a 24 hour period. The vertical circles are not meridians, the vertical circles are just there to create a sense of depth in the picture.

At mid-latitude the tangential velocity of co-rotating with Earth is about 330 meters per second. Inertial wind that flows with a velocity of 10 meter per second with respect to the Earth is oscillating between moving at 320 meters per second and moving at 340 meters per second.

The tendency in the atmosphere to move in inertial oscillations is a form of what in fluid dynamics is called Taylor columns.

[edit] Taylor columns

In fluid dynamics, a fluid that is rotating without moving with respect to the vessel that contains it is called a fluid in solid body rotation. The surface is parabolical in shape then. The force, acting on every part of the fluid is proportional to the distance to the center of rotation. Because of that the behavior of the rotating fluid is rather different from the behavior of a non-rotating fluid. Among other things, this leads to a phenomenon called Taylor columns, which can be demonstrated by having a strongly buoyant object (like a pingpong ball) rise in a rotating fluid.

Taylor columns. Rigidity of the water because it is rotating. The ball will rise slower than in non-rotating water

In a rotating fluid the ball will rise slower than in a non-rotating fluid. Fluid that is shifted from its position in the body of fluid as a whole tends to be directed back to the point it is shifted away from. The faster the rotation rate, the smaller the radius of the inertial circles.

In a non-rotating fluid the fluid is pushed aside above the rising ball and closes in underneath it, offering relatively little resistance to the ball. In a rotating fluid the ball needs to push up a whole column of fluid above it, and it needs to drag a whole column of fluid along beneath it in order to rise to the surface.

The Taylor-Proudman theorem describes this and an other related phenomena. The Taylor-Proudman theorem is widely used when considering limnological flows, astrophysical flows (such as solar and Jovian dynamics) and some industrial problems such as turbine design. ³

[edit] Molecular physics

In polyatomic molecules, the molecule motion can be described by a rigid body rotation and internal vibration of atoms about their equilibrium position. As a result of the vibrations of the atoms, the atoms are in motion relative to the rotating coordinate system of the molecule. A Coriolis effects will therefore be present and will cause the atoms to move in a direction perpendicular to the original oscillations. This leads to a mixing in molecular spectra between the rotational and vibrational levels.

[edit] Derivations in Angular Mechanics

The dynamics of motion in a centripetal force field, with the centripetal force proportional to the distance.

Orbital motion in that force field has the following properties: both circular and elliptical orbits are stable, and all stable orbits have the same period of rotation. This means that when a torque is exerted the radius of circular motion will increase, but the period of rotation will not increase.

Derivation of formula for most simple, most symmetric case.
The centripetal force is described by the formula $F = m \omega_e^2 r$ , where $ω e$ is the angular velocity of stable circular orbit. The object is free to move in any direction parallel to the surface, but it is subject everywhere to the centripetal force.

[edit] Torque

The moment of inertia: $I = m r 2$
The angular momentum: $L = I ω = m r 2 ω$
torque: $τ = F r$

Let $v r$ be velocity in radial direction. Let $ω e$ be the angular velocity of circular orbit in the centripetal force field. (The e stands for equilibrium)
The derivative of angular momentum with respect to time equals the torque.

$\tau = F r = \frac{dL}{dt} = \frac {d(m \omega_e r^2)}{dt} = 2m \omega r \frac{dr}{dt}$

$\Leftrightarrow F = 2m \omega_e v_r$

In the previous derivation the second force present (the first force being the centripetal force) acted perpendicular to the radial directrion, it exerted a torque.
Next to consider is the case that the second force acts in radial direction.

[edit] Radial force other than the global centripetal force

Let $F e$ stand for the global centripetal force. This global centripetal force is a given. It is a function of distance to the center, and it is unchanging in time. Stable circular orbit in that field circles at the equilibrium angular velocity $ω e$ (The e stands for 'equilibrium'.)
Let $F v$ stand for the total centripetal force, to be exerted on an object moving at some angular velocity $ω$ that is not the equilibrium angular velocity. Let $Δω$ be the difference with equilibrium angular velocity. Let $v t$ be the tangential velocity relative to $ω e$ . Then $(Δω) r = v t$ .

F = F v - F e = - m (ω e + Δω) 2 r - ( - m (ω e) 2 r)

= - m r ((ω e + Δω) 2 - (ω e) 2)

$= - m r (\omega_e^2 + 2 \omega_e \Delta \omega + (\Delta \omega)^2 - \omega_e^2)$

= - 2 m ω e Δω r - m (Δω) 2 r

= - 2 m ω e v t - m (Δω) 2 r

[edit] No force present other than the global centripetal force

In the idealized situation of a centripetal force that is proportional to the distance to the center of rotation, and all other factors negligable, the set of stable orbits consists of ellipses.

The velocity profile of such an ellipse is such that it can be mathematically described with a cosine and a sine. (Of course, this is no coincidence. It is a theorem of newtonian dynamics that any dynamics taking place in two dimensions can be described as a linear combination of two linear motions, perpendicular to each other)

The parametric equation is as follows:

x = a * cos(ω)

y = b * sin(ω)

The motion as a function of $ω$ can be seen as a vector combination of two uniform circular motions. In the case of the animations to the right a combination of a counterclockwise circular motion with radius (a + b)/2 and a clockwise circular motion with radius (a - b)/2. The parametric equation:

$x =(\frac{a+b}{2})\cos\omega + (\frac{a-b}{2})\cos\omega$

$y =(\frac{a+b}{2})\sin\omega - (\frac{a-b}{2})\sin\omega$

After transforming to a rotating coordinate system the overall circular motion is eliminated and only the eccentricity of the elliptical orbit remains:

$x = (\frac{a-b}{2})\cos (2 \omega)$

$y = - (\frac{a-b}{2})\sin (2 \omega)$

[edit] References

[edit] Physics and meteorology references

Durran, D. R., 1993: Is the Coriolis force really responsible for the inertial oscillation? Bull. Amer. Meteor. Soc., 74, 2179–2184; Corrigenda. Bulletin of the American Meteorological Society, 75, 261
1200 KB PDF-file of the above article

Durran, D. R., and S. K. Domonkos, 1996: An apparatus for demonstrating the inertial oscillation. Bulletin of the American Meteorological Society, 77, 557–559.
1300 KB PDF-file of the above article

Persson, A., 1998 How do we Understand the Coriolis Force? Bulletin of the American Meteorological Society 79, 1373-1385.
374 KB PDF-file of the above article

Norman Ph. A., 2000 An Explication of the Coriolis Effect. Bulletin of the American Meteorological Society: Vol. 81, No. 2, pp. 299–303.
200 KB PDF-file of the above article

[edit] Historical references

Grattan-Guinness, I., Ed., 1994: Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Vols. I and II. Routledge, 1840 pp.
1997: The Fontana History of the Mathematical Sciences. Fontana, 817 pp. 710 pp.

Khrgian, A., 1970: Meteorology—A Historical Survey. Vol. 1. Keter Press, 387 pp.

Kuhn, T. S., 1977: Energy conservation as an example of simultaneous discovery. The Essential Tension, Selected Studies in Scientific Tradition and Change, University of Chicago Press, 66–104.

Kutzbach, G., 1979: The Thermal Theory of Cyclones. A History of Meteorological Thought in the Nineteenth Century. Amer. Meteor. Soc., 254 pp.

[edit] External links

Note 1: Coriolis effect misconceptions

Note 2: Rotating turntable setup The concave turntable used at MIT for educational purposes.

Note 3: Taylor columns The counterintuitive behavior of a rotating fluid. Demonstration at MIT for educational purposes

How do we understand the Coriolis force? PDF-file. 13 pages. A discussion of the physics of the Coriolis effect by the meteorologist Anders Persson.

The Coriolis Effect PDF-file. 17 pages. A general discussion by Anders Persson of various aspects of the coriolis effect, including Foucault's Pendulum and Taylor columns.

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