Citizendia
Your Ad Here

Figure 1: In the inertial frame of reference (upper part of the picture), the black object moves in a straight line. However, the observer (red dot) who is standing in the rotating frame of reference (lower part of the picture) sees the object as following a curved path.
Figure 1: In the inertial frame of reference (upper part of the picture), the black object moves in a straight line. However, the observer (red dot) who is standing in the rotating frame of reference (lower part of the picture) sees the object as following a curved path.

The Coriolis effect is an apparent deflection of moving objects when they are viewed from a rotating frame of reference. A rotating frame of reference is a special case of a Non-inertial reference frame that is rotating relative to an Inertial reference frame. The effect is named after Gaspard-Gustave Coriolis, a French scientist who described it in 1835, though the mathematics appeared in the tidal equations of Pierre-Simon Laplace in 1778. Gaspard-Gustave de Coriolis or Gustave Coriolis (21 May 1792 – 19 September 1843 was a French Mathematician, Mechanical engineer and The theory of tides is the application of Continuum mechanics to interpret and predict the tidal deformations of planetary and satellite bodies and their atmospheres The Coriolis effect is caused by the Coriolis force, which appears in the equation of motion of an object in a rotating frame of reference. The Coriolis force is an example of a fictitious force (or pseudo force), because it does not appear when the motion is expressed in an inertial frame of reference, in which the motion of an object is explained by the real impressed forces, together with inertia. A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent Force that acts on all masses in a non-inertial In Physics, an inertial frame of reference is a Frame of reference which belongs to a set of frames in which Physical laws hold in the same and simplest The vis insita or innate force of matter is a power of resisting by which every body as much as in it lies endeavors to preserve in its present state whether it be of rest or of moving In a rotating frame, the Coriolis force, which depends on the velocity of the moving object, and centrifugal force, which does not depend on the velocity of the moving object, are needed in the equation to correctly describe the motion. In Physics, velocity is defined as the rate of change of Position. In Physics, velocity is defined as the rate of change of Position.

Perhaps the most commonly encountered rotating reference frame is the Earth. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 Freely moving objects on the surface of the Earth experience a Coriolis force, and appear to veer to the right in the northern hemisphere, and to the left in the southern. Northern Hemisphere is the half of a Planet that is North of the Equator —the word hemisphere literally means 'half ball' Southern Hemisphere is the half of a Planet that is South of the Equator —the word hemisphere literally means 'half ball' Movements of air in the atmosphere and water in the ocean are notable examples of this behavior: rather than flowing directly from areas of high pressure to low pressure, as they would on a non-rotating planet, winds and currents tend to flow to the right (left) of this direction north (south) of the equator. This effect is responsible for the rotation of large cyclones (see Coriolis in meteorology). In Meteorology, a cyclone refers to an area of closed circular fluid motion rotating in the same direction as the Earth. In physics the Coriolis effect is an apparent deflection of moving objects when they are viewed from a Rotating frame of reference.

Contents

Formula

See also: Fictitious force

In non-vector terms: at a given rate of rotation of the observer, the magnitude of the Coriolis acceleration of the object is proportional to the velocity of the object and also to the sine of the angle between the direction of movement of the object and the axis of rotation. A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent Force that acts on all masses in a non-inertial

The vector formula for the magnitude and direction the Coriolis acceleration is

\boldsymbol{ a}_C = -2 \, \boldsymbol{ \Omega \times v}

where (here and below) v is the velocity of the particle in the rotating system, and Ω is the angular velocity vector which has magnitude equal to the rotation rate ω and is directed along the axis of rotation of the rotating reference frame, and the × symbol represents the cross product operator. Do not confuse with Angular frequency The unit for angular velocity is rad/s In Mathematics, the cross product is a Binary operation on two vectors in a three-dimensional Euclidean space that results in another vector which

The equation may be multiplied by the mass of the relevant object to produce the Coriolis force:

\boldsymbol{ F}_C = -2 \, m \, \boldsymbol{\Omega \times v}.

See fictitious force for a derivation. A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent Force that acts on all masses in a non-inertial

The Coriolis effect is the behavior added by the Coriolis acceleration. The formula implies that the Coriolis acceleration is perpendicular both to the direction of the velocity of the moving mass and to the frame's rotation axis. So in particular:

Rotating sphere

Figure 2: Coordinate system at latitude φ with x-axis east, y-axis north and z-axis upward (that is, radially outward from center of sphere).
Figure 2: Coordinate system at latitude φ with x-axis east, y-axis north and z-axis upward (that is, radially outward from center of sphere).

Consider a location with latitude \varphi on a sphere that is rotating around the north-south axis. [1] A local coordinate system is set up with the x axis horizontally due east, the y axis horizontally due north and the z axis vertically upwards. The rotation vector, velocity of movement and Coriolis acceleration expressed in this local coordinate system (listing components in the order East (e), North (n) and Upward (u)) are:

\boldsymbol{ \Omega} = \omega \begin{pmatrix} 0 \\ \cos \varphi \\ \sin \varphi \end{pmatrix}\ ,     \boldsymbol{ v} = \begin{pmatrix} v_e \\ v_n \\ v_u \end{pmatrix}\ ,
\boldsymbol{ a}_C =-2\boldsymbol{\Omega \times v}=-2\omega \begin{vmatrix} \boldsymbol{i}&\boldsymbol{j}&\boldsymbol{k} \\0& \cos \varphi & \sin \varphi \\ v_e & v_n & v_u \end{vmatrix}= 2\,\omega\, \begin{pmatrix} v_n \sin \varphi-v_u \cos \varphi \\ -v_e \sin \varphi \\ v_e \cos\varphi\end{pmatrix}\ ,

where the cross product is evaluated as the determinant of a matrix. In Mathematics, the cross product is a Binary operation on two vectors in a three-dimensional Euclidean space that results in another vector which (Vectors i, j, k are unit vectors in the e, n and u directions. ) When considering atmospheric or oceanic dynamics, the vertical velocity is small and the vertical component of the Coriolis acceleration is small compared to gravity. For such cases, only the horizontal (East and North) components matter. The restriction of the above to the horizontal plane is (setting vu=0):

\boldsymbol{ v} = \begin{pmatrix} v_e \\ v_n\end{pmatrix}\ ,     \boldsymbol{ a}_c = \begin{pmatrix} v_n \\ -v_e\end{pmatrix}\ f\ ,   where f = 2 \omega \sin \varphi \, is called the Coriolis parameter. The Coriolis frequency, f, is equal to twice the rotation rate of the Earth multiplied by the Sine of the Latitude.

By setting vn = 0, it can be seen immediately that (for positive \varphi and \omega\,) a movement due east results in an acceleration due south. Similarly, setting ve = 0, it is seen that a movement due north results in an acceleration due east — that is, standing on the horizontal plane, looking along the direction of the movement causing the acceleration, the acceleration always is turned 90° to the right. That is: [2]

On a merry-go-round in the night
Coriolis was shaken with fright
Despite how he walked
'Twas like he was stalked
By some fiend always pushing him right

– D. Morin: Introduction to classical mechanics: with problems and solutions

As a different case, consider equatorial motion setting φ = 0°. In this case, Ω is parallel to the North or n-axis, and:

\boldsymbol{ \Omega} = \omega \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}\ ,     \boldsymbol{ v} = \begin{pmatrix} v_e \\ v_n \\ v_u \end{pmatrix}\ ,  \boldsymbol{ a}_C =-2\boldsymbol{\Omega \times v}= 2\,\omega\, \begin{pmatrix}-v_u \\0 \\ v_e \end{pmatrix}\ .

Accordingly, an eastward motion (that is, in the same direction as the rotation of the sphere) provides an upward acceleration known as the Eötvös effect, and an upward motion produces an acceleration due west. In the early 1900s a German team from the Institute of Geodesy in Potsdam carried out gravity measurements on moving ships in the Atlantic Indian and Pacific Oceans

For additional examples, see rotating spheres and dropping ball in the article on centrifugal force, and carousel in fictitious force. A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent Force that acts on all masses in a non-inertial A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent Force that acts on all masses in a non-inertial

Causes

The Coriolis effect exists only when using a rotating reference frame. It is mathematically deduced from the law of inertia. The vis insita or innate force of matter is a power of resisting by which every body as much as in it lies endeavors to preserve in its present state whether it be of rest or of moving Hence it does not correspond to any actual acceleration or force, but only the appearance thereof from the point of view of a rotating system.

The Coriolis effect exhibited by a moving object can be interpreted as being the sum of the effects of two different causes of equal magnitude.

The first cause is the change of the velocity of an object in time. The same velocity (in an inertial frame of reference where the normal laws of physics apply) will be seen as different velocities at different times in a rotating frame of reference. The apparent acceleration is proportional to the angular velocity of the reference frame (the rate at which the coordinate axes changes direction), and to the velocity of the object. This gives a term -\boldsymbol\Omega\times\mathbf{v}. The minus sign arises from the traditional definition of the cross product (right hand rule), and from the sign convention for angular velocity vectors. For the related yet different principle relating to electromagnetic coils see Right hand grip rule.

The second cause is change of velocity in space. Different points in a rotating frame of reference have different velocities (as seen from an inertial frame of reference). In order for an object to move in a straight line it must therefore be accelerated so that its velocity changes from point to point by the same amount as the velocities of the frame of reference. The effect is proportional to the angular velocity (which determines the relative speed of two different points in the rotating frame of reference), and the velocity of the object perpendicular to the axis of rotation (which determines how quickly it moves between those points). This also gives a term -\boldsymbol\Omega\times\mathbf{v}.

Corrections to common misconceptions about the Coriolis effect

Cannon on turntable

Figure 3: Cannon on a rotating turntable. To hit the target located at position 1 at time t = 0s, the cannon must be aimed ahead of the target at angle θ. That way, by the time the cannonball reaches position 3 on the periphery, the target also will be at that position. In an inertial frame of reference, the cannonball travels a straight radial path to the target (curve yA). However, in the frame of the turntable, the path is arched (curve yB), as also shown in the figure.
Figure 3: Cannon on a rotating turntable. To hit the target located at position 1 at time t = 0s, the cannon must be aimed ahead of the target at angle θ. That way, by the time the cannonball reaches position 3 on the periphery, the target also will be at that position. In an inertial frame of reference, the cannonball travels a straight radial path to the target (curve yA). However, in the frame of the turntable, the path is arched (curve yB), as also shown in the figure.

Figure 1 is an animation of the classic illustration of Coriolis force. Figure 3 is a graphical version. The question posed is: given the radius of the turntable R, the rate of angular rotation ω, and the speed of the cannonball (assumed constant) v, what is the correct angle θ to aim so as to hit the target at the edge of the turntable?

This question is very readily answered in the inertial frame of reference. One way to handle it is to calculate the time to interception, which is tf = R / v . Then, the turntable revolves an angle ω tf in this time. If the cannon is pointed an angle θ = ω tf = ω R / v, then the cannonball arrives at the periphery at position number 3 at the same time as the target. No discussion of Coriolis force can arrive at this solution as simply, so the reason to treat this problem is to use an easily visualized situation to demonstrate Coriolis formalism.

Formulation

Figure 4: Successful trajectory of cannonball as seen from the turntable for two rates of rotation ω. Notice that the y-axis scale is magnified compared to the x-axis.
Figure 4: Successful trajectory of cannonball as seen from the turntable for two rates of rotation ω. Notice that the y-axis scale is magnified compared to the x-axis.

The trajectory in the inertial frame (denoted A) is a straight line radial path at angle θ. The position of the cannonball in ( x, y ) coordinates at time t is:

\mathbf{r}_A (t) = vt\ \left( \cos (\theta ),\ \sin (\theta )\right) \ .

In the turntable frame (denoted B), the x- y axes rotate at angular rate ω, so the trajectory becomes:

\mathbf{r}_B (t) = vt\ \left( \cos ( \theta - \omega t),\ \sin ( \theta - \omega t)\right) \ ,

and two examples of this result are plotted in Figure 4.

Next, the trajectory rB is time differentiated twice to obtain the acceleration. Following that, the acceleration is re-expressed in terms of the general expression from fictitious force:

\mathbf{a}_{B} = \mathbf{a}_A - 2 \boldsymbol\Omega \times \mathbf{v}_{B} - \boldsymbol\Omega \times (\boldsymbol\Omega \times \mathbf{r}_B ) - \frac{d \boldsymbol\Omega}{dt} \times \mathbf{r}_B \ ,

in which the term in Ω × vB is the Coriolis acceleration and the term in Ω × ( Ω × rB) is the centrifugal acceleration. A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent Force that acts on all masses in a non-inertial This exercise demonstrates that one could start from this general expression and derive the trajectories of Figure 4. However, working forward from the acceleration to the trajectory is more complicated than the reverse procedure used here, a procedure made possible by knowing the answer in advance.

As a result of this analysis an important point appears: all the fictitious accelerations must be included to obtain the correct trajectory. In particular, besides the Coriolis acceleration, the centrifugal force plays an essential role. It is easy to get the impression from verbal discussions of the cannonball problem, which are focussed on displaying the Coriolis effect particularly, that the Coriolis force is the only factor that must be considered;[3] emphatically, that is not so. [4] A turntable for which the Coriolis force is the only factor is the parabolically contoured turntable described next. A somewhat more complex situation is the idealized example of flight routes over long distances, where the centrifugal force of the path and aeronautical lift are countered by gravitational attraction. In the context of a Fluid flow relative to a body the lift force is the component of the Aerodynamic force that is Perpendicular to the flow In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star [5][6]

Visualization of the Coriolis effect

Figure 5: A fluid assuming a parabolic shape as it is rotating
Figure 5: A fluid assuming a parabolic shape as it is rotating
Figure 6: Object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an ellipse-shaped trajectory. Left: the motion as observed from the inertial point of view. The gravitational force pulling the object toward the bottom (center) of the dish is proportional to the distance of the object from the center. This force causes the elliptical motion. Right: the motion as seen from a co-rotating point of view. In this frame, the inward gravitational force is balanced by the outward centrifugal force. The only unbalanced force is Coriolis, and the motion is an inertial circle.
Figure 6: Object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an ellipse-shaped trajectory.

Left: the motion as observed from the inertial point of view. The gravitational force pulling the object toward the bottom (center) of the dish is proportional to the distance of the object from the center. This force causes the elliptical motion.
Right: the motion as seen from a co-rotating point of view. In this frame, the inward gravitational force is balanced by the outward centrifugal force. The only unbalanced force is Coriolis, and the motion is an inertial circle.

To demonstrate the Coriolis effect, a parabolic turntable can be used. On a flat turntable, the inertia of a co-rotating object would force it off the edge. But if the surface of the turntable has the correct parabolic bowl shape and is rotated at the correct rate, then the component of gravity tangential to the bowl surface will exactly equal the centripetal force necessary to keep the water rotating at its velocity and radius of curvature. (See banked turn. The centripetal force is the external force required to make a body follow a curved path ) This contoured surface allows the Coriolis force to be displayed in isolation. When a container of fluid is rotating on a turntable, the surface of the fluid naturally assumes the correct parabolic shape. In Mathematics, the parabola (pəˈræbələ from the Greek παραβολή) is a Conic section, the intersection of a right circular This fact may be exploited to make a parabolic turntable by using a fluid that sets after several hours, such as a synthetic resin. Resin, not to be confused with Rosin, is a Hydrocarbon Secretion of many Plants particularly coniferous trees.

Discs cut from cylinders of dry ice can be used as pucks, moving around almost frictionlessly over the surface of the parabolic turntable, allowing effects of Coriolis on dynamic phenomena to show themselves. Dry ice is solid Carbon dioxide. It is commonly used as a versatile cooling agent To get a view of the motions as seen from the reference frame rotating with the turntable, a video camera is attached to the turntable so as to co-rotate with the turntable. Because this reference frame rotates several times a minute, rather than only once a day like the Earth, the Coriolis acceleration produced is many times larger, and so easier to observe on small time and spatial scales, than is the Coriolis acceleration caused by the rotation of the Earth.

In a manner of speaking, the Earth is analogous such a turntable. The rotation has caused the planet to settle on a spheroid shape such that the normal force, the gravitational force, and the centrifugal force exactly balance each other on a "horizontal" surface. (See equatorial bulge. An equatorial bulge is a bulge which a planet may have around its Equator, distorting it into an Oblate spheroid. )

The Coriolis effect caused by the rotation of the Earth can be seen indirectly through the motion of a Foucault pendulum. The Foucault pendulum (fuːˈkoʊ "foo-KOH" or Foucault's pendulum, named after the French physicist Léon Foucault, was conceived as

Draining in bathtubs and toilets

A misconception in popular culture is that water in bathtubs or toilets always drains in one direction in the Northern Hemisphere, and in the other direction in the Southern Hemisphere as a consequence of the Coriolis effect. Northern Hemisphere is the half of a Planet that is North of the Equator —the word hemisphere literally means 'half ball' Southern Hemisphere is the half of a Planet that is South of the Equator —the word hemisphere literally means 'half ball' This idea has been perpetuated by several television programs, including an episode of The Simpsons and one of The X-Files. " Bart vs Australia " is the sixteenth episode of The Simpsons ' sixth season, which originally aired on the Fox network The X-Files is a Peabody, Golden Globe and Emmy Award -winning American Science fiction television series created by Chris Carter [7] In addition, several science broadcasts and publications (including at least one college-level physics textbook) have made this incorrect statement. [8]

Some sources that incorrectly attribute draining direction to the Coriolis force also get the direction wrong. If the Coriolis force were the dominant factor, drain vortices would spin counterclockwise in the northern hemisphere and clockwise in the southern. V erification of the O rigins of R otation in T ornadoes Ex periment or VORTEX, is a field project that seeks to understand how a

In reality the Coriolis effect is a few orders of magnitude smaller than various random influences on drain direction, such as the geometry of the container and the direction in which water was initially added to it. An order of magnitude is the class of scale or magnitude of any amount where each class contains values of a fixed ratio to the class preceding it Most toilets flush in only one direction, because the toilet water flows into the bowl at an angle. [9] If water shot into the basin from the opposite direction, the water would spin in the opposite direction. [10]

When the water is being drawn towards the drain, the radius of its rotation around the drain decreases, so its rate of rotation increases from the low background level to a noticeable spin in order to conserve its angular momentum (the same effect as ice skaters bringing their arms in to cause them to spin faster). In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position As shown by Ascher Shapiro in a 1961 educational video (Vorticity, Part 1), this effect can indeed reveal the influence of the Coriolis force on drain direction, but only under carefully controlled laboratory conditions. Ascher H Shapiro (born May 20 1916 in Brooklyn, New York — died November 26 at Jamaica Plain, Boston In a large, circular, symmetrical container (ideally over 1m in diameter and conical), still water (whose motion is so little that over the course of a day, displacements are small compared to the size of the container) escaping through a very small hole, will drain in a cyclonic fashion: counterclockwise in the Northern hemisphere and clockwise in the Southern hemisphere—the same direction as the Earth rotates with respect to the corresponding pole.

Coriolis in meteorology

Figure 7: This low pressure system over Iceland spins counter-clockwise due to balance between the Coriolis force and the pressure gradient force.
Figure 7: This low pressure system over Iceland spins counter-clockwise due to balance between the Coriolis force and the pressure gradient force. A low pressure area, or " low " is a region where the Atmospheric pressure is lower in relation to the surrounding area Iceland, officially the Republic of Iceland ( ( Ísland or Lýðveldið Ísland (

Perhaps the most important instance of the Coriolis effect is in the large-scale dynamics of the oceans and the atmosphere. In meteorology, it is convenient to use a rotating frame of reference where the Earth is stationary. The fictitious centrifugal and Coriolis forces must then be introduced. The former, however, is canceled by the non-spherical shape of the earth (see the turntable analogy above). Hence the Coriolis force is the only fictitious force to have a significant impact on calculations.

Flow around a low-pressure area

Figure 8: Schematic representation of flow around a low-pressure area in the Northern hemisphere. The pressure-gradient force is represented by blue arrows, the Coriolis acceleration (always perpendicular to the velocity) by red arrows
Figure 8: Schematic representation of flow around a low-pressure area in the Northern hemisphere. The pressure-gradient force is represented by blue arrows, the Coriolis acceleration (always perpendicular to the velocity) by red arrows

If a low-pressure area forms in the atmosphere, air will tend to flow in towards it, but will be deflected perpendicular to its velocity by the Coriolis acceleration. A system of equilibrium can then establish itself creating circular movement, or a cyclonic flow. The force balance is largely between the pressure gradient force acting towards the low-pressure area and the Coriolis force acting away from the center of the low pressure.

Instead of flowing down the gradient, large scale motions in the atmosphere and ocean tend to occur perpendicular to the pressure gradient. This is known as geostrophic flow. The geostrophic wind is the Theoretical Wind that would result from an exact balance between the Coriolis force and the Pressure gradient force On a non-rotating planet fluid would flow along the straightest possible line, quickly eliminating pressure gradients. Note that the geostrophic balance is thus very different from the case of "inertial motions" (see below) which explains why mid-latitude cyclones are larger by an order of magnitude than inertial circle flow would be.

This pattern of deflection, and the direction of movement, is called Buys-Ballot's law. In Meteorology, Buys Ballot's law may be expressed as follows In the Northern Hemisphere, stand with your back to the Wind; the low pressure In the atmosphere, the pattern of flow is called a cyclone. In Meteorology, a cyclone refers to an area of closed circular fluid motion rotating in the same direction as the Earth. In the Northern Hemisphere the direction of movement around a low-pressure area is counterclockwise. In the Southern Hemisphere, the direction of movement is clockwise because the rotational dynamics is a mirror image there. At high altitudes, outward-spreading air rotates in the opposite direction. [11] Cyclones cannot form on the equator, because in the equatorial region the Coriolis parameter is small.

Inertial circles

Figure 9: Schematic representation of inertial circles of air masses in the absence of other forces, calculated for a wind speed of approximately 50 to 70 m/s. Note that the rotation is exactly opposite that normally experienced with air masses in weather systems around depressions.
Figure 9: Schematic representation of inertial circles of air masses in the absence of other forces, calculated for a wind speed of approximately 50 to 70 m/s. Note that the rotation is exactly opposite that normally experienced with air masses in weather systems around depressions.

An air or water mass moving with speed v\, subject only to the Coriolis force travels in a circular trajectory called an 'inertial circle'. Since the force is directed at right angles to the motion of the particle, it will move with a constant speed, and perform a complete circle with frequency f. The magnitude of the Coriolis force also determines the radius of this circle:

R=v/f\,.

On the Earth, a typical mid-latitude value for f is 10−4 s−1; hence for a typical atmospheric speed of 10 m/s the radius is 100 km, with a period of about 14 hours. In the ocean, where a typical speed is closer to 10 cm/s, the radius of an inertial circle is 1 km. These inertial circles are clockwise in the northern hemisphere (where trajectories are bent to the right) and anti-clockwise in the southern hemisphere.

If the rotating system is a parabolic turntable, then f is constant and the trajectories are exact circles. On a rotating planet, f varies with latitude and the paths of particles do not form exact circles. Since the parameter f varies as the sine of the latitude, the radius of the oscillations associated with a given speed are smallest at the poles (latitude = ±90°), and increase toward the equator.

Length scales and the Rossby number

Further information: Rossby number

The time, space and velocity scales are important in determining the importance of the Coriolis effect. The Rossby number, named for Carl-Gustav Arvid Rossby, is a Dimensionless number used in describing fluid flow Whether rotation is important in a system can be determined by its Rossby number, which is the ratio of the velocity, U, of a system to the product of the Coriolis parameter, f, and the length scale, L, of the motion:

Ro = \frac{U}{fL}. The Rossby number, named for Carl-Gustav Arvid Rossby, is a Dimensionless number used in describing fluid flow

A small Rossby number signifies a system which is strongly affected by rotation, and a large Rossby number signifies a system in which rotation is unimportant.

An atmospheric system moving at U = 10 m/s occupying a spatial distance of L = 1000 km, has a Rossby number of approximately 0. 1. A man playing catch may throw the ball at U = 30 m/s in a garden of length L = 50 m. The Rossby number in this case would be about = 6000. Needless to say, one does not worry about which hemisphere one is in when playing catch in the garden. However, an unguided missile obeys exactly the same physics as a baseball, but may travel far enough and be in the air long enough to notice the effect of Coriolis. Long-range shells in the Northern Hemisphere landed close to, but to the right of, where they were aimed until this was noted. (Those fired in the southern hemisphere landed to the left. ) In fact, it was this effect that first got the attention of Coriolis himself. [12] [13]

The Rossby number can also tell us about the bathtub. If the length scale of the tub is about L = 1 m, and the water moves towards the drain at about U = 60 cm/s, then the Rossby number is about 6 000. Thus, the bathtub is, in terms of scales, much like a game of catch, and rotation is likely to be unimportant.

Other terrestrial effects

The Coriolis effect strongly affects the large-scale oceanic and atmospheric circulation, leading to the formation of robust features like jet streams and western boundary currents. Atmospheric circulation is the large-scale movement of air and the means (together with the smaller Ocean circulation) by which Heat is distributed on the surface Jet streams are fast flowing relatively narrow air currents found at the Tropopause, the transition between the Troposphere (where temperature decreases Such features are in geostrophic balance, meaning that the Coriolis and pressure gradient forces balance each other. A geostrophic current results from the balance between gravitational forces and the Coriolis effect. Coriolis acceleration is also responsible for the propagation of many types of waves in the ocean and atmosphere, including Rossby waves and Kelvin waves. Rossby (or planetary) waves are giant Meanders in high-altitude winds that are a major influence on Weather. A Kelvin wave is a wave in the ocean or atmosphere that balances the Earth's Coriolis force against a topographic boundary such as a coastline It is also instrumental in the so-called Ekman dynamics in the ocean, and in the establishment of the large-scale ocean flow pattern called the Sverdrup balance. In standard boundary-layer theory the effects of viscous Diffusion are usually balanced by convective Inertia. The Sverdrup balance, or Sverdrup relation, is a theoretical relationship between the Wind stress exerted on the surface of the open Ocean and

Other aspects of the Coriolis effect

The practical impact of the Coriolis effect is mostly caused by the horizontal acceleration component produced by horizontal motion.

There are other components of the Coriolis effect. Eastward-traveling objects will be deflected upwards (feel lighter), while westward-traveling objects will be deflected downwards (feel heavier). This is known as the Eötvös effect. In the early 1900s a German team from the Institute of Geodesy in Potsdam carried out gravity measurements on moving ships in the Atlantic Indian and Pacific Oceans This aspect of the Coriolis effect is greatest near the equator. The force produced by this effect is similar to the horizontal component, but the much larger vertical forces due to gravity and pressure mean that it is generally unimportant dynamically.

In addition, objects traveling upwards or downwards will be deflected to the west or east respectively. This effect is also the greatest near the equator. Since vertical movement is usually of limited extent and duration, the size of the effect is smaller and requires precise instruments to detect.

Coriolis elsewhere

Coriolis flow meter

A practical application of the Coriolis effect is the mass flow meter, an instrument that measures the mass flow rate and density of a fluid flowing through a tube. A mass flow meter, also known as inertial flow meter and coriolis flow meter, is a device that measures how much fluid is flowing through a tube Mass flow rate is the movement of Mass per Time. Its unit is mass divided by Time, so Kilogram per Second in SI The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different The operating principle, introduced in 1977 by Micro Motion Inc. , involves inducing a vibration of the tube through which the fluid passes. The vibration, though it is not completely circular, provides the rotating reference frame which gives rise to the Coriolis effect. While specific methods vary according to the design of the flow meter, sensors monitor and analyze changes in frequency, phase shift, and amplitude of the vibrating flow tubes. The changes observed represent the mass flow rate and density of the fluid.

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. 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. A quantum mechanical system or particle that is bound, confined spacially can only take on certain discrete values of energy as opposed to classical particles which

Ballistics

The Coriolis effects became important in external ballistics for calculating the trajectories of very long-range artillery shells. External ballistics is the part of the science of Ballistics that deals with the behaviour of a non-powered projectile in flight Artillery (from French artillerie) is a military Combat Arm which employs any apparātus machine The most famous historical example was the Paris gun, used by the Germans during World War I to bombard Paris from a range of about 120 km (75 mi). The Paris Gun (Paris-Geschütz was the name of an Artillery piece with which the Germans bombarded Paris during World War I. World War I (abbreviated WWI; also known as the First World War, the Great War, and the War to End All Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city

Insect flight

Flies (Diptera) and moths (Lepidoptera) utilize the Coriolis effect when flying: their halteres, or antennae in the case of moths, oscillate rapidly and are used as vibrational gyroscopes. True flies are Insects of the Order Diptera ( Greek: di = two and pteron = wing possessing a single pair of Lepidoptera is an order of Insect that includes Moths and butterflies. This article concerns insect anatomy For halteres as used in ancient sports see Halteres (ancient Greece Halteres (hælˈtɪəriːz singular [14] See Coriolis effect in insect stability. In this context, the Coriolis effect has nothing to do with the rotation of the Earth.

See also

Notes and references

  1. ^ William Menke & Dallas Abbott (1990). In Fluid dynamics, a secondary flow is a relatively minor flow superimposed on the primary flow where the primary flow usually matches very closely the flow pattern predicted Ferrel's law, named after William Ferrel, is a natural law in Physical geography and Meteorology. The centripetal force is the external force required to make a body follow a curved path A reactive centrifugal force is the reaction Force to a Centripetal force. There are two types of Circular motion: uniform circular motion and Non-uniform circular motion. A gyroscope is a device for measuring or maintaining orientation, based on the principles of Angular momentum. The geostrophic wind is the Theoretical Wind that would result from an exact balance between the Coriolis force and the Pressure gradient force "Binormal" redirects here For the category-theoretic meaning of this word see Normal morphism. Statics is the branch of Mechanics concerned with the analysis of loads ( Force, torque/moment) on Physical systems in Static equilibrium Kinetics in physics In physics kinetics used to be the branch of Classical mechanics that was concerned with the relationship between the motion of bodies Applied mechanics is a branch of the Physical sciences and the practical application of Mechanics. Analytical mechanics is a term used for a refined highly mathematical form of Classical mechanics, constructed from the Eighteenth century onwards as a formulation In physics the term dynamics customarily refers to the time evolution of physical processes Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects Geophysical Theory. Columbia University Press, pp. 124-126. ISBN 0231067925.  
  2. ^ David Morin (2008). Introduction to classical mechanics: with problems and solutions. Cambridge University Press, p. 466. ISBN 0521876222.  
  3. ^ George E. Owen (2003). Fundamentals of Scientific Mathematics, original edition published by Harper & Row, New York, 1964, Courier Dover Publications, p. 23. ISBN 0486428087.  
  4. ^ Morton Tavel (2002). Contemporary Physics and the Limits of Knowledge. Rutgers University Press, p. 88. ISBN 0813530776.  
  5. ^ James R Ogden & M Fogiel (1995). High School Earth Science Tutor. Research & Education Assoc. , p. 167. ISBN 0878919759.  
  6. ^ James Greig McCully (2006). Beyond the moon: A Conversational, Common Sense Guide to Understanding the Tides. World Scientific, pp. 74-76. ISBN 9812566430.  
  7. ^ "X-Files coriolis error leaves viewers wondering" from Skeptical Inquirer
  8. ^ "Bad Coriolis" from Penn State College of Earth and Mineral Sciences
  9. ^ "Who Knew? The No-Spin Zone" from Berkeley Science Review (PDF)
  10. ^ "Flush Bosh" from snopes.com
  11. ^ Cloud Spirals and Outflow in Tropical Storm Katrina from Earth Observatory (NASA)
  12. ^ Stephen D. The Skeptical Inquirer is a bimonthly American Magazine published by the Committee for Skeptical Inquiry (CSI with the subtitle The College of Earth and Mineral Sciences is a constituent semi-autonomous part Penn State University, University Park, Pennsylvania. Snopes (ˈsnoʊps also known as the Urban Legends Reference Pages, is a Web site that is the most widely-known resource for validating or debunking Urban legends The NASA Earth Observatory is an online publishing organization of the National Aeronautics and Space Administration of the United States (US The National Aeronautics and Space Administration ( NASA, ˈnæsə is an agency of the United States government, responsible for the nation's public space program Butz (2002). Science of Earth Systems. Thomson Delmar Learning, p. 305. ISBN 0766833917.  
  13. ^ James R. Holton (2004). An Introduction to Dynamic Meteorology. Academic Press, p. 18. ISBN 0123540151.   <ref>{{cite book |title=Ballistics: Theory and Design of Guns and Ammunition |author=Donald E. Carlucci & Sidney S. Jacobson |page=pp. 224-226 |url=http://books. google. com/books?id=pX9Tzs7VuSoC&pg=PA224&dq=artillery+Coriolis+example&lr=&as_brr=0&sig=8oNcRBNDeBFxL3bYGDDe1YUBpUk#PPA225,M1 |isbn=1420066188 |publisher=CRC Press |year=2007}}</li> <li id="cite_note-13">'''[[#cite_ref-13|^]]''' "Antennae as Gyroscopes", Science, Vol. 315, 9 Feb 2007, p. 771 </li></ol></ref>

    Further reading: physics and meteorology

    Further reading: historical

    • 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.


    External links

© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
 Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic