科里奥利效应.docx

1、科里奥利效应Coriolis effectFigure 1: In the inertial frame of reference (upper part of the picture), the black object moves in a straight line, without significant friction with the disc. However, the observer (red dot) who is standing in the rotating (non-inertial) frame of reference (lower part of the p

2、icture) sees the object as following a curved path due to the Coriolis and centrifugal forces present in this frame.In physics, the Coriolis effect is a deflection of moving objects when they are viewed in a rotating reference frame. In a reference frame with clockwise rotation, the deflection is to

3、 the left of the motion of the object; in one with counter-clockwise rotation, the deflection is to the right. The mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave Coriolis, in connection with the theory of water wheels, and also in the tid

4、al equations of Pierre-Simon Laplace in 1778. And even earlier, Italian scientists Giovanni Battista Riccioli and his assistant Francesco Maria Grimaldi described the effect in connection with artillery in the 1651 Almagestum Novum, writing that rotation of the Earth should cause a cannon ball fired

5、 to the north to deflect to the east.1 Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.Newtons laws of motion govern the motion of an object in a (non-accelerating) inertial frame of reference. When Newtons laws are transformed to a uniformly rotati

6、ng frame of reference, the Coriolis and centrifugal forces appear. Both forces are proportional to the mass of the object. The Coriolis force is proportional to the rotation rate and the centrifugal force is proportional to its square. The Coriolis force acts in a direction perpendicular to the rota

7、tion axis and to the velocity of the body in the rotating frame and is proportional to the objects speed in the rotating frame. The centrifugal force acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame. These additional forces are

8、 termed either inertial forces, fictitious forces or pseudo forces.2 They allow the application of Newtons laws to a rotating system. They are correction factors that do not exist in a non-accelerating or inertial reference frame.Perhaps the most commonly encountered rotating reference frame is the

9、Earth. The Coriolis effect is caused by the rotation of the Earth and the inertia of the mass experiencing the effect. Because the Earth completes only one rotation per day, the Coriolis force is quite small, and its effects generally become noticeable only for motions occurring over large distances

10、 and long periods of time, such as large-scale movement of air in the atmosphere or water in the ocean. Such motions are constrained by the 2-dimensional surface of the earth, so only the horizontal component of the Coriolis force is generally important. This force causes moving objects on the surfa

11、ce of the Earth to veer to the right (with respect to the direction of travel) in the northern hemisphere, and to the left in the southern. 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 o

12、f this direction north of the equator, and to the left of this direction south of it. This effect is responsible for the rotation of large cyclones (see Coriolis effects in meteorology).Gaspard-Gustave Coriolis published a paper in 1835 on the energy yield of machines with rotating parts, such as wa

13、terwheels.3 That paper considered the supplementary forces that are detected in a rotating frame of reference. Coriolis divided these supplementary forces into two categories. The second category contained a force that arises from the cross product of the angular velocity of a coordinate system and

14、the projection of a particles velocity into a plane perpendicular to the systems axis of rotation. Coriolis referred to this force as the compound centrifugal force due to its analogies with the centrifugal force already considered in category one.45 By the early 20th century the effect was known as

15、 the acceleration of Coriolis.6 By 1919 it was referred to as Coriolis force7 and by 1920 as Coriolis force.8In 1856, William Ferrel proposed the existence of a circulation cell in the mid-latitudes with air being deflected by the Coriolis force to create the prevailing westerly winds.9Understanding

16、 the kinematics of how exactly the rotation of the Earth affects airflow was partial at first.10 Late in the 19th century, the full extent of the large scale interaction of pressure gradient force and deflecting force that in the end causes air masses to move along isobars was understood.citation ne

17、ededIn 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.The vector formula f

18、or the magnitude and direction of the Coriolis acceleration iswhere (here and below) is the acceleration of the particle in the rotating system, is the velocity of the particle in the rotating system, and is the angular velocity vector which has magnitude equal to the rotation rate and is directed a

19、long the axis of rotation of the rotating reference frame, and the symbol represents the cross product operator.The equation may be multiplied by the mass of the relevant object to produce the Coriolis force:.See fictitious force for a derivation.The Coriolis effect is the behavior added by the Cori

20、olis acceleration. The formula implies that the Coriolis acceleration is perpendicular both to the direction of the velocity of the moving mass and to the frames rotation axis. So in particular: if the velocity is parallel to the rotation axis, the Coriolis acceleration is zero. if the velocity is s

21、traight inward to the axis, the acceleration is in the direction of local rotation. if the velocity is straight outward from the axis, the acceleration is against the direction of local rotation. if the velocity is in the direction of local rotation, the acceleration is outward from the axis. if the

22、 velocity is against the direction of local rotation, the acceleration is inward to the axis.The vector cross product can be evaluated as the determinant of a matrix:where the vectors i, j, k are unit vectors in the x, y and z directions.CausesThe Coriolis effect exists only when one uses a rotating

23、 reference frame. In the rotating frame it behaves exactly like a real force (that is to say, it causes acceleration and has real effects). However, Coriolis force is a consequence of inertia, and is not attributable to an identifiable originating body, as is the case for electromagnetic or nuclear

24、forces, for example. From an analytical viewpoint, to use Newtons second law in a rotating system, Coriolis force is mathematically necessary, but it disappears in a non-accelerating, inertial frame of reference. For example, consider two children on opposite sides of a spinning roundabout (carousel

25、), who are throwing a ball to each other (see Figure 1). From the childrens point of view, this balls path is curved sideways by the Coriolis effect. Suppose the roundabout spins counter-clockwise when viewed from above. From the throwers perspective, the deflection is to the right.11 From the non-t

26、hrowers perspective, deflection is to left. For a mathematical formulation see Mathematical derivation of fictitious forces.An observer in a rotating frame, such as an astronaut in a rotating space station, very probably will find the interpretation of everyday life in terms of the Coriolis force ac

27、cords more simply with intuition and experience than a cerebral reinterpretation of events from an inertial standpoint. For example, nausea due to an experienced push may be more instinctively explained by Coriolis force than by the law of inertia.1213 See also Coriolis effect (perception). In meteo

28、rology, a rotating frame (the Earth) with its Coriolis force proves a more natural framework for explanation of air movements than a non-rotating, inertial frame without Coriolis forces.14 In long-range gunnery, sight corrections for the Earths rotation are based upon Coriolis force.15 These example

29、s are described in more detail below.The acceleration entering the Coriolis force arises from two sources of change in velocity that result from rotation: the first 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 physi

30、cs 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 change direction), and to the component of velocity of the object in a p

31、lane perpendicular to the axis of rotation. This gives a term . The minus sign arises from the traditional definition of the cross product (right hand rule), and from the sign convention for angular velocity vectors.The second is the change of velocity in space. Different positions in a rotating fra

32、me 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 to the component of the velocity of the object in a plane perpendicular to the axis of rotation (which determines how qui