What Is Coriolis Force?

Coriolis force is also called Coriolis force in some places. It is called Coriolis force for short. A description. Coriolis force comes from the inertia of an object's movement.

Chinese name: Coriolis force

Foreign name: Coriolis force

Coriolis force profile

The Coriolis force of a linear motion of a particle in a rotating system is based on Newtonian mechanics. In 1835, the French meteorologist Coriolis proposed that in order to describe the motion of the rotating system, an imaginary force needs to be introduced into the equation of motion. This is the Coriolis force. After introducing the Coriolis force, one can handle the motion equations in the rotating system as easily as the motion equations in the inertial system, which greatly simplifies the processing of the rotation system. Because the earth on which humans live is a huge rotating system, Coriolis force quickly achieved successful applications in the field of fluid motion.

Coriolis force physics definition

In a rotating system, the mass points that move in a straight line have a tendency to continue to move along the original movement direction due to inertia. However, because the system itself is rotating, the position of the mass points in the system will change after a period of movement Changes, and the direction of its original movement trend, if observed from the perspective of the rotating system, a certain degree of deviation will occur.

As shown in the figure above, when a mass moves linearly relative to the inertial system, its trajectory is a curve relative to the rotating system. Based on the rotation system, we think that there is a force that drives the particle trajectory to form a curve.

Corioli This force is Coriolis.

According to the theory of Newtonian mechanics, taking the rotating system as the reference system, the tendency of this particle's linear motion to deviate from its original direction is attributed to an external force, which is the Coriolis force. From a physics perspective, Coriolis forces, like centrifugal forces, are not forces that actually exist in the inertial frame, but are manifestations of inertia in the non-inertial frame, and are also inertial forces introduced in the inertial reference frame For easy calculation.

Coriolis force is calculated as follows:

F = -2m × v '

Where F is the Coriolis force; m is the mass of the mass point; v ' is the speed of movement (vector) relative to the mass of the rotating reference frame; is the angular velocity of the rotation system (vector); × represents the outer product of two vectors Symbol ( × v ' : the size is equal to the size of times the size of v and then the sine of the angle between the two vectors, and the direction meets the right-hand spiral rule).

Coriolis force mathematical derivation

Coriolis force does not actually exist, it is caused by the difference between the uniform linear motion that the person considers in the rotating system and the uniform linear motion in the inertial system. For a person in a rotating system, a uniform linear motion refers to a motion in which the speed of an object relative to the turntable does not change. For people in the inertial system, constant-speed linear motion refers to motion that does not change relative to ground speed. Therefore, the Coriolis force can be calculated by calculating the displacements in the extremely short time dt according to the standard of uniform linear motion of the two reference frames, and then analyzing the difference between the two displacements in the rotating frame.

As the encyclopedia here does not support the formula well, the detailed derivation process and graphic explanations can be found in reference ^[1] .

Coriolis influence

Coriolis Forces in Earth Science

Graphically turning deflection forces

Due to the existence of rotation, the earth is not an inertial frame, but a rotating frame of reference, so the motion of particles on the ground will be affected by Coriolis forces. The geostrophic bias force in the field of earth sciences is a component of the Coriolis force along the surface of the earth. Geostrophic bias helps to explain some geographic phenomena, such as one side of a river channel tends to scour more strongly than the other (geospheric bias).

Coriolis Foucault

Foucault Swing can be considered as a reciprocating rectilinear motion. Swing on the earth will be affected by the rotation of the earth. As long as there is a certain angle between the direction of the swing surface and the angular velocity direction of the earth's rotation, the swing surface will be affected by the Coriolis force, and a torque opposite to the direction of the earth's rotation will be generated, so that the swing surface will rotate. In 1851, French physicist Foucault predicted the existence of this phenomenon and proved it experimentally. He used a 67-meter-long wire rope and a 27-kg metal ball to form a single pendulum. A pointer was inlaid, and this huge single pendulum was suspended from the church dome. Experiments have confirmed that the pendulum surface will slowly rotate to the right in the northern hemisphere (the Foucault pendulum rotates with the earth). Since Foucault first proposed and completed this experiment, the experiment was named Foucault Pendulum Experiment.

Coriolis force trade wind and monsoon

Trade wind The area of the earth's surface at different latitudes receives different amounts of sunlight, which affects the flow of the atmosphere. A series of atmospheric pressure zones have been formed in the direction of latitude extension of the earth's surface, such as the so-called "polar high pressure zone", "subpolar low pressure zone", and Subtropical high pressure zone. " Driven by the pressure difference of these air pressure bands, the air will move along the longitude direction, and this movement along the longitude direction can be regarded as the linear motion of the particle in the rotating system, which will be deflected by the influence of Coriolis force . It is not difficult to see from the calculation formula of Coriolis force that the atmospheric flow in the northern hemisphere will deflect to the right, and the atmospheric flow in the southern hemisphere will deflect to the left. Under the combined action of Coriolis force, atmospheric pressure difference and surface friction, it was originally The north-south atmospheric flow becomes the northeast-southwest or southeast-northwest flow.

With the change of seasons, the north-south drift of the pressure bands on the earth's surface along the latitude direction will cause seasonal changes in the wind direction in some places, the so-called monsoon. Of course, this must also involve the difference in air pressure caused by the difference in specific heat between land and sea.

The Coriolis force causes the direction of the monsoon to shift to a certain extent, resulting in east-west movement factors. In the past, human navigation relying on wind power largely concentrated in the direction of latitude. The existence of the monsoon created human navigation. Great convenience, so it is also called trade wind.

Coriolis force tropical cyclone

tropical wind The formation of tropical cyclones (called typhoons in the North Pacific) was influenced by Coriolis forces. The driving force behind the tropical cyclone is the pressure difference between a low pressure center and the surrounding atmosphere. The air in the surrounding atmosphere is driven to the low pressure center by the pressure difference. This movement is deflected by the Coriolis force. This results in a rotating airflow. This rotation is counterclockwise in the northern hemisphere and clockwise in the southern hemisphere. Due to the effect of rotation, the low-pressure center is maintained for a long time.

Regarding the launching direction of sinks and the like: The launching direction of the toilet, for example, is indeed affected by the Coriolis force, but this effect is insignificant. The direction in which the toilet is launched depends more on the shape of the toilet sink. The same goes for other types of sinks.

5 Effect on the molecular spectrum Coriolis force has an effect on the vibrational spectrum of molecules. The vibration of a molecule can be regarded as a linear motion of a particle. The overall rotation of the molecule will affect the vibration, so that the original independent vibration and rotation are coupled. In addition, due to the existence of Coriolis force, the original vibration is independent of each other. Energy communication also occurs between modes, and this energy communication will affect the infrared and Raman spectral behavior of the molecule.

Coriolis force application

People use Coriolis force principle to design some instruments for measurement and motion control.

Coriolis force flowmeter

Gas mass flowmeter The mass flow meter allows the measured fluid to pass through a rotating or vibrating measuring tube. The flow of fluid in the pipe is equivalent to linear motion. The rotation or vibration of the measuring tube will generate an angular velocity. The rotation or vibration is driven by an external electromagnetic field. , Has a fixed frequency, so the Coriolis force on the fluid in the pipeline is only related to its mass and velocity, and the product of mass and velocity, that is, the velocity, is the mass flow that needs to be measured. Coriolis force can measure its mass flow.

The same principle applies to powder dosing scales, where powder can be regarded as a fluid treatment.

Coriolis Gyro

The rotating gyroscope will reflect various forms of linear motion, and the movement can be measured and controlled by recording the Coriolis force on the gyroscope parts.

Gyroscope experiment * §2.7 Coriolis acceleration

Coriolis force acceleration

The two reference systems can rotate with each other. For example, the test tube reference system and the desktop reference system are relatively rotated when the high-speed centrifuge is started. The particles in the test tube move linearly along the test tube, but they move spirally relative to the table. Transformations between rotating coordinate systems are also required.

Consider the disk S rotating relative to the desktop S. As shown in Figure 2-17. Let the rotational angular velocity be a constant vector, pointing to the positive direction of the z-axis perpendicular to the disk surface, the rotation axis is located at the center O of the disk, and the desktop origin O Coincidence with it. Suppose the vector A is fixed on S . Note that the speed expression (2.2.10) is

Coriolis The increment of A in dt is

dA = A t + dt A t = × A dt

If the vector also has an increment dA relative to S , the increment relative to S will be

dA = ( × A) dt + dA Then we have the general relationship:

Or write the symbolic equation:

Obviously, the speed vector can be obtained by substituting the position vector into the above equation:

The derivation of the apostrophe in the formula only indicates that it is performed in the S system, and it does not indicate that there is no difference in time. This also applies to other vectors. For example, any vector can be replaced by two vectors from the origin. The above approach can be generalized to the three-dimensional situation. The symbolic equation (2.7.2) is linear (meeting the distribution law). For the velocity vector, we have

It can be seen from the observer of the S system that the acceleration is composed of 3 parts. The first term is in the S system.

Acceleration. When the mass is stationary in the S system, the significance of the third term can be clearly seen:

× × r =- · (2.7.5)

That is, centripetal acceleration. The second term is called Coriolis acceleration. This term has a non-zero value only when the mass moves in the S system. * (2.7.4) and plane pole Are the acceleration expressions (§1.5) in the coordinates consistent? If the angular velocity is not a constant vector, are (2.7.3) and (2.7.4) correct? If it is not correct, how should it be modified?

Below we discuss the effect of the rotation of the earth. The rotating earth is taken as the S system, and a non-rotating earth (translation frame) is the S system. In the earth reference frame, the gravity acceleration of the particle is

g = g0-2 × v- × ( × r) (2.7.6)

we know

g09.8m / s2

= 7.292 × 10-5rad / s

In contrast, the centrifugal term is much smaller,

| × × r | 2R3.39 × 10-2m / s2 << g0

Incorporating it into the effective gravitational acceleration, (2.7.6) can be written as

mg = mgeff- 2m × v (2.7.7)

The last term is the "force" of Coriolis on a moving object. It should be noted that this term is completely transformed from the coordinate system, or it is due to the observer's view and level in the rotating coordinate system. The difference in the moving coordinate system is generated. Generally we can say that Coriolis 'force' is a kinematic effect. * Is Coriolis force related to latitude? Is there a difference between the northern and southern hemispheres?

According to the formula (2.7.7), we can judge the deviation of the falling body. Roughly speaking, the falling speed (zero-order approximation) is in the -r direction. For the northern hemisphere, it can be determined that the speed will be toward the east, which is -2m × v k × er = ej direction. The so-called falling east is what this means. If we consider from (2.7.6), what will happen?

* Discussion: Will the thrown object fall at the throw point?

The motion of the surface is also affected by Coriolis forces. From Figure 2-18, we can see that rotation causes the motion to deviate to the right hand direction. We can decompose the velocity to obtain a quantitative result:

-2 × (ve + vjej) = 2 (ve × k + vjej × k)

= 2 vcosej + vje

= 2cos (vej + vje)

+ 2vjsiner

The radial term in the equation can be ignored due to the existence of the g term. The first two terms accurately show that the acceleration points to the right-hand side of the direction of motion.

Coriolis force demo illustration A typical example of Coriolis force is a cyclone in the atmosphere. In a weather forecast program, you may have seen a counterclockwise cyclone in a satellite cloud. This cyclone is clockwise in the southern hemisphere. Foucault (1819-1868) pendulum is an excellent example of the rotation of the earth. In 1850, Foucault used a pendulum with a length of 67m at the Pantheon in Paris. The deflection of the pendulum plane clearly tells people that the earth is at Rotating.

Coriolis force is also expressed in microscopic phenomena. For example, it complicates the vibration of rotating molecules, and makes the molecular rotation and vibrational energy spectrum interact with each other.