Coriolis effect Totally Explained

Everything about The Coriolis Effect totally explained

The Coriolis effect is an apparent deflection of moving objects when they're viewed from a rotating frame of reference. 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. 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 doesn't 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. In a rotating frame, the Coriolis force, which depends on the velocity of the moving object, and centrifugal force, which doesn't depend on the velocity of the moving object, are needed in the equation to correctly describe the motion.
Perhaps the most commonly encountered rotating reference frame is the Earth. 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. 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'd 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).

Formula

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

vec a_C = -2 , vec omega 	imes vec v

where (here and below)

vec v

is the velocity of the particle in the rotating system, and

vec omega

is the angular velocity vector which has magnitude equal to the rotation rate and is directed along the axis of rotation of the rotating reference frame, and the

imes

symbol represents the cross product operator.
The equation may be multiplied by the mass of the relevant object to produce the Coriolis force:
ť

vec F_C = -2 , m , vec omega 	imes vec v

.

See fictitious force for a derivation.

Examples

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:

if the velocity is parallel to the rotation axis, the Coriolis acceleration is zero
if the velocity is straight 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 velocity is against the direction of local rotation, the acceleration is inward to the axis

For example, consider a location with latitude

varphi

on a sphere that's rotating around the north-south axis. 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 are:
ť

vec omega = omega egin

.

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 doesn't 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.)
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. Such features are in geostrophic balance, meaning that the Coriolis and pressure gradient forces balance each other. Coriolis acceleration is also responsible for the propagation of many types of waves in the ocean and atmosphere, including Rossby waves and Kelvin waves. 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.

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. 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's 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. 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 isn't 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.

Ballistics

The Coriolis effects became important in external ballistics for calculating the trajectories of very long-range artillery shells. 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).

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. See Coriolis effect in insect stability

. In this context, the Coriolis effect has nothing to do with the rotation of the Earth.

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