User:William M. Connolley/Coriolis effect

'' In my view, the coriolis effect is primarily a change-of-coordinates-acceleration (in which it resembles gravity). Starting off by calling it the Coliolis force is thus wrong: it mistakes the cause for the effect. ''

The Coriolis effect is a change-of-coordinates acceleration, first described by Gaspard-Gustave Coriolis in 1835.

In changing from one coordinate system rotating relative to another (canonically, changing from an essentially inertial coordinate system (such as the "frame of the fixed stars") to a rotating frame of reference such as that of the Earth's surface), a term appears in the equation of motion described by the formula for Coriolis acceleration:


 * $$2\left(\mathbf{v} \times \mathbf{\omega}\right),$$

where bold indicates vector quantities, v is the velocity and &omega; is the angular velocity of the coordinate system. Note that this equation ignores the second-order term in &omega;, which in geophysical terms is small, and can in any case (when considering the equations of motion for a fluid on a planet) be absorbed into the gravitational potential term. The equation is transformed into an equation for force by multiplying by the mass of the object.



This equation means that the acceleration will be proportional to the velocity of the object and the rotation of the coordinate system, in a direction perpendicular to the velocity (and thus will do no work). If an object is travelling on earth in the northern hemisphere, the Coriolis force will deflect the object to the right. In the southern hemisphere the reverse is true, while at the equator the horizontal component of the force is zero for horizontal motions. For instance, the effect breaks up the atmospheric circulation from the tropics to the polar regions into a series of cells in which the surface winds have a prevailing eastward or westward component.

The Coriolis force plays a strong role in weather patterns, where it affects prevailing winds and the rotation of storms, as well as in the direction of ocean currents. Above the atmospheric boundary layer, friction plays a relatively minor role, as air parcels move mostly parallel to each other. Here, an approximate balance between pressure gradient force and Coriolis force exists, causing the geostrophic wind, which is the wind effected by these two forces only, to blow along isobars (along lines of constant geopotential height, to be precise). Thus a northern hemispheric low pressure system rotates in a counterclockwise direction, while northern hemispheric high pressure systems or cyclones on the southern hemisphere rotate in a clockwise manner, as described by Buys-Ballot's law.

The Coriolis effect must also be considered in astronomy, and stellar dynamics, where it affects phenomena such as the rotational direction of sunspots. The flight paths of airplanes, artillery shells, and missiles must account for the Coriolis effect or risk being off course by significant amounts. (See external ballistics.)

The Coriolis effect can also be observed in the motion of a simple pendulum - see Foucault pendulum for more details.

See Taylor-Proudman theorem for a startling consequence of the Coriolis effect: in a rotating reference frame, if the flow has low Rossby number but high Reynolds number, all steady solutions to the Navier-Stokes equations have the property that the fluid velocity is uniform along any line parallel to the rotation axis. In oceanic flow, it is possible to ignore the non-vertical components of the Earth's rotation, so if the conditions of the theorem apply ($$Re >\!\!> 1$$ is universal but using $$0.1{\rm m/s}$$ as a typical flow speed and using 4km as a depth, $$f=10^{-4}{\rm s}^{-1}$$ gives $$Ro\simeq 0.25$$ which is marginal), the fluid velocity is identical at all points along any single vertical line (known as a Taylor column). 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.

Although the Coriolis acceleration is relatively small and does not have an observable influence on small systems such as the whirlpool of a draining bathtub, toilet or sink, the Coriolis effect can have (in addition to its obvious atmospheric effects) a visible effect over large amounts of time and has been observed to cause uneven wear on railroad tracks and cause rivers to dig their beds deeper on one side.

A practical application of the Coriolis force is the mass flow meter, an instrument that measures the mass flow rate of a fluid through a tube. The instrument 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 works by applying a vibrating force to a curved tube through which the fluid passes. The Coriolis effect creates a force on the tube perpendicular to both the direction of vibration and the direction of flow. This force is measured to give the mass flow rate. Coriolis flow meters can also be used with non-Newtonian fluids, which tend to give inaccurate results with volume flow meters. The same instrument can be used to measure the density of the fluid, since this affects the resonant frequency of the vibrating tube. A further advantage of this instrument is that the fluid is contained in a smooth tube, with no moving parts that would need to be cleaned and maintained, and that would impede the flow EDN Access 2003-06-30

Effects due to the Coriolis force also appear in atomic 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 force is therefore 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.

Insects of the group Diptera use two small vibrating structures at the side of their bodies to detect the effects of the Coriolis force. These so called Halteres play an important role in these insects' ability to perform aerobatics.

Is the Coriolis force "fictitious"?
It is common to see the Coriolis force described as "making it look like a force is acting upon the object, but actually there is no real force acting on the object". This prompts the question, "what is a real force"? From the viewpoint of general relativity, all coordinate systems are equivalent in describing physical processes, but in changing from one system to another things that look like forces will arise. For example, at the surface of Earth it is possible to (locally) remove the gravitational force by changing to a coordinate system accelerating towards the centre of Earth. But no-one would call gravity "fictitious".