Fronts and Coriolis

Fronts

• Fronts - boundaries between air masses of different temperature. – If warm air is moving toward cold air, it is a “warm

front”. On weather maps a red line with scallops on it.

– If cold air is moving toward warm air, then it is a “cold front”. Shown as a blue line with arrow points on it.

– If neither air mass is moving very much, it is called a “stationary front”, shown as an alternating red and blue line.

• Usually, a cold front will be associated with a warm front, with a low pressure center, connecting them. – This frontal "system" can be thought of as

separating a cold air mass from a warm air mass,

• The two different types of fronts simply indicate which direction those portions of the different air masses are moving.

• Fronts

The Effect of Rotation

• The earth is not stationary

• The observation of a particle in motion are judged relative to coordinates of latitude and longitude that rotate with the earth

• So a moving particle is referenced to a moving grid

• This creates apparent forces that seem to deflect the motion of these particles.

Coriolis

• The rotation of the earth coupled with negligible friction between the atmosphere and the earth results in an apparent deflection in the path of moving parcels of air when they are viewed from the surface of the globe.

Coriolis

• This is merely an artifact of our point of view

• On earth our reference frame is the globe, which is rotating, and things over the earth would move relative to the rotation.

• If we were far out in space, our reference frame would be the stars and the path of moving objects would not appear to deflect.

Coriolis

• Movie

• Movie

• Illustration 1

• Illustration 2

Earth’s Rotation

• Points on the surface of the earth rotate eastward at a speed that depends on latitude.

Coriolis Effect

• An air mass that appears stationary at one latitude will be moving eastward with the rotating earth at a velocity equal to the rotational velocity of the earth’s surface at that latitude.

Coriolis Effect

• If the air mass then moves closer to the equator, it will move over points on the surface that have a higher eastward velocity than it does.

• Consequently, to an observer on the surface, the air mass will appear to lag behind the eastward rotation of the planet, or it will appear to be moving westward.

Coriolis Effect

• If the air mass moves farther away from the equator, it will travel over points on the surface that have a slower eastward velocity than it does.

• Consequently, to an observer on the earth’s surface, the air mass will appear to speed ahead of the planet, or it will appear to be deflected to the east (see fig. 7.10)

Coriolis Effect

• The centripetal force is needed to keep an object in orbit– This is the tension of a string holding a ball that

is twirled around your head

• What happens to the object when you let go of the string?

Coriolis Effect

• When a ball is thrown off a merry-go-round, it flies off in a straight line

• The velocity (speed and direction) of the ball is due to the rotation of the merry-go-round plus the throw– We can decompose the velocity into the two

components

Coriolis Effect

• Velocity of an orbiting object can be expressed as – the angular velocity

• The angle moved through per unit time

– the orbital velocity• Distance traveled along orbital path

Coriolis Effect

• Orbital velocity increases with distance from center of rotation

• Angular velocity is constant, say for a merry-go-round or the world, regardless of distance from the center of rotation

Coriolis Effect

• Angular velocity, orbital velocity and centripetal force are related– For an objects at some distance from the center

of rotation, if the angular velocity (rate of rotation) is increased, the orbital velocity is also increased, and a larger centripetal force is needed to keep the object in orbit

• The tension on the string needs to increase

Coriolis Effect

• Gravity and centripetal force differ in that gravity is directed toward the center of the earth

• Centripetal force is directed toward the center of rotation

• Therefore gravity and centripetal force act in the same direction only at the equator– The difference in direction increases with

latitude

Coriolis Effect

• Centripetal force can be resolved into two components– One parallel to the earths surface and directed

N-S– The other directed toward the center of the

earth

Coriolis Effect

• Compared to gravity– Centripetal force required to keep an object on

the surface of the earth is very small– Centripetal force required to balance changes in

speed relative to the earth’s surface is very small

• Therefore any changes are easily compensated by gravity and pressure changes

Coriolis Effect

• On a spherical earth, centripetal forces parallel to the earth’s surface would not be compensated by gravity– Gravity would be perpendicular to the surface

everywhere

Coriolis Effect

• The earth was molten at one time allowing the redistribution of mass into an oblate spheroid.

• Thus, gravity does not act exactly perpendicular to the surface (except at poles and equator).– The small component of gravity parallel to the

surface balances the centripetal force

Coriolis Effect

• East-West motions cause orbital changes due to imbalance between the gravitational forces parallel to the surface of the earth and the centripetal forces parallel to the surface of the earth

Coriolis Effect

• An air mass that moves eastward will be rotating in the direction of the earth’s rotation at a faster rate of speed than the earth is. – The orbital velocity will be greater, but the centripetal

force provided by the gravitational component parallel to the surface is too small to maintain this orbit

• This will cause it to be subjected to a greater centrifugal, or outward, force and hence it will move towards the equator and further away from the axis of rotation (see fig. 7.11).

Coriolis Effect

• An air mass that moves westward will be rotating in the direction of the earth’s rotation at a slower rate of speed than the earth is.– The orbital velocity will be less, the centripetal force

provided by the gravitational component parallel to the surface is too large to maintain this orbit

• This will cause it to be subjected to a smaller centrifugal force and hence it will move away from the equator and closer to the axis of rotation (see fig. 7.11).

Coriolis Summary

• The movements can be summarized by saying that objects in frictionless motion will appear to be deflected to the right of their direction of movement in the Northern Hemisphere and to the left in the Southern Hemisphere.

• Go over these concepts and convince yourself.

Coriolis Magnitude

• The magnitude of the Coriolis effect increases with increasing latitude because the rate of change in the rotation of the earth increases with increasing latitude as well.

• f = 2 sin • Where f = magnitude, = angular velocity,

and = latitude

Coriolis Magnitude

• f = 2 sin • The Coriolis effect reaches a maximum at

the poles and

• Decreases to zero at the equator when the direction of the apparent deflection reverses itself from one hemisphere to the other.

Coriolis Magnitude

• This is easily seen in the following table:

• Change per band of latitude of the rotational velocity per degree of latitude.– ∆ Lat ∆ ω Rate of change– 0 ‑ 30 º 250 km/hr 8.3 km/hr/deg– 30 ‑ 60 º 600 km/hr 20.0 km/hr/deg– 60 ‑ 90 º 850 km/hr 28.3 km/hr/deg

Coriolis Magnitude

• Assume a current at 1 m s-1 (about 2 knots)

• At 90° latitude f = 1.5 x 10-4 m s-2

• At 45° latitude f = 1.0 x 10-4 m s-2

• At 0° latitude f = 0 m s-2

• Starting at rest, it would take 40 hours at these accelerations to reach 30 mph.

Coriolis

• Effect on wind direction

• Inertial Circle flat

• Inertial circle flat disk with friction

Inertial Circles