Download Fronts and the Coriolis Effect

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
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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-goround 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.
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∆ Lat
0 - 30 º
30 - 60 º
60 - 90 º
∆ω
250 km/hr
600 km/hr
850 km/hr
Rate of change
8.3 km/hr/deg
20.0 km/hr/deg
28.3 km/hr/deg
Coriolis Magnitude
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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