Earth, Wind and Forces

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Air Pressure

Air pressure is equal to the weight of the column of air above that location, be it at the ground or at a level off the ground. Pressure is force / area, and average air pressure at sea level (the bottom of the atmosphere) is 1.033 kg / square centimeter; 10,332 kg / square meter; or 14.7 lb / square inch. 


Another way to think about it: put a bowling ball on every square inch of a surface exposed to air. The palm of a hand is on the order of 10 square inches, so there are at least 147 lbs of air (10 bowling balls!) pushing against its surface. 


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Pressure Gradient Force

What gets air moving?  It’s an unbalanced force resulting from uneven heating of the Earth’s surface by the Sun (see the Sun-Earth Connection) that creates a pressure gradient (change pressure over distance). 


Air in the tropics is warmed by conduction at the surface and rises, and polar air is cooled by conduction and sinks. This sets in motion three circulation cells (convection cells) between the tropics and each of the poles (see image on the right).  The polar downwelling air is on both ends the diagram and the rising tropical air is in the middle of the diagram. 


Why is there an odd number of circulation cells in each hemisphere? Why couldn’t there be two? If there were two circulation cells between the warm tropics and cold poles, the sinking air from the equator ward cell would run into the rising air from the polar cell, which would shut off the circulations. With this pattern in global temperature gradient (cold at the poles and hot in the tropics), there must always be an odd number of cells in each hemisphere. However, as we will see using the Earth, Wind, and Forces software, the seasonal heating patterns cause the lengths and heights of each the circulation cells to change during the year.


How do we go from temperature gradient to pressure gradient? Air continues to rise as long as it is less dense than its surroundings.  About 20 km off the ground in the tropics the air begins to warm. This is the beginning of the stratosphere, also referred to as the ozone layer (it turns out the Sun's ultraviolet light combines with oxygen in Earth's atmosphere to create this warmed layer that is well off the ground). The warm air in the stratosphere is less dense than the rising tropical air so the air stops rising and it spreads toward the poles.  Since the effect of friction with the ground decreases with height, air moving near the stratosphere has essentially zero friction, so there is no resistance to flow. Air spreads out faster at the top of the rising column of air than it can converge at the bottom of the column of air, so there is less air in the column of air, which decreases air pressure at the ground, reinforcing the pressure gradient that moves air converging at the equator.  


At the poles, the sinking air near the ground is slowed by friction. Air is added to the top of the column of air faster than leaves at the bottom, and a high pressure forms. A pressure gradient has formed between the tropics and the poles, keeping these large circulation cells moving throughout the year.

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Friction

Friction is the force resisting the motion of objects, be it solid objects sliding past each other or moving fluid layers. There are a number of types of friction, but the one we will be dealing with for the fluids moving on Earth is fluid friction which describes the molecular interaction between layers of a viscous gas or liquid that are moving relative to each other.


Since friction opposes the motion of objects, it acts in the direction opposite to the motion and is proportional to the speed of the moving fluid. When the fluid isn’t moving, there isn’t any friction acting on it.

Coriolis Force

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Earth's Rotation

Earth is a rotating sphere, and how fast an object on its surface depends on its distance from the axis of rotation. Since the axis of rotation intersects the Earth’s surface at the poles, when standing on the North Pole, you aren’t moving due to Earth’s rotation. The fastest one can move on Earth is when furthest from the axis - so at the equator. If you have played on a merry-go-round, it was quite easy to be in the center and quite a challenge to hold on at the edge!


Speed is the distance travelled divided by the time of travel. The circumference of a circle is 2 π radius. The Earth’s radius is 6371 km, which means someone standing on the equator is moving at 40,0030 km / 24 hours = 1668 km/hr = 1036 mph. And we don’t even notice! (‘How fast am I going?’ activity)

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Angular Momentum

When an object changes latitude, it changes distance to the axis of rotation, and this is where we need to explore angular momentum. Momentum, which is equal to an object’s mass times its velocity, is a quantity that measures how difficult it will be to stop a moving object. Imagine trying to stop a shopping cart pushed at you from across an aisle, and that of a two ton truck moving at the same speed. It is much easier to stop the cart compared to the truck. But if the cart were moving at highway speeds, this would be much harder to stop than at lower speeds.  


Rotating objects also have a version of momentum, but it is called angular momentum, and it indicates how difficult it will be to stop the object from rotating. Angular momentum is the calculated by multiplying the momentum by the radius of rotation, so mass x velocity x radius. In this case the velocity is the tangential velocity or the speed at any point during the rotation.


Momentum and angular momentum have an important property: they remain constant unless acted upon by an unbalanced force. For rotating objects, this is called the conservation of angular momentum. When an ice skater goes into a spin and they pull in their arms and legs inward, they spin faster. They slow down when they move their limbs away from the axis of rotation. In all cases, the skater’s angular momentum is constant. As the radius of the skater decreases, they spin faster, and as their radius increases, they rotate slower.


For additional reading and video, see this website.

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The End Result: Coriolis Force

Since Earth is rotating, water and gas on or above it surface have angular momentum. When a fluid moves from one latitude to another on Earth, it changes the distance to the axis of rotation, so the rate of rotation changes to maintain constant angular momentum. We’ll focus on air, but the following applies to any fluid moving along the Earth’s surface or objects traveling through the atmosphere.  Explore movies of water in a rotating water tank to explore how fluids move on any planet.


If the air is pushed toward the poles by a pressure gradient force (PGF), it gets closer to the axis of rotation, and as with the skater, the air moves faster in its west-to-east motion, moving to the east of the air it is moving into. And when air moves toward the equator, it slows its west-to-east motion and moves to the west of the air it is moving into. When looking along the initial path of the northward or southward push, in the Northern Hemisphere, the air moves to the right. In the Southern Hemisphere, the air moves to the left of the initial push.


But what about air that moves initially to the west or east? It is staying at the same latitude, so it isn’t changing its distance to the axis of rotation. In the case of moving eastward, the air will be moving faster than it needs to stay at the Earth’s surface, it moves perpendicularly away from the axis of rotation (see spinning marshmallow activity). Gravity pulls the air back to the ground, but this is toward the center of the Earth, so the air moves toward the equator. The air moves to the right of the eastward push in the northern hemisphere and to the left of the push in the southern hemisphere.


When air moves westward, it is moving slower than air that would stay at the same distance from the axis of rotation, so it would move perpendicularly toward the axis. But the ground gets in the way, and the slope of the surface would push it toward the poles (remember the air is not sinking toward the Earth’s center but perpendicular to the axis of rotation). And, as with the other cases, air is moves to the right of the westward push in the northern hemisphere and to the left in the southern.


Notice that the only time the eastward or westward pushed air won’t bend is at the equator since the gravitational pull toward the center of the Earth and the perpendicular direction to the axis of rotation are parallel. This gives an indication that there isn’t a Coriolis Force acting on air moving along the equator, so there must be a relationship between latitude and the magnitude of Coriolis Force. Using the ‘How Fast Am I Going’ calculations, Coriolis Force is proportional to sin(latitude), so it is at a maximum at the poles (sin 90º = 1) and zero at the equator (sin 0º = 0).


Coriolis Force is always perpendicular to the wind and is proportional to the wind’s speed (there isn’t any Coriolis Force acting on air that isn’t moving).


For more, see this supporting article on Coriolis Force.

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Centrifugal Force: When the Wind Changes Direction

Centrifugal force is an apparent force that results from an object to resist a change in direction.  If we spin a marshmallow tied to a string, we feel a "force" pulling the ball outward. It isn't an actual force, rather, you feel the effect of creating the inward-pointing centripetal force.


The centrifugal force acts in the direction outward from the radius of curvature.


The magnitude of the centrifugal force is proportional to  the wind speed (increases as wind speed increases) and inversely proportional to the radius of curvature (increases as the radius of curvature decreases).

Earth, Wind, and Forces Software

Vectors

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Graphically and mathematically explore quantities that have both magnitude and direction.

Color Vectors

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Navigate the world of color using vectors.

Adding Vectors

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Explore the two most common ways to add vectors: graphically and mathematically.

Forces

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Analyze sets of interacting forces to see if they are balanced or not.

Wind

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Change pressure gradient, Coriolis, friction, and centrifugal forces to see how wind changes when pushed by straight isobars or those around high and low pressure centers.

Global Wind

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Explore global wind patterns throughout the year - and at different times during Earth's history.


Download the software here.

In Nature, Present is Not Always the Key to the Past

Earth Through Time

The Earth is 4.5 billion years old, and there have been some amazing changes of the planet over this time.  To start with, our solar system formed from the coalescing of a gas and dust cloud (see a movie for excellent visualizations of this process).  The transformation of the kinetic energy of these coalescing solid particles melted the material on impact, so when the Earth formed, it was completely molten.  But Earth wasn't the only planet to form - there were up to 20 initial planets in our newborn solar system, but these collided over time.  One collision of a protoplanet with Earth created our moon, and this has been helped stabilize Earth's rotation, in particular, its obliquity (see the Sun-Earth and Star-Planet Connections).  


When the moon formed, Earth made a revolution every 6-8 hours, which would have significantly changed how the winds moved in our atmosphere since Coriolis force depends on how fast Earth rotates.  But the moon's gravity creates tides on Earth, which create friction that slowly slows Earth's rotation.  Today, Earth takes 24 hours to complete a revolution (actually it is 23 hours 56 minutes 4.1 seconds), so today's winds behave differently than in the past, and with continued slowing, they will continue to change.  Use the Earth, Wind, and Forces software to explore possible global wind patterns throughout Earth's history.  Note: This is only one variable that affect wind, but it has a very significant impact. 

Northern Hemisphere winds for today's Earth (left) and when the moon formed (right).

Northern Hemisphere winds for today's Earth (left) and when the moon formed (right).