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Chapter 6 Atmospheric Forces
We constantly attempt to control the motion of objects around us. We push chairs, open doors, lift books, and throw balls. These actions require the application of a force. Applying a force to an object often moves the object. Wind is air in motion that arises from a combination of forces. Violent, destructive winds result from a complex interplay of different forces, just as gentle summer breezes.
Weather involves the wind, or the lack of wind, and thus forces. Complex interactions link winds, temperature, pressure, moisture, clouds, and precipitation to one another. These connections result in forces and provide the energy to drive various atmospheric circulations. The purpose of this chapter is to explain the forces of nature responsible for the winds and to illustrate how to use weather maps to interpret wind direction and speed. This chapter is an introduction to atmospheric dynamics.
In introducing atmospheric dynamics we will make use of simple diagrams, or models. While simple, and sometimes unrealistic, these models provide a conceptual view of how the atmosphere works. We will use these models to explain observations of the ‘real world.’ We will also begin to explore the coupling between circulations of the upper troposphere and the surface wind. The different spatial scales of weather systems are also defined in this chapter. Detailed discussions and examples of these scales of motion are the topics of following Chapters.
Magnitude and Direction of Forces
Weather results from the interaction of many forces. When discussing these interactions we are concerned with the direction and magnitude, or strength, of the force exerted on an object. These two factors, represented in diagrams by arrows, determine what effect the force has on the object. The arrow points in the same direction as the force. The length of the shaft represents the magnitude.
Two or more forces can act to pull or push at the same point on a body. A single force, the net force or resultant, which reproduces the same effect on the body as the separate forces, can replace these forces. Suppose we apply two forces to a body that will only act to move the object. If the two forces act in the opposite direction and with different magnitudes, the object will move in the direction of the stronger force (as in a tug-of-war). A single force can represent these two forces whose direction is the same as the stronger force and whose magnitude is the difference between the two forces (Figure 6.1).
Force exerted on an object equals the body’s mass times the acceleration that is produced. Force has a direction and a magnitude.
Forces often act at an angle to each other. In this situation we need an approach to determine the magnitude and direction of the net force. One way is to graphically construct a parallelogram (Figure 6.2) using two forces to represent two of the sides. The diagonal of the parallelogram represents the net force of the two given forces. The length of the diagonal represents the magnitude of the combined forces. The direction of the net force is along the diagonal and away from where the two forces are applied.
Laws of Motion
Applying a force often results in movement. When an object is changing its position with reference to another body, we say it is in motion. As with force, motion has a magnitude and a direction. The speed of the object, the distance traveled in a given amount of time, is the magnitude of the motion.
Wind Gust is an abrupt and momentary increase in the wind speed.
Wind is air in motion. Weather reports include wind speed and direction. Wind speed is reported on weather maps in knots--one nautical mile per hour (equivalent to 1.1508 statute miles per hour or 0.5144 meters per second). If the wind speed is strong (greater than 15 knots) and highly variable, the weather report will include wind gusts, the maximum observed wind speed.
Wind direction is reported as the direction from which the wind is blowing. It is reported with respect to compass directions or the number of degrees east of north. A north wind blows from the north to the south (Figure 6.3). Windward refers to the direction the wind is coming from, while leeward denotes the direction the wind is blowing towards. The prevailing wind direction of a region is the most frequently observed wind direction during a given period of time.
Acceleration is the time rate of change of velocity. An object that is accelerated under goes a change in speed and/or a change in direction of motion.
Wind that changes speed or direction has undergone acceleration. If a body increases its speed at a constant rate, it undergoes a uniform acceleration. A free falling body is a good example of an object that undergoes uniform acceleration. If we neglect air resistance, a falling body undergoes an acceleration of 9.8 meters per second for each second it falls. The object’s velocity increases 9.8 meters per second after each passing second. This downward acceleration results from the earth’s gravitational pull and is called the acceleration of gravity. Galileo discovered that the acceleration of two falling objects is the same, even if their weights are very different. Astronaut David Scott demonstrated this on August 2, 1971 by dropping a hammer and a feather at the same moment while on the moon. The moon has no atmosphere so there was no significant friction from air that would affect the fall of the feather more than the hammer in our atmosphere. The objects hit the ground at the same time, though the acceleration was less than 9.8 meters per second per second.
In the seventeenth century Sir Isaac Newton established the fundamental laws which describe the motion of bodies: the law of inertia, the law of momentum, and the law of reaction.
Newton's First Law: Law of Inertia
Newton’s first law of motion states that a body at rest tends to stay at rest while a body in motion tends to stay in motion traveling at a constant speed and in a straight line until acted upon by an outside force. If a bus suddenly starts the passengers lurch backward. The passengers are initially at rest and tend to remain at rest when the bus first starts. The moving bus is exerting a force that eventually gets the passengers moving at the same speed. If the bus suddenly stops, the passengers surge forward. They tend to remain in motion. If the bus makes a quick, sudden right turn the passengers, who want to continue traveling in a straight line, are crammed towards the left side of the bus. The resistance of an object to changing its velocity is called inertia.
Air at rest will tend to stay at rest until a force puts it in motion. We will discuss the forces that generate wind in the next section.
Newton's Second Law: Law of Momentum
The momentum of an object is its mass multiplied by its velocity. Two objects can have the same speed, but the one with more mass has greater momentum. Newton’s second law states: When a force acts on a body, the body’s momentum is changed by an amount that is proportional to the applied force and the amount of time the force acts on the body. Hitting a baseball with a bat is good example of this law. If you want to hit the ball far, you have to swing the bat hard to increase the force applied to the ball on contact. You also want to follow through with your swing to keep the bat in contact with the ball as long as possible.
Applying a force to an object changes its momentum by changing the speed at which it travels. A light breeze will not move a sailboat as fast as a strong steady wind. Back to our bus for a final example, as the bus accelerates, its momentum, and the momentum of the passengers inside, increases.
Law of Reaction
Firing a gun moves a bullet forward, but there is an equal force in the backward direction referred to as the ‘kick.’ Newton’s third law states that for every action (force) there is an equal and opposite reaction (force). When a cup of coffee is placed on a table, a downward force is exerted on the table because of gravity. The table exerts an equal and opposite force in order to support the cup.
Forces that Move the Air
There are different forces that act to move air (Figure 6.4). The weight of air is a force that always acts downward, towards the center of the earth. Other forces are the pressure gradient force, Coriolis force, friction, and centripetal force. We must examine these four forces to determine which direction the wind will blow and which direction storms will move.
Pressure Gradient Force
Spray paint cans exhibit warning labels that the contents are under pressure. When the nozzle is squeezed, or the sides punctured, the large pressure difference between the air and the inside of the can force the contents out of the can. Generating pressure differences is also important in flying and sailing (Box 7.1) Pressure differences exert a force and when not balanced by other forces cause movement. The force that results from pressure differences in a fluid such as our atmosphere is called the pressure force or the pressure gradient force. Air moves because of a pressure gradient force. The existence of a pressure gradient force is essential for sustaining winds.
The pressure gradient force (PG) always acts from high pressure towards low pressure. Its magnitude is equal to the pressure gradient, or the rate of change in pressure with distance at a specific time divided by the air density.
When pressure changes rapidly over a small distance, the pressure gradient force is large. Strong winds result from large pressure gradients.
On the surface weather map, measured atmospheric pressure at the surface is converted to sea level pressure and analyzed. As noted in Chapter 1, when comparing the pressure of two cities it is important to reference the pressure measurements to the same altitude. If the pressures are not referenced to the same altitude, when analyzing differences in pressure between the two cities, we will just see differences in the altitude of the cities, since atmospheric pressure always decreases with altitude. Measured surface pressure is adjusted to what the pressure would be if the city were at sea level. To accomplish this we need to determine the pressure that would be exerted by a column of air that extends from the location of the weather station too sea level, and add this pressure to the observed pressure (Figure 6.5). The web page discusses how these corrections are made. On average, this correction is approximately 1 mb for each location 10 m of altitude
Isobars of constant sea level pressure are drawn at 4 mb intervals starting at 1000 mb. Figure 6.6 is an example of a surface weather map. The winds near Chicago are greater than those winds near Oklahoma City. The isobars are spaced closer together over the Great Lakes than over Oklahoma. Since the pressure difference between any two isobars is fixed, the closer the isobars the larger the pressure gradient, the stronger the pressure gradient force, and the greater the wind speed.
Isobaric map is commonly used to study the weather above the surface. This constant pressure chart includes information on the temperature, wind speed and direction, humidity, and the altitude at a given pressure.
The surface map plots atmospheric pressure adjusted to sea level. Another type of weather map plots the altitude of a given pressure surface. This map is commonly used when analyzing the weather above the surface and is called a constant-pressure chart or isobaric chart. Constant-pressure charts are commonly drawn for 850, 700, 500, 300, 250, and 100 millibars. Figure 6.7 is an example of a 500 mb map corresponding to November 10, 1976. The units of altitude are called geopotential meters and are nearly equivalent to geometric meters measured with a ruler. Isobaric maps are useful for portraying horizontal pressure gradients. The spacing between the lines of constant height (isoheight) portray the pressure gradient force. To see this consider Figure 6.8. The colored surface is a constant pressure surface of 850 mb. Anywhere on this surface the pressure is 850 mb. The altitude of this 850 mb surface varies, the altitude is higher at City A than at City B. Above this figure is an analysis of the pressure gradient force along this 850 mb surface. Atmospheric pressure always decreases with increasing altitude, so the steeper the pressure surfaces the greater the pressure gradient force. The magnitude of the pressure gradient force is weak near City B and stronger near City A. Also shown in Figure 6.8 are constant-height lines of the 850 mb pressure surface. The magnitude of the pressure gradient force is proportional to the spacing of the contour lines. The closer the constant-height lines the greater the pressure gradient force. The direction of the pressure gradient force is perpendicular to the lines of constant-height, and point towards lower heights.
To summarize, on an isobaric map the lines of constant-height of the pressure surface indicate the direction of the pressure gradient force and the magnitude. Referring back to Figure 6.7, the stronger winds are located in regions where the spacing of the constant-height lines is a minimum, as expected because this is where the pressure gradient force is the largest. However, the winds are not in the direction of the pressure gradient force! The winds, in general, are blowing to the right of the pressure gradient force, and are nearly parallel to the isoheight lines! This suggests that there must be more than one force acting on the winds.