newton's laws of motion - university of...

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Introduction to Climatology GEOGRAPHY 300

Tom Giambelluca University of Hawai‘i at Mānoa

Atmospheric Pressure, Wind, and

The General Circulation

Isaac Newton (1642-1727)

Philosophiæ Naturalis Principia Mathematica (1687) "Mathematical Principles of Natural Philosophy”

•  Newton’s Laws of Motion •  Newton’s Law of Universal Gravitation •  Theoretical Derivation of Kepler’s Laws of Planetary Motion •  Laid the Groundwork for the Field of Calculus

Newton's Laws of Motion 1st Law: Law of Inertia: If no net force acts on a particle, the particle will not change velocity. An object at rest will stay at rest, and an object in motion, will continue at constant velocity unless acted on by external unbalanced force. 2nd Law: Law of Acceleration: The rate of change of velocity (acceleration) of a particle of constant mass is proportional to the net external force acting on the particle. where a = acceleration, F = force, and m = mass.

a = Fm

orF =m ⋅a

Newton's Laws of Motion

Newton's Laws apply only in an inertial reference frame.

An inertial reference frame cannot be accelerating; must be at rest or moving at a constant velocity (constant speed and direction).

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Pressure

Pressure = Force per Unit Area In our environment, gravity is constantly accelerating objects downward. Gravitational acceleration (g) is approximately constant within the earth's atmosphere:

P = FA

g = 9.8

ms

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s= 9.8 m

s2= 9.8ms−2

Pressure The weight of an object is the force determined by gravitational acceleration and the mass of the object: Weight = F = m × a Pressure = Force per Unit Area = P = F/A Atmospheric Pressure is the force exerted by the weight of the atmosphere above a given point.

Pressure Pressure always decreases as you go up:

Pressure

Measuring Atmospheric Pressure The Torricelli Tube: the original barometer (invented in 1643 by Evangelista Torricelli) Mean sea level atmospheric pressure: 1013.2 mb = 101.32 kPa = 101,320 Pa

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Pressure

Equation of State (Ideal Gas Law):

P = ρRT where P = pressure (Pa), ρ = density (kg m-3), R = universal gas constant (287 J kg-1 K-1), and T = temperature (K) Changes in temperature or density cause changes in pressure.

High Pressure

Pressure Gradients

A Change in Pressure over a Distance

A pressure gradients is important because it exerts a force on air which acts to move air from high pressure to low pressure:

Pressure Gradient Force

Pressure Gradients

Vertical Pressure Gradient Because of the relationship between elevation and pressure, a strong vertical pressure gradient is always present. Which direction is the resulting strong vertical pressure gradient force acting? What effect does vertical pressure gradient force have on air motion?

Pressure Gradients

Hydrostatic Equilibrium Upward vertical pressure gradient force is balanced by an equal force oriented in the opposite direction.

GRAVITY

The balance between vertical pressure gradient force and gravitational acceleration (Hydrostatic Balance) limits vertical motion in the atmosphere.

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Pressure Gradients

Horizontal Pressure Gradients Visualize the lower atmosphere seen from a cross sectional perspective. In the diagram below, upward in the atmosphere is toward the top. The horizontal line represents sea level. Go up from the ground until the pressure drops to 1000 mb. Do that from several different locations

Pressure Gradients

Horizontal Pressure Gradients Connecting the points forms a 2-dimensional surface of all points having the same pressure; we call this an isobaric surface; in profile, as in the drawing above, we see the edge of the isobaric surface; it is a line of equal pressure, called an isobar.

Pressure Gradients

Horizontal Pressure Gradients

If we went higher in the atmosphere, we would encounter isobaric surfaces with successively lower pressure values.

Pressure Gradients

Horizontal Pressure Gradients In the pressure diagrams just shown, the isobaric surfaces were seen as flat and horizontal. In that situation no horizontal pressure gradients are present. Therefore, no wind would occur. The air would remain still.

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Pressure Gradients

Horizontal Pressure Gradients In the previous diagram note that the distance between the 1000 and 900 mb surfaces is less than the distance between the 900 and 800 mb surfaces. Why is that?

Answer: As you go up, the density of air decreases, therefore the distance necessary to reduce the pressure by 100 mb is greater as you go higher. Another way to think about this is that the mass of air between any 2 isobaric surfaces 100 mb apart is the same, i.e. you can equate the pressure difference with a given mass of air. But at higher elevations, the air is less dense, so you have to go farther to reduce the mass of air above you by the amount necessary to lower the pressure by 100 mb.

Pressure Gradients

How Do We Get Horizontal Pressure Gradients? We know that air density is affected by air temperature. Warm air is less dense than cold air. The isobaric surfaces will have to be farther apart for warm air than for cold air.

Pressure Gradients

Horizontal Pressure Gradients Suppose you have one area with warm air and another area with cold air:

Pressure Gradients

Horizontal Pressure Gradients Now we see horizontal differences in pressure. Along the ground, the cold air has higher pressure:

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Pressure Gradients

Horizontal Pressure Gradients Higher up, we see the pressure gradient is reversed:

Pressure Gradients

Horizontal Pressure Gradients The resulting circulation, if no other forces were acting, would be a cell such as:

Pressure Gradients

Sea Breeze and Land Breeze

SEA BREEZE

Pressure Gradients

Sea Breeze and Land Breeze

LAND BREEZE

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Pressure Gradients

Horizontal Pressure Gradients The spacing of the isobars indicates the strength of the gradient and, therefore, the speed of the wind.

Pressure Gradients

Horizontal Pressure Gradients The horizontal pressure gradient can also be represented by the slope of an isobaric surface. Regarding the height of a pressure surface, areas where it is higher correspond to high pressure areas and vice versa. The steeper the slope of the isobaric surface, the stronger the horizontal pressure gradient.

Pressure Gradients

Horizontal Pressure Gradients

Horizontal pressure patterns in the upper atmosphere are shown using pressure surface height maps.

CORIOLIS EFFECT

The rotation of the earth on its axis means that the surface of the earth is constantly accelerating. In our non-inertial reference frame, large-scale motion such as atmospheric winds and ocean currents appear to be deflected away from the direction of the forces acting.

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CORIOLIS EFFECT

At the start (t1), a force causes an object to start moving south. The object continues in the same direction, but the Earth is rotating. As a result, an hour later (t2), the path of the object appears to have veered off to the right, as viewed from the ground.

Let's try to understand Coriolis effect by looking at the Earth from above the North Pole:

CORIOLIS EFFECT

How about in the Southern Hemisphere? Let's look at the Earth from above the South Pole: Now the object appears to have veered to the left of its original direction.

CORIOLIS EFFECT Geostrophic Wind

Up in the atmosphere, away from the frictional influence of the earth's surface, the two important forces controlling wind speed and direction are horizontal pressure gradient force and coriolis. The balance between these two forces is called Geostrophic Balance. The wind resulting from this balance is called the Geostrophic Wind.

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Geostrophic Wind

Take a situation where the isobars are running east-west with low pressure towards the north and high pressure towards the south. In that case, the pressure gradient force acting on air is directed from south to north:

Geostrophic Wind

In the absence of other forces, the wind would therefore blow from south to north. But, due to the earth's rotation, coriolis acts on the moving air, always directed at 90° to the right of the direction of motion in the Northern Hemisphere. That changes the direction of the wind. The pressure gradient force and Coriolis force come into balance when they are oriented in opposite directions. That balance occurs when wind is directed at 90° to the right of the pressure gradient force in the Northern Hemisphere (and 90° to the left of the pressure gradient force in the Southern Hemisphere).

Geostrophic Wind

The Geostrophic Wind always flows parallel to the isobars:

Geostrophic Wind

Some other examples:

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Geostrophic Wind

Southern Hemisphere examples:

Pressure Cells

Often the pressure distribution produces cells of low or high pressure. In that case, the isobars are more or less circular, and wind would flow around the cells parallel to the isobars. Strictly speaking, geostrophic wind only applies to straight wind flow. But for curved flow such as wind moving around low or high pressure cells, we can use the geostrophic wind as an approximation.

Pressure Cells

For a low pressure cell, pressure gradient force is directed inward toward the center of the cell:

Pressure Cells But, Coriolis will deflect the wind to the right of the pressure gradient in the Northern Hemisphere:

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Pressure Cells

That produces a counterclockwise wind pattern around low pressure centers in the Northern Hemisphere:

Pressure Cells

The direction of flow is opposite (clockwise) for low pressure cells in the Southern Hemisphere:

Pressure Cells

For a high pressure cell, the pressure gradient force is oriented outwards from the center of the cell:

Pressure Cells

Coriolis causes wind to be directed to the right of the pressure gradient force in the Northern Hemisphere:

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Pressure Cells

And that produces clockwise circulation of air around high pressure cells in the Northern Hemisphere:

Pressure Cells In the Southern Hemisphere, air flows counterclockwise around high pressure cells: In either hemisphere, we call high pressure cells anticyclones and low pressure cells cyclones. The flow direction around an anticyclone is always refered to as anticyclonic, and around a cyclone the flow is always called cyclonic.

Pressure Cells

In either hemisphere, we call high pressure cells anticyclones and low pressure cells cyclones. The flow direction around an anticyclone is always referred to as anticyclonic, and around a cyclone the flow is always called cyclonic.

Gradient Wind

In reality, geostrophic balance is only possible with straight flow. Curved flow, such as that around a high or low pressure cell, requires that pressure gradient force and Coriolis be out of balance. For flow around an anticyclone (high pressure), Coriolis has to be stronger than pressure gradient force. Therefore the wind speed has to be greater than it would be for straight flow. Conversely, for flow around a cyclone, Coriolis has to be weaker than pressure gradient force, requiring wind speed to be lower than for straight flow.

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Gradient Wind Surface Wind Near the earth's surface, frictional force comes into play. Friction acts to slow the wind, and therefore can be thought of as always acting in the direction opposite of the wind direction. When the friction vector is added into the picture, the force vectors are no longer balanced:

Surface Wind Balance is achieved when the wind direction changes so that wind is directed across the isobars at an angle instead of flowing parallel to the isobars. The direction of Coriolis and friction depend on the wind direction. So when the wind shifts, they shift. With the wind crossing the isobars at an angle toward low pressure, the forces come into balance:

Surface Wind And for the Southern Hemisphere:

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Surface Wind Near surface winds when isobars are straight and parallel: Northern Hemisphere:

Surface Wind Near surface winds when isobars are straight and parallel: Sothern Hemisphere:

Surface Wind For curved flow around high or low pressure cells: Northern Hemisphere:

Surface Wind For curved flow around high or low pressure cells: Southern Hemisphere:

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Surface Wind Surface Pressure Patterns and Wind

Surface Pressure Patterns and Wind Upper Level Pressure Patterns and Wind

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The General Circulation of the Atmosphere

Hadley: 1-cell model of atmospheric circulation

George Hadley (1682-1744)


3-cell model of atmospheric circulation • Hadley cell • Ferrel Cell • Polar Cell

William Ferrel (1817-1891)


3-cell model of atmospheric circulation • Hadley cell • Ferrel Cell • Polar Cell

William Ferrel (1817-1891)


See animation of idealized atmospheric circulation: http://kingfish.coastal.edu/marine/Animations/Hadley/hadley.html

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Belts of Pressure and Zonal Winds Pressure Belts •  Intertropical Convergence Zone (ITCZ, Low Pressure) •  Sub-Tropical High Pressure Belt •  Polar Front (Low Pressure) •  Polar High

Zonal Winds •  Trade Winds: Tropical Easterlies •  Mid-Latitude Westerlies •  Polar Easterlies

The General Circulation of the Atmosphere Mean Pressure Patterns January

The General Circulation of the Atmosphere Mean Pressure Patterns July

The General Circulation of the Atmosphere Components of the Hadley-Cell Circulation •  ITCZ

–  vigorously lifted air in the equatorial region –  produces huge thunderstorms –  visible in satellite images as a line of clouds –  shifts seasonally –  shifts more over land areas –  remains in the Northern Hemisphere over the central

and eastern Pacific Ocean

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The General Circulation of the Atmosphere Components of the Hadley-Cell Circulation •  Poleward flowing air aloft

–  gradually cools by radiation –  starts to sink due to cooling, and convergence

•  Subtropical high pressure belt –  zone of subsiding (sinking) air and high pressure

around 30 degrees north and south –  subsiding air causes this region to have very little

precipitation –  the great subtropical deserts, such as the Sahara

and Kalahari Deserts are located in this zone –  subsiding air also produces the trade wind inversion

The General Circulation of the Atmosphere Components of the Hadley-Cell Circulation •  Trade winds

–  return flow of air from decending limb of Hadley cell back to the equator

–  flow has strong easterly component in both hemispheres due to Coriolis

The General Circulation of the Atmosphere Movement of the ITCZ •  Seasonal shifts

–  Moves north during northern hemisphere summer and vice versa

–  Over land, the seasonal shift is greater

–  Accounts for seasonal rainfall in some equatorial/tropical land areas, such as the Amazon basin and the Sahel

The General Circulation of the Atmosphere Upper-Level Westerly Winds •  Thickness Patterns

–  The pressure gradient force, and hence the wind velocity, is determined by the slope of the isobaric surfaces.

–  In the presence of a horizontal temperature gradient, the thickness of each pressure layer changes horizontally. As a result the isobaric surfaces tilt more and more toward the colder air.

–  Lines of constant thickness are parallel to lines of constant temperature, i.e. the thickness pattern and the temperature pattern are the same. This is because the temperature pattern creates the thickness pattern.

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Upper-Level Westerly Winds •  The Thermal Wind

–  The Thermal Wind can be thought of as a vector added to wind at one level to give the wind at a higher level. The size and direction of the Thermal Wind vector are determined by the thickness pattern (temperature pattern) of the air layer in between.

–  The Thermal Wind is always pointed so that warm air is on its right side (in the Northern Hemisphere).


Upper-Level Westerly Winds •  The Thermal Wind

–  As a consequence of the Thermal Wind, air flow in the mid-latitudes becomes more and more westerly as you go up in altitude.


Upper-Level Westerly Winds •  The Polar Front Jet Stream

–  The north-south temperature gradient is strongest along the Polar Front.

–  As a result, the Thermal Wind is strongest there, and the upper-level westerlies become extremely strong.

–  The Polar Front Jet is a narrow stream of very fast moving air in the upper atmosphere.


Upper-Level Westerly Winds •  Meanders in the upper level westerly winds

–  Mid-latitude isotherms do not always run exactly east-west, for example,because of ocean-continent temperature contrasts.

–  Wave-patterns are common in the westerly wind flow.

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Upper-Level Westerly Winds •  Rossby Waves

–  Large waves in the westerly flow are known as Rossby waves. –  Rossby waves constantly change in position and amplitude with

major consequences for mid-latitude weather.

The General Circulation of the Atmosphere Rossby Waves •  Vorticity, Upper-Level Divergence and Convergence

–  Vorticity is a measure of the rotation of a parcel of air. –  Vorticity can be positive (cyclonic) or negative (anticyclonic).


–  Earth Vorticity: •  is the rotation imparted by the earth’s rotation. •  is related to Coriolis. •  is maximum at the poles and zero at the equator •  Is cyclonic (counterclockwise in the Northern Hemisphere) •  Is anticyclonic in the Southern Hemisphere


–  Relative Vorticity: •  is the additional rotation due to the spin of the air, curved flow of air,

or shear in the air flow

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–  Absolute Vorticity: •  is the sum of Earth Vorticity and Relative Vorticity

–  The Law of Conservation of Angular Momentum: •  a familiar example of conservation of angular momentum is the

increase in spin rate of an ice skater when the arms and leg are pulled in closer to the axis of rotation:


–  The Law of Conservation of Angular Momentum: •  when applied to air, can be simply stated as: The absolute vorticity of

an air column divided by the height of the air column must remain constant. Or another way of stating it is: The absolute vorticity of an air column multiplied by the area of the air column must remain constant.

–  Level of Non-Divergence: •  Generally, air is either divergent or convergent aloft (in the upper

atmosphere) and the opposite in the lower atmosphere. There is a gradual change from divergence to convergence, or vise versa as you go from the surface upward. Somewhere in between the surface and the upper atmosphere is a level where the air is neither convergent nor divergent: The Level of Non-Divergence.


–  The Law of Conservation of Angular Momentum: •  Conservation of Angular Momentum requires that air crossing a

mountain barrier must compensate for the decreased height of the air column by curving in an anticyclonic direction (clockwise in the N. Hemisphere).

•  For example, westerly flow encountering the Rocky Mountains of western North America, will turn to the right as it passes the mountains, becoming northwesterly. As a result, the air is flowing toward lower latitudes, and its Earth Vorticity is decreasing as a result. At the level of non-divergence, the air must turn in a cyclonic direction (counterclockwise in the northern hemisphere) to conserve angular momentum. This causes the flow to change direction, becoming southwesterly. Succeeding changes in latitude will cause alternating anticyclonic and cyclonic changes in direction, setting up a series of waves downstream of the mountain barrier. The equatorward dips in the flow are called "troughs" and the poleward meanders are called "ridges".


–  These waves in the westerly flow are known as Rossby waves. –  Rossby waves can also be triggered by SST anomalies. –  Cyclogenesis: Above the level of non-divergence, angular momentum

conservation can be maintained by convergence or divergence of the air, i.e. by increasing or decreasing the air column height, or in other words, by decreasing (converging) or increasing (diverging) the horizontal area of the air column. Air moving downstream of a Rossby wave trough is moving from high positive relative vorticity (cyclonic curvature) to zero relative vorticity (straight flow). The resulting decrease in absolute vorticity is compensated for (above the level of non-divergence) by a decrease in the air column height, i.e. an increase in the area or diameter of the column. In other words the air aloft diverges. This causes air below to rise, setting in motion the process of developing a low pressure center at the surface. As air rises, surface air will converge: lower level convergence. But as long as the upper level divergence is greater than the lower level convergence, the low pressure center (cyclone, storm) will continue to strengthen.

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–  As a result of this relationship between the voriticy changes in upper level flow and surface pressure, Rossby waves exert strong control on the formation and movement of midlatitude storms. These storms tend to form beneath the area of upper-level divergence downstream of a Rossby wave trough, and subsequently move in a path that tracks the upper-level wind. In the northern hemisphere, midlatitude cyclones tend to move from southwest to northeast as they go from intitial disturbance to maturity and occlusion.

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