Atmospheric DynamicsThe atmosphere is a fluid

What are the properties of fluids?

1. Flow under the influence of forcesImportant forces for the atmosphere (and ocean):

• Gravity• Friction• Pressure gradient• The so-called “fictitious forces”: Coriolis, Centrifugal

2. Generally considered continuous, although they are in fact composed of discrete atoms/molecules

3. Come in two general forms:• Liquids• Gases

Forces and Motions

Gravity – “heavy” fluid sinks / “light” fluid risesExample: buoyancy, like in a lava lamp – “BLOOP… BLOOP…”

Friction – drag force acting on the fluid on account of its coming in contact with a rigid surface

Example: excess drag on one side of a spinning baseball causes a net force (in this case, on the ball) in that direction – “STRIKE ONE!”

Pressure Gradient – motion ensues from high-pressure to low-pressure under this force

Example: fill your hose, set it on the ground, step on one end: what happens? Under your foot is high pressure, at the open end the pressure is low – “SQUIRT!”

Forces and Motions

FICTICIOUS FORCES

Centrifugal Force – if you wish to move in a circle, you must overcome your inertia, i.e. your tendency to move in straight lines unless you are acted on by a force

Example: sharp left turn in your car – “WHOA!”

Coriolis Force – motion relative to a rotating surface is apparently affected by this force

Example: rather like playing catch on a merry-go-round – “SMACK!”

Forces and MotionsNewton’s Second Law:

In words, a net force acting on an object causes it to accelerate by an amount proportional to the sum of forces and inversely proportional to its mass. If the net force acting on an object is zero, the object will move in a straight line at constant speed (Newton’s First Law).

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vF i

i

∑ =v F net = m

v a

Density, Pressure and Temperature

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ρ =m

V

Density

Mass per unit volume

mks units: kg m-3 – “kilograms per cubic meter”cgs units: g cm-3 – “grams per cubic centimeter”

Density, Pressure and Temperature

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p =F

A

Pressure

Force per unit area

mks units: kg s-2 m-1 – Pa “Pascals”other units: bar, mb, atm, hPa

Density, Pressure and Temperature

Temperature (and the Ideal Gas Law)

Temperature: Average kinetic energy of moleculesunits: Kelvins (K), degrees Celcius (oC)

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pV = mRT: pressure exerted by vapor: volume occupied by vapor

: mass of vapor: specific gas constant of substance

: temperature of vapor (must be in K)€

p

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V

€

m

€

R

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T

Density, Pressure and Temperature

Use definition of density to formulate yet another version of the Ideal Gas Law

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p = ρRT

: pressure exerted by the vapor: density of the vapor

: specific gas constant of the substance: temperature of the vapor

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ρ

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p

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R

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T

BuoyancyArchimedes' principle

Vitruvius (De architectura IX.9–12) recounts the famous story of Archimedes making this discovery while in the bath. He was given the task of finding out if a goldsmith, who worked for the king, was carefully replacing the king's gold with silver. While doing this Archimedes decided he should take a break so went to take a bath. While entering the bath he noticed that when he placed his legs in, water spilled over the edge. Struck by a moment of realisation, he shouted "Eureka!" He informed the king that there was a way to positively tell if the smith was cheating him. Knowing that gold has a higher density than silver, he placed the king's crown and a gold crown of equal weight into a pool. Since the king's crown caused more water to overflow, it was, therefore, less dense, Archimedes concluded that it contained silver, causing the smith to be executed. The actual record of Archimedes' discoveries appears in his two-volume work, On Floating Bodies.

source: http://en.wikipedia.org/wiki/Buoyancy

BuoyancyArchimedes' principle

Buoyancy Force = weight of the displaced fluid

Weight: force of gravity

Example Problem:The volume of a lake freighter hull is V = 300 m X 30 m X 20 m = 1.8 x 105 m3. If the density of lake water is 1000 kg m-3, what is the buoyancy force acting on the ship if it is nearly submerged (i.e. the water line is at the deck)? What is the cargo capacity, assuming the mass of the ship is negligible compared to the mass of the cargo it is carrying (this is probably a fairly bad assumption)?

Solution: The mass of displaced water is 1.8 x 108 kg and the weight of this water is then about 1.8 x 109 N. Thus, the buoyancy force acting on the ship will be about 2 billion Newtons. The cargo capacity would be somewhat less than 1.8 x 108 kg, depending on exactly how massive the empty ship itself is.

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Fg = mg

How does buoyancy affect motion in fluids?

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ρ2

ambient fluid

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ρ1

parcel

Will the parcel rise, fall or remain still?

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V

How does buoyancy affect motion in fluids?

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FB = ρ 2VgForces acting on the parcel:1. Gravity2. Buoyancy

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Fg = −ρ1Vg€

V

Apply Newton’s Second Law:

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Fi

i

∑ = ma

So, if the parcel is more dense than the ambient fluid ( ), it will sink. Examples: ocean convection/deep water formation

However, if the parcel is less dense than the environment ( ), it will rise.

Examples: hot air balloons, dirigibles, moist air in atmospheric convection

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FB + Fg = ρ1Va

ρ 2Vg − ρ1Vg = ρ1Va

a =ρ 2 − ρ1

ρ1

⎛

⎝ ⎜

⎞

⎠ ⎟g

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ρ1 > ρ 2

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ρ2 > ρ1

How is buoyancy generated in the atmosphere?

There are two main ways that buoyancy (and therefore motion) is generated in the atmosphere:

1. Add/Subtract moisture, since H2O has a lower molecular weight than dry air composed of N2, O2 and Ar

2. Increase/Decrease temperature

(or a combination of the two, of course)

Global Energy Budget (revisited)

Atmospheric MotionThe Tropics: The Hadley Circulation

Atmospheric MotionThe Tropics: Precipitation Patterns

Atmospheric MotionThe Tropics: Precipitation Patterns

(Seasonal Cycle in Soil Moisture)

http://geography.uoregon.edu/envchange/clim_animations/animated%20gifs/soilwo_web.gif

Why do we have jet streams?Angular Momentum Conservation

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vL

m=

v r ×

v v

angular momentum per unit mass

distance to rotation axis

east-west wind speed

Figure Skater

Atmosphere

Atmospheric MotionThe Extra-tropics: The Jet Streams

Atmospheric MotionThe Hadley Cell and Angular Momentum

Schematic of the General Circulation

What is weather?

Midlatitude weather systems are instabilities of the zonal jet. A perfectly symmetric jet is unstable and begins to “meander”, producing mobile high and low pressure systems.

Weather is the response of the fluid atmosphere to a local imbalance in the energy budget.

The meandering jet stream

What is weather?

Midlatitude weather systems are instabilities of the zonal jet. A perfectly symmetric jet is unstable and begins to “meander”, producing mobile high and low pressure systems.

Weather is the response of the fluid atmosphere to a local imbalance in the energy budget.

Global Energy Budget (revisited)

The function of large-scale atmospheric motions, including

“weather” phenomena, is to transport thermal energy from

the equator to the poles, thereby balancing the GLOBAL

ENERGY BUDGET.

Moving warm air to the poles and cold air to the tropics…

Global Energy Budget

Balanced global energy budget comprises radiative energy input and output as well as

1.Sensible heat transport (temperature)2.Latent heat transport (water vapor)

We just spent some time on the sensible heat budget; let’s look at water vapor transport…

The Hydrological Cycle

The Hydrological Cycle

The Hydrological Cycle

The Hydrological CycleHow in the world does evaporation and precipitation

constitute heat transport in the atmosphere?!?

1. dump some radiative energy into tropical ocean surface and evaporate water – the energy is not used to heat the ocean but to evaporate the water

2. move the newly evaporated water vapor toward the poles in atmospheric circulations

3. condense the water vapor in extra-tropical clouds/rain – energy released by condensation warms extra-tropical air

Net Result: Radiative energy deposited in the tropics has been used to warm extra-tropical air!