Atmospheric Dynamics
The atmosphere is a fluid
What are the properties of fluids?
1.
2.
3.
Flow under the influence of forces
Important forces for the atmosphere (and ocean):
•
Gravity
•
Friction
•
Pressure gradient
•
The so-called “fictitious forces”: Coriolis, Centrifugal
Generally considered continuous, although they are in fact composed of
discrete atoms/molecules
Come in two general forms:
•
Liquids
•
Gases
Forces and Motions
Gravity – “heavy” fluid sinks / “light” fluid rises
Example: 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 Motions
Newton’s Second Law:
v v
v
 Fi  Fnet  ma
i
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).
Density, Pressure and Temperature
Density
Mass per unit volume
m

V
mks units: kg m-3 – “kilograms per cubic meter”
cgs units: g cm-3 – “grams per cubic centimeter”

Density, Pressure and Temperature
Pressure
Force per unit area
F
p
A
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 molecules
units: Kelvins (K), degrees Celcius (oC)
pV  mRT
p: pressure exerted by vapor
V : volume occupied by vapor
m : mass of vapor
R: specific gas constant of substance
T : temperature of vapor (must be in K)

 



Density, Pressure and Temperature
Use definition of density to formulate yet another version of the
Ideal Gas Law
p  RT
p : pressure exerted by the vapor
 : density of the vapor
R : specific gas constant of the substance
 T : temperature of the vapor



Buoyancy
Archimedes' 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
Buoyancy
Archimedes' principle
Buoyancy Force = weight of the displaced fluid
Weight: force of gravity
Fg  mg
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.
How does buoyancy affect motion in
fluids?
ambient fluid
parcel
V
2

1


Will the parcel rise, fall or remain still?
How does buoyancy affect motion in
fluids?
Forces acting on the parcel:
1.
Gravity
2.
Buoyancy
FB  2Vg

V

Fg  1Vg
Apply Newton’s Second Law:
 F  ma
i
i

FB  Fg  1Va
 2Vg  1Vg  1Va
 2  1 
a  
g
 1 
So, if the parcel is more dense than the ambient fluid (1  2), it will sink.
Examples: ocean convection/deep water formation

However, if the parcel is less dense than the environment ( 

2
 1), it will
rise.
Examples: hot air balloons, dirigibles, moist air in atmospheric convection

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 Motion
The Tropics: The Hadley Circulation
Atmospheric Motion
The Tropics: Precipitation Patterns
Atmospheric Motion
The 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
v
L v v
 r v
m
angular momentum
per unit mass
distance to
rotation axis
east-west wind
speed
Figure Skater
Atmosphere
Atmospheric Motion
The Extra-tropics: The Jet Streams
Atmospheric Motion
The 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 Cycle
How 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!