Introduction & Overview
What is atmospheric dynamics?
Goal of the class
Understand how atmosphere (and ocean) moves
Thus, how to predict future state of the
atmosphere
Understand the atmospheric structure
(distribution of temperature, wind, )
Develop t

Balance. in the vertical too
Gradient wind balance
V2
fV
R
n
Balanced flow (no friction)
More complicated (3- way balance), however, better approximation than
geostrophic (as allows for centrifugal acceleration due to curvature of parcel
trajectory)
Sol

Turbulence and boundary layers
Challenge
Have our boundary layer equations, which are (more or less) exact.
But we dont know how to evaluate the eddy terms
Challenge is to derive a theory, which can be used to express eddy terms as a function of
mean term

Turbulence and boundary layers
Weather and turbulence
Big whorls have little whorls which feed on
the velocity; and little whorls have lesser
whorls and so on to viscosity
Lewis Fry Richardson
Momentum equations
du
1 p
fv
Frx
dt
x
dv
1 p
fu
Fry
dt

The general circulation:
midlatitude storms
Motivation for this class
Provide understanding basic motions of the
atmosphere:
Ability to diagnose individual weather
systems, and predict how they will change
Understand the importance of atmospheric
flow,

Circulation
(and its good friend vorticity)
Why was Sandy so fierce?
Vorticity
Vorticity is the measure of spin and rotation in a fluid at a point
(c.f., circulation, which is the rotation for some region of fluid)
Vorticity is defined as the curl of the

The PBL influence
Grand challenges
Observed Hurricane Sandy got bigger when
went over land
Tuesday
Thursday
Sandy before and after
Grand challenges
Observed Hurricane Sandy got bigger when went over
land
Our balloons changed direction with height
Flow

Geostrophic adjustment
Todays class
Why are atmospheric waves/systems about
500km in size?
Why are these close to geostrophic?
Recall of potential vorticity
(adjustment to steady state under constraint
that potential vorticity is conserved)
4
Geostroph

Circulation theorem
Divergence and vorticity
Some context
Atmospheric flow mostly horizontal
Described by (2d) horizontal momentum equations
(and hydrostatic equation)
Balanced flow useful, but does not allow prediction.
But we know
Many motions of inter

The Vorticity Equation
Potential vorticity
Circulation theorem is really good
Circulation theorem implies a conserved quantity
dP
0
dt
P f g
p
2
PV for barotropic fluid
General form of Ertels potential vorticity: P f g const
p
Consider isentropic flow

Rossby waves
(waves in vorticity)
Stationary (topographically forced) waves
NCEP Reanalysis Z500
January mean
2
Vorticity equation
Change in relative (vertical component of) vorticity at a point,
u
x v y w z
t
f
v
y
u v
f
x y
w v w u
x z y z

Outline:
1) The Continuity Equation
-Derivation
-Work through two problems
2) Research spotlight: the
Madden-Julian Oscillation
-Its basic features
-Standing engimas
Atmospheric Dynamics
October 3, 2012
The Continuity Equation in words
In any steady stat

Thermal wind balance
Goals
1 puzzle remains for the first half of the semester: the
relationship between wind and temperature
Recall geostrophic balance
Recall hydrostatic balance
Recall continuity (divergence equation)
Combined we can explain a larg

Pressure and mass conservation
1
Todays goals
Some definitions:
Gravity. What is a shallow atomsphere
Coordinates.
The concept of a parcel
(or finite element in the fluid)
Vertical variations in pressure
Vertical variation in temperature
(Seemingly obvi

Thermodynamic energy
1
Announcements
September 27th: No class.
This room will be used for a computing
tutorial.
Office hours change: 3-5pm Tuesdays.
(also right after class until 2pm is OK)
Guest lecture Thursday.
Key concepts to date
We have a basis

Stability and waves
Goals
Unconditional stability
Conditional stability
Buoyancy
Buoyancy waves
Moist adiabatic lapse rate
Archimedes principle
A body immersed in a fluid is buoyed up by a force equal to
the weight of the displaced fluid.
Consider an a

Your Dry Air Parcel
1. Do the properties of your air parcel change?
How do they change?
Why do they change?
By what physical processes?
Represent these changes in your drawing.
2. Write down the 1st Law of Thermodynamics.
How do the terms of the equation

Instability and convection
Goals
Unconditional stability
Conditional stability/instability
Onset of convection
Thermodynamics in 2d.
Example!
DC3 experiment (summer 2012 near CO)
Buoyancy and potential temperature
With small vertical displacement (up), pa

Thermodynamic equation
and advection
Announcements!
Thursday 27th: This room is unavailable!
Review/HW tutorial session in
Ekeley Sciences W230 the reading room
Also, reminder HW1 dues Thursday
Goals
Thermodynamics in 2d
Define, examine advection
Co

Why does wind tend to follow pressure contours?
geopotential height
(contours)
wind speed + direction
Consider Conservation of Angular Momentum
Absolute angular momentum
u 2
u u
2
R
( R R)
R
R R
Another form of the same equation
planetary
rotation =

Balanced flow
Things we know
Primitive equations are very comprehensive,
but there may be a number of vast
simplifications that may be relevant (e.g.,
geostrophic balance).
Seems that there are things in the atmosphere
which spin (like highs and lows, a

Balanced flow
Recall
Considered large-scale synoptic flow, had a
Rossby number of about 0.1
Ro = U/Lf
Rossby number in.
Atmosphere
f~1x10-4 s-1, U ~10 ms-1, L ~1000 km
Ro = 0.1
Ocean
f~1x10-4 s-1, U ~0.1 ms-1, L ~10-100 km
Ro < 0.1!
Recall angular vel

Vorticity
Tuesday
Thursday
Why vorticity?
A 2d flow can be described by any two quantities:
e.g., u and v, and D, and
Since earth is rotating, having quantities that are related to
rotation would seem sensible
Since mid-latitude flow is almost geostro