Lecture 3: Applications of Basic Equations
Pressure C
P
Coordinates:
di t Advantage
Ad t
andd Disadvantage
Di d t
Momentum Equation Balanced Flows
Thermod namic & Momentum
Thermodynamic
Moment m Eq.s
Eq s Thermal Wind Balance
Continuity Equation Surface P

Outline
1. Review
Momentum equation(s)
Geopotential and atmospheric thickness
Transformation of vertical coordinates
2. Material Derivative
Lagrangian and Eulerian reference frames
Material (total, substantive) derivative
Mathematical tools needed for Hom

Couple of Links you should know
about
http:/www.lib.umich.edu/ejournals/
Library electronic journals
http:/portal.isiknowledge.com/portal.c
gi?Init=Yes&SID=4Ajed7dbJbeGB3KcpBh
Web o Science
Material from Chapter 6
Quasi-geostrophic theory
Quasi-geos

Rest of Course
Wrap up quasi-geostrophic theory (Chapter 6)
Potential vorticity
Vertical velocity
Will NOT do Q vectors
We will have a lecture on the Eckman layer (Chapter 5)
Boundary layer, mix friction with rotation
We will have a lecture on Kelv

Outline
Review
Coriolis Force
Vertical structure and vertical coordinate
Should be review. So we are going fast.
You have the power to slow us down.
Our momentum equation
2
du
1
a
r
2
p (u) g 0
2
dt
(a z ) r
+ other forces
Now using the texts conventi

Lecture 4: Circulation and Vorticity
Circulation
Bjerknes
j
Circulation Theorem
Vorticity
Potential Vorticity
y
Conservation of Potential Vorticity
ESS227
Prof. Jin-Yi Yu
Measurement of Rotation
Circulation and vorticity are the two primary
measures of r

Lecture 5: Waves in Atmosphere
Perturbation Method
Properties of Wave
Shallow Water Gravity Waves
Rossby Waves
ESS227
Prof. Jin-Yi Yu
Perturbation Method
With this method, all filed variables are separated into
two parts: (a) a basic state part and (b) a

Material from Chapter 4
Vorticity, Vorticity, Vorticity
Relative and planetary vorticity
Mid-latitude disturbances
Vorticity, divergence, in 3-D
Two important definitions
barotropic density depends only on
pressure. And by the ideal gas equation,
sur

Outline
1. Review: Material Derivative
2. Conservation of Mass and Scale
analysis
Lagrangian and Eulerian derivations of
continuity equation
Scale analysis of the momentum equations
Scale analysis of the continuity equation
Material Derivative
Calculate t

A Diversion
Santa Ana Winds
Quasi-Geostrophic
Derive a system of equations that is close
to geostrophic and hydrostatic balance,
but includes the effects of ageostrophic
wind
Comes from scale analysis of equations of
motion in pressure coordinates
Sca

Quasi-Geostrophic
Derive a system of equations that is close
to geostrophic and hydrostatic balance,
but includes the effects of ageostrophic
wind
Comes from scale analysis of equations of
motion in pressure coordinates
Scale analysis = make assumption

Vorticity, Vorticity, Vorticity
Two important definitions
barotropic density depends only on
pressure. And by the ideal gas equation,
surfaces of constant pressure, are
surfaces of constant density, are surfaces
of constant temperature.
baroclinic densi