Study Guide (lecture # 13)
Book pages: 130-145
Review:
(lecture # 12)
- "Global" definitions of APE
- limited area APE -- Interpretation of:
- efficiency factor
- diabatic processes
Today's topics:
- conversion between APE & KE
(mathematical, conceptual, intuitive discussions)
- zonal & eddy energetics (formulas)
Jargon:
“closed” domain, “equivalent barotropic”,
non-dimensional form, perturbation form, static state
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Limited area energetics (conclusion):
(Section 4.5.2)
Main point repeatedly seen today:
-
“warm air rising and/or cold air sinking converts APE into KE”
Conversion between APE & KE
- demonstration of link mathematically
- only contributors to average of omega*alpha are by alpha
deviations from horizontal average
- only contributor to (V dot Del Phi) is divergent
advection
- conceptual model for developing & decaying stages
must focus on relatively warmer and colder regions
CKA>0 for developing stage (APE -> KE)
CKA<0 for decaying stage
magnitude of CKA during developing stage > than during decay stage
- implies that global average CKA is >0
- expressed in quasi-geostrophic theory as a vertical heat flux, hence:
- "warm air rising and/or cold air sinking converts APE
into KE"
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Eddy versus Zonal Average Energetics:
(Start Section 4.6)
- instead of limited volume, divide APE & KE into [ ] and eddy parts;
calculate zonal mean of each.
- can match terms with what seen before in: (4.16), (4.20), (4.30), and (4.34).
- 4 “reservoirs” of energy: AZ, AE,
KZ, KE
- generation (2 terms), destruction (2 terms)
- conversions (4 terms)
- CZ (AZ to KZ)
can be approximated using [v] and [ug] which are more
easily measured than [ omega ] and [ alpha ]