Class number 2 /27  Jan 24,  2011 More on thermodynamics

Loose ends from last class:

Today's material:

Recasting the 3 variables needed for moist air thermodynamics (at equilibrium).

1. pressure -- altitude for all practical purposes
2. total water mixing ratio q -- conserved, linearly mixing (Dewpoint is monotonic, but not linear)
   
3. Conserved heat or entropy type variable... (handout)
   
• dry entropy, moist entropy, saturation moist entropy
  
• theta, theta-e, saturation theta-e
• dry static energy (s), moist static energy h, saturation """ h*?
• Desirable properties: conservation, linearity in mixing.
• Poor man's pseudo-buoyancy (parcel T excess) in s-h-h* diagrams

Relevant journal literature: (somewhat random selection)

Defining the variables

Budgets of entropy in convecting atmopsheres

From thermo to vertical momentum dynamics: book stuff

• Reversible vs. pseudoadiabatic T during ascent (fig)
  
• Density temperature and virtual temperature
• Equations of motion (including w) - the full PGF
• The buoyancy "force" on a density anomaly
• Buoyancy viewed as a vorticity source
  
• Buoyancy and nonhydrostatic PGF "" " "
  
• What is nonhydrostatic p'
• p' in a density current   a warm bubble   a cloud in shear
• Net upward force on a crenellated buoyant blob (in 2D): pdf
  
• crenellated solutions by fft in matlab   figure   code1   code2
  

How to invert (entropy, qv, p) to get density (for buoyancy): HOMEWORK

Open questions, assignments, and loose ends for next class:

Testable questions about today's material:

• {p, T, theta} -- no (why?) 
• {q, RH, T}  
  
• {qtot, p, h}
  
• {}