• Simplify Omega eqn by:
  1. assume sinusoidal variation in x, y, and P
  2. use same wavelength L in x and y directions

• Notes:
  1. sinusoidal P variation consistent with bowstring model
  2. for shorter wavelengths (= larger wavenumber k) the Laplacian terms would have more weight.
  3. want to separate contribution for the size of the solenoid from the size of the coefficient in each term:
     • use the n's to measure the size of the solenoids.
       • Each n is the number of unit-sized solenoids that fit within the solenoid observed.
       • small n means the solenoid has small area
       • smaller n means the advection would be larger
     • use the C's to measure the coefficients. These are functions of L (and hence of k).

• Terms not equally weighted: (consult Table 4.1)
  • for small wavelength (~ 2000 km = L): thickness advection has much larger coefficient. So for given size solenoids thickness advection stronger
  • for middle-size wavelength (~ 4000 km = L): the two coefficients are comparable.
  • for large wavelength (~ 6000 km = L): differential vorticity advection has much larger coefficient.
  • Note: the relative weighting changes in a similar sense for the surface pressure tendency (right side of Table 4.1). However, vorticity advection has a stronger effect in general (e.g. for the middle-size waves).

• How might you use this information?
  • might expect T advection to be more important influence on vertical motion (and surface P changes) when looking at a short wave
  • T advection not important for planetary waves: vorticity advection more important for vertical motion (and surface P changes).

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