• Notes:

  1. Define "omega" as pressure velocity: DP/Dt
  2. Define "d" as partial derivative and D as a total derivative, except when used alone,
  3. When "D" used alone: it indicates Divergence.
  4. C (= -D) indicates convergence
  5. Recall continuity eqn in P coor: D = du/dx + dv/dy = - d(omega)/dP
  6. Note that the vertical integral of D = the surface omega: when the integral goes to the top of the atmosphere (P=0)

• "Bowstring" model

  • Assumes that omega has a single max
  • Max is in middle troposphere at 500 mb. (In reality it is between 400 -700 mb typically)
  • omega much smaller at the surface and tropopause

• Some consequences of a bowstring profile of omega

  • d/dP of omega = 0 where omega is a max -- this is the nondivergent level.
  • d/dP of omega will have opposite sign in upper and lower atmosphere. Hence D reverses sign between upper and lower troposphere.
  • "Dines compensation"
    • since omega at surface is small, it follows from vertical integral of D that levels where D>0 are nearly cancelled by D<0 at other levels.
  • can draw a circulation in a vertical cross section with:
    • D<0 below a region of rising motion and D>0 above it.
    • D>0 below a region of sinking motion and D<0 above it.

• Typical peak values in midlatitude cyclones:

  • D ~ 1 - 5 x 10^-7 s^-1
  • omega ~ 0.1 - 0.7 Pa s^-1
  • omega at surface ~ 0.01 - 0.05 x Pa s^-1

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