• Section 2: Orographic effects on development & cyclone motion
  1. effective vertical motion from topography (p. 201-203)
     Omega_s = (local chg of P_s) - (rho g V_s * Grad H)
     where subscript s refers to values at the surface of the smoothed topography, whose elevation is given by H.
  2. Since ground is source of motion, Omega is greatest at the ground and decreases monotonically above. This pattern differs from the "bowstring model".
     Divergence (D) can then be deduced:
     where Omega < 0 is where D > 0 (i.e. upslope motion)
     And, Omega > 0 is where D < 0 (i.e. downslope motion)

  3. The divergence pattern can be inserted into the QG vorticity eqn. Where:
     d zeta_a/dt = - f D
     upslope means D>0 so Zeta_a decreases -- consistent with vortex tube compression.
     downslope means D<0 so Zeta_a increases -- consistent with vortex tube stretching that "spins up" the rotation.

  4. Lee side trough tends to form as a result of westerlies encountering a north-south oriented mountain range. Theoretical basis can invoke conservation of potential vorticity (PV).
     For the shallow water equations, PV has a simple definition:
     PV = ( Zeta_a ) / h
     where the h here is the pressure interval between two isentropic surfaces.

  5. Surface cyclones (and anticyclones) have air circulating around them, so as they approach a mountain range one side of the low will have upslope motion and the opposite side will have downslope.
     The vorticity changes cause the low to be distorted as it approaches.
     For example, Fig. 9.9: A low approaching the Pacific northwest motion is held back on its northwest side and advanced on its southeast side (in both cases where downslope motion builds vorticity)
     The approaching low may appear to "jump" across the mountain as it reinforces a lee side trough even while part of the parent low is held back on the windward side. Fig. 9.11

  6. A Corrolary to the last item applies to a "quasi-stationary" low on an area of sloping topography.
     Example: consider a North-south mountain rage. On the lee side a low moves south because downslope motion on the south side increases vorticity there, upslope motion on the north side decreases vorticity there. Fig. 9.11b is relevant as is a schematic diagram in the notes.
     On the west side of that range, the low moves northward by the same reasoning.
     Highs move the same direction as do the lows.

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