4.12.2a_Tibet_Wu Guoxiong Tibet-CEOP.ppt[]

Ertel Potential Vorticity Equation
PV:
v
P = αζ
a
W ρP
= a
⋅ ∇θ
; (1)
v
= ζ ⋅ ∇θ
. (2)
PV equation:
Advection form:
∂P
P V P F
a Q
t
+ v
⋅ ∇ = v
=
∂
⋅ ∇ + v
& α θ αζ
⋅ ∇ . (3)
Divergence form:
dW ∂W
VW F a Q
dt t
+ ∇ ⋅ v
= v
=
∂
⋅∇ + v
θ ζ ⋅∇
. (4)
Dissipation
Heating