Geopotential Tendency Equation
Based on QG theory
- QG Vorticity equation
- Geopotential tendency equation
QG equations
Dgug
Dt − f0va − βyvg = 0 Dgvg
Dt + f0ua + βyug = 0
∂ua
∂x + ∂va
∂y + ∂ω
∂p = 0
Dg
Dt ( ∂Φ
∂p ) + σω = − J cp
R p
Geopotential Tendency Equation
QG vorticity equation
QG thermodynamic energy equation
∂
∂t
ζg+ v
g⃗⋅ ∇ ( f +
ζg) = f
0∂ω
∂p
D
gDt ( ∂Φ
∂p ) + σω = − J
c
pR p
Geopotential Tendency Equation
Ingredient (function of and )
Φ ω
∇
2(∂Φ
∂t
)= − f
0v
g⃗⋅ ∇ ( f +
ζg) + f
02∂ω
∂p
∂
∂t ( − ∂Φ
∂p ) = − v
g⃗ ⋅ ∇ ( − ∂Φ
∂p ) + σω + J
c
pR p
Geopotential Tendency Equation
Ingredient (function of and )
Geopotential tendency equation
Φ ω
∇
2(∂Φ
∂t
)= − f
0v
g⃗⋅ ∇ ( f +
ζg) + f
02∂ω
∂p
∂
∂t ( − ∂Φ
∂p ) = − v
g⃗ ⋅ ∇ ( − ∂Φ
∂p ) + σω + J
c
pR p
∇2 + ∂
∂p ( f02
σ ∂
∂p ) ( ∂Φ
∂t ) = − f0vg⃗ ⋅ ∇( f + ζg) − ∂∂p [− f02
σ v g⃗ ⋅ ∇(− ∂Φ∂p )]
