Vorticity
85
Summary
There are basically four mechanisms of vorticity change in a rotating, stratified liquid, i.e., vortex stretching, vortex tilting, baroclinic
vorticity production and vorticity diffusion.
The concept of potential vorticity Π λ refers to a family of possible
scalar invariants in flows, usually parameterized by a conserved quantity λ, whose general form is
Π λ =
ω +2Ω
ρ
·∇λ
where ω is the local vorticity vector.
For the constant density shallow-water equations, the most commonly
used invariant is the shallow-water potential vorticity
Π=
ζ + f
H
where ζ is the vertical component of the vorticity vector, f the Coriolis
parameter and H the total layer depth.
85
Summary
There are basically four mechanisms of vorticity change in a rotating, stratified liquid, i.e., vortex stretching, vortex tilting, baroclinic
vorticity production and vorticity diffusion.
The concept of potential vorticity Π λ refers to a family of possible
scalar invariants in flows, usually parameterized by a conserved quantity λ, whose general form is
Π λ =
ω +2Ω
ρ
·∇λ
where ω is the local vorticity vector.
For the constant density shallow-water equations, the most commonly
used invariant is the shallow-water potential vorticity
Π=
ζ + f
H
where ζ is the vertical component of the vorticity vector, f the Coriolis
parameter and H the total layer depth.