The vorticity equation describes the production and destruction of vorticity in a stratified, Boussinesq fluid
D ω → D t = ( ω → ⋅ ∇ ) u → ⏟ stretching/tilting − g ρ 0 ∇ × ( ρ k ^ ) ⏟ baroclinic production + ν ∇ 2 ω → ⏟ viscous diffusion {\displaystyle {\frac {D{\vec {\omega }}}{Dt}}=\underbrace {({\vec {\omega }}\cdot \nabla ){\vec {u}}} _{\text{stretching/tilting}}-\underbrace {{\frac {g}{\rho _{0}}}\nabla \times (\rho {\hat {k}})} _{\text{baroclinic production}}+\underbrace {\nu \nabla ^{2}{\vec {\omega }}} _{\text{viscous diffusion}}}
