Vorticity equation

The vorticity equation describes the production and destruction of vorticity in a stratified, Boussinesq fluid

${\frac {D{\vec {\omega }}}{Dt}}=\underbrace {({\vec {\omega }}\cdot \nabla ){\vec {u}}} _{\text{stretching/tilting}}-\underbrace {{\frac {g}{\rho _{0}}}\nabla \times (\rho {\hat {k}})} _{\text{baroclinic production}}+\underbrace {\nu \nabla ^{2}{\vec {\omega }}} _{\text{viscous diffusion}}$