Potential vorticity dynamics on a β-plane — atmospheric wave propagation and jet stream meandering
Parameters
∂q/∂t + J(ψ,q) = 0 q = ∇²ψ - ψ/L_d² + βy
Rossby waves propagate westward relative to the mean flow. Baroclinic instability occurs when vertical shear overcomes stratification, releasing potential energy to grow large-scale eddies (cyclones/anticyclones).