Diabatically forced quasi-geostrophic potential vorticity
= Diabatically forced quasi-geostrophic potential vorticity
{title2=$D_gq/Dt=(f_0/N^2)R_z$}
For a <Boussinesq approximation>, constant <buoyancy frequency> $N$, and <buoyancy> heating rate $R$, the <quasi-geostrophic potential-vorticity equation> becomes $D_gq/Dt=(f_0/N^2)R_z$, where $q=\nabla_h^2\psi+(f_0^2/N^2)\psi_{zz}+\beta y$. Heating changes the vertical gradient of buoyancy and therefore produces a potential-vorticity tendency proportional to its height derivative.