Buoyancy displacement variable ($b_x=-N^2\theta$)

In a radially stratified shearing sheet, one can normalize the scalar buoyancy perturbation by writing $b_x=-N^2\theta$ and $D_t\theta =u_x+\xi {\nabla }^2\theta$. With this convention $\theta$ has dimensions of length, rather than temperature; $\xi$ is thermal diffusivity.