= Solution
The <quasi-geostrophic potential vorticity> perturbation combines relative <vorticity>, $\nabla_h^2\psi'$, with the stretching contribution $f_0^2\partial_z(N^{-2}\psi'_z)$. The latter measures how buoyancy surfaces and rotating fluid columns are displaced in a stratified fluid. Even a flow with no vertical dependence can have nonzero relative vorticity, while its explicit stretching term vanishes.
For a vertically uniform plane wave with horizontal wavenumbers $(k,l)$, $q'=-(k^2+l^2)\psi'$. Substitution gives
$$
\omega-Uk=-\frac{\beta k}{k^2+l^2},\qquad
\boxed{c_{px}-U=-\frac{\beta}{k^2+l^2}<0\quad(\beta>0).}
$$
Thus phase propagates westward relative to the current. Physically, northward parcel displacement carries lower background planetary vorticity into a region with larger $f$, requiring negative relative vorticity to conserve total <potential vorticity>; southward displacement requires positive relative vorticity. The velocity induced by that vorticity pattern shifts the displacement wave westward. This is a statement about phase motion, not a claim that every Rossby-wave packet has westward group velocity.
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