 Westward tilt and poleward eddy heat flux

For a disturbance proportional to $\mathrm{Re}[a(z)e^{i\varphi (z)}{e}^{ik(x-ct)}]$, westward phase tilt means ${\varphi }_z>0$ for $k>0$. With $v^{\prime }={\psi }_x^{\prime }$ and $b^{\prime }=f_0{\psi }_z^{\prime }$, a zonal average gives the displayed positive flux in the northern hemisphere, up to any meridional amplitude and time-growth factors. When the background buoyancy decreases northward, this flux extracts mean available potential energy and supports growing eddies.