= Westward tilt and poleward eddy heat flux
{title2=$\overline{v'b'}=(f_0k/2)|\Psi|^2\phi_z$}
For a disturbance proportional to $\operatorname{Re}[a(z)e^{i\phi(z)}e^{ik(x-ct)}]$, westward phase tilt means $\phi_z>0$ for $k>0$. With $v'=\psi'_x$ and $b'=f_0\psi'_z$, 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.
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