= Eady-wave phase tilt and heat flux
{title2=$\overline{v'b'}=f_0A^2kK\alpha/2$}
For $\psi'=A[\cosh(Kz)\cos(kx)-\alpha\sinh(Kz)\sin(kx)]$ with $k,K,\alpha>0$, its <phase> increases with height and its crests tilt westward. The derivative $b'=f_0\psi'_z$ has decreasing continuous <phase> and eastward-tilting crests. Multiplying $v'=\psi'_x$ by $b'$ and averaging over a zonal <wavelength> gives the displayed <eddy buoyancy flux>, using $\cosh^2(Kz)-\sinh^2(Kz)=1$. Its sign is poleward for the associated eastward-increasing <thermal wind> in either hemisphere. An untilted separable perturbation has zero zonally averaged flux under periodic endpoint conditions.
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