 Displacement pseudomomentum of an internal gravity wave

The displayed displacement convention is the negative of the usual positive-frequency wave pseudomomentum $k\overline{E}/\omega$ for a rightgoing internal gravity wave. Here energy per unit reference mass density is $\overline{E}=|\hat{\sigma }{|}^2/(2N^2)$. From the buoyancy polarization of a plane internal gravity wave, horizontal averaging gives $\overline{{\zeta }_{x}p}=km|\hat{\sigma }{|}^2/(2N^2{K}^2)=c_{gz}P$, where $p$ is kinematic pressure. The sign convention changes both density and flux and leaves their propagation at the group velocity unchanged.