Wave pseudomomentum ($\mathbf{p}=\mathbf{k}\mathcal{A}$)

The wavevector times wave action gives the canonical momentum associated with translations of a wave's phase. It describes momentum exchange with a slowly varying mean fluid flow, rather than simply the spatial average of oscillating fluid momentum. For horizontal wavenumber $k$, its horizontal component is $kE/\hat{\omega }$. A convention using displacement pseudomomentum of an internal gravity wave instead has the opposite sign.