There is a long-standing debate in the literature of stratified flows over topography concerning the correct dimensionless number to refer to as a Froude number. Common definitions using external quantities of the flow include
$U/(ND)$,
$U/(Nh_{0})$, and
$Uk/N$, where
$U$ and
$N$ are, respectively, scales for the background velocity and buoyancy frequency,
$D$ is the depth, and
$h_{0}$ and
$k^{-1}$ are, respectively, height and width scales of the topography. It is also possible to define an internal Froude number
$Fr_{\unicode[STIX]{x1D6FF}}=u_{0}/\sqrt{g^{\prime }\unicode[STIX]{x1D6FF}}$, where
$u_{0}$,
$g^{\prime }$, and
$\unicode[STIX]{x1D6FF}$ are, respectively, the characteristic velocity, reduced gravity, and vertical length scale of the perturbation above the topography. For the case of hydrostatic lee waves in a deep ocean, both
$U/(ND)$ and
$Uk/N$ are insignificantly small, rendering the dimensionless number
$Nh_{0}/U$ the only relevant dynamical parameter. However, although it appears to be an inverse Froude number, such an interpretation is incorrect. By non-dimensionalizing the stratified Euler equations describing the flow of an infinitely deep fluid over topography, we show that
$Nh_{0}/U$ is in fact the square of the internal Froude number because it can identically be written in terms of the inner variables,
$Fr_{\unicode[STIX]{x1D6FF}}^{2}=Nh_{0}/U=u_{0}^{2}/(g^{\prime }\unicode[STIX]{x1D6FF})$. Our scaling also identifies
$Nh_{0}/U$ as the ratio of the vertical velocity scale within the lee wave to the group velocity of the lee wave, which we term the vertical Froude number,
$Fr_{vert}=Nh_{0}/U=w_{0}/c_{g}$. To encapsulate such behaviour, we suggest referring to
$Nh_{0}/U$ as the lee-wave Froude number,
$Fr_{lee}$.