  Oceanic near-inertial waves - internal waves with frequencies close to the
local Coriolis frequency $f_0$ - are strongly influenced by the presence of
mean currents. To study this influence, Young and Ben Jelloul (1997) derived an
asymptotic model that describes the slow modulation of the amplitude of these
waves about their rapid oscillation at frequency $f_0$. Here we show that this
model can be obtained within a variational framework, by (Whitham) averaging
the Lagrangian of the hydrostatic-Boussinesq equations over the wave period
$2\pi/f_0$. The derivation leads to a variational formulation of the Young-Ben
Jelloul model from which its conservation laws can be obtained systematically.
