  Mountain-generated inertia-gravity waves (IGWs) affect the dynamics of both
the atmosphere and the ocean through the mean force they exert as they interact
with the flow. A key to this interaction is the presence of critical-level
singularities or, when planetary rotation is taken into account, inertial-level
singularities, where the Doppler-shifted wave frequency matches the local
Coriolis frequency. We examine the role of the latter singularities by studying
the steady wavepacket generated by a multiscale mountain in a rotating linear
shear flow at low Rossby number. Using a combination of WKB and saddle-point
approximations, we provide an explicit description of the form of the
wavepacket, of the mean forcing it induces, and of the mean-flow response.
  We identify two distinguished regimes of wave propagation: Regime I applies
far enough from a dominant inertial level for the standard ray-tracing
approximation to be valid; Regime II applies to a thin region where the
wavepacket structure is controlled by the inertial-level singularities. The
wave--mean-flow interaction is governed by the change in Eliassen--Palm (or
pseudomomentum) flux. This change is localised in a thin inertial layer where
the wavepacket takes a limiting form of that found in Regime II. We solve a
quasi-geostrophic potential-vorticity equation forced by the divergence of the
Eliassen--Palm flux to compute the wave-induced mean flow. Our results,
obtained in an inviscid limit, show that the wavepacket reaches a
large-but-finite distance downstream of the mountain (specifically, a distance
of order $k_*^{1/2} \Delta^{3/2}$, where $k_*^{-1}$ and $\Delta$ measure the
wave and envelope scales of the mountain) and extends horizontally over a
similar scale.
