Numerical simulations are carried out to determine the steady-state gravity
-wave structure above a circularly-symmetric, bell-shaped hill when the win
d backs with height. Two types of idealized basic state flow are considered
; one representing the advection of a uniform baroclinic shear flow, and th
e other being a flow of constant speed but with a wind vector that rotates
uniformly in height. Of particular interest is the nature of the critical l
evel processes that must appear at all heights due to the three-dimensional
ity of the wave field and the rotation of the wind vector. As suggested by
linear theory, a critical level or asymptotic wake is found downwind of the
hill at any height, where 'downwind' refers to the wind at that level only
. For small hills (where the nondimensional mountain height << unity), the
simulated vertical momentum flux profiles are in very good agreement with l
inear hydrostatic wave theory if it is assumed that wave-component critical
-level absorption is total (i.e. no wave transmission or reflections are pe
rmitted). The vertical momentum fluxes generated by a 1 km high hill show n
onlinear enhancement by a factor of about 1.5. An interesting feature of th
e gravity-wave field generated by this 1 km mountain is an asymptotic wake
that is dominated by a single intense shear layer in which the Richardson n
umber is order unity.