  While it is known that trapped lee waves propagating at low levels in a
stratified atmosphere exert a drag on the mountains that generate them, the
distribution of the corresponding reaction force exerted on the atmospheric
mean circulation, defined by the wave momentum flux profiles, has not been
established, because for inviscid trapped lee waves these profiles oscillate
indefinitely downstream. A framework is developed here for the unambiguous
calculation of momentum flux profiles produced by trapped lee waves, which
circumvents the difficulties plaguing the inviscid trapped lee wave theory.
Using linear theory, and taking Scorer's two-layer atmosphere as an example,
the waves are assumed to be subject to a small dissipation, expressed as a
Rayleigh damping. The resulting wave pattern decays downstream, so the momentum
flux profile integrated over the area occupied by the waves converges to a
well-defined form. Remarkably, for weak dissipation, this form is independent
of the value of Rayleigh damping coefficient, and the inviscid drag, determined
in previous studies, is recovered as the momentum flux at the surface. The
divergence of this momentum flux profile accounts for the areally-integrated
drag exerted by the waves on the atmosphere. The application of this framework
to this and other types of trapped lee waves potentially enables the
development of physically-based parametrizations of the effects of trapped lee
waves on the atmosphere.
