  Stationary gravity waves, such as mountain lee waves, are effectively
described by Grimshaw's dissipative modulation equations even in high altitudes
where they become nonlinear due to their large amplitudes. In this theoretical
study, a wave-Reynolds number is introduced to characterize general solutions
to these modulation equations. This non-dimensional number relates the vertical
linear group velocity with wavenumber, pressure scale height and kinematic
molecular/eddy viscosity. It is demonstrated by analytic and numerical methods
that Lindzen-type waves in the saturation region, i.e. where the wave-Reynolds
number is of order unity, destabilize by transient perturbations. It is
proposed that this mechanism may be a generator for secondary waves due to
direct wave-mean-flow interaction. By assumption the primary waves are exactly
such that altitudinal amplitude growth and viscous damping are balanced and by
that the amplitude is maximized. Implications of these results on the relation
between mean-flow acceleration and wave breaking heights are discussed.
