  We analyze the linear stability of monoclinal traveling waves on a constant
incline, which connect uniform flowing regions of differing depths. The
classical shallow-water equations are employed, subject to a general resistive
drag term. This approach incorporates many flow rheologies into a single
setting and enables us to investigate the features that set different systems
apart. We derive simple formulae for the onset of linear instability, the
corresponding linear growth rates and related properties including the
existence of monoclinal waves, development of shocks and whether instability is
initially triggered up- or downstream of the wave front. Also included within
our framework is the presence of shear in the flow velocity profile, which is
often neglected in depth-averaged studies. We find that it can significantly
modify the threshold for instability. Constant corrections to the governing
equations to account for sheared profiles via a 'momentum shape factor' act to
stabilize traveling waves. More general correction terms are found to have a
nontrivial and potentially important quantitative effect on the properties
explored. Finally, we have investigated the spatial properties of the dominant
(fastest growing) linear modes. We derive equations for their amplitude and
frequency and find that both features can become severely amplified near the
front of the traveling wave. For flood waves that propagate into a dry
downstream region, this amplification is unbounded in the limit of high
disturbance frequency. We show that the rate of divergence is a function of the
spatial dependence of the wave depth profile at the front, which may be
determined straightforwardly from the drag law.
