  We study by a combination of analytical and numerical methods
multidimensional stability and transverse bifurcation of planar hydraulic shock
and roll wave solutions of the inviscid Saint Venant equations for inclined
shallow-water flow, both in the whole space and in a channel of finite width,
obtaining complete stability diagrams across the full parameter range of
existence. Technical advances include development of efficient multi-d Evans
solvers, low- and high-frequency asymptotics, explicit/semi-explicit
computation of stability boundaries, and rigorous treatment of channel flow
with wall-type physical boundary. Notable behavioral phenomena are a novel
essential transverse bifurcation of hydraulic shocks to invading planar
periodic roll-wave or doubly-transverse periodic herringbone patterns, with
associated metastable behavior driven by mixed roll- and herringbone-type waves
initiating from localized perturbation of an unstable constant state; and
Floquet-type transverse ``flapping'' bifurcation of roll wave patterns.
