  This note aims at demonstrating the advantage of moving-water well-balanced
schemes over still-water well-balanced schemes for the shallow water equations.
We concentrate on numerical examples with solutions near a moving-water
equilibrium. For such examples, still-water well-balanced methods are not
capable of capturing the small perturbations of the moving-water equilibrium
and may generate significant spurious oscillations, unless an extremely refined
mesh is used. On the other hand, moving- water well-balanced methods perform
well in these tests. The numerical examples in this note clearly demonstrate
the importance of utilizing moving-water well-balanced methods for solutions
near a moving-water equilibrium.
