The fluxes of the momentum and continuity equations, Γ(w), provide information about the speed of the waves. The eigenvalues of the Jacobian matrix of the fluxes evaluated at a direction provided by an arbitrary unit vector are

where c is the wave celerity,

The eigenvalues of the Jacobian of the fluxes provide information about the velocity at which information is propagated. When | u ⋅ n| > c, the eigenvalues have different sign and information is propagated both upward and downward. If | u ⋅ n| < c, all eigenvalues have the same sign and all waves travel in the same direction.

The Froude number Fr is a dimensionless number typically used to define the flow regime by specifying the ratio of the inertial forces to gravity forces. In case of the Shallow Water Equations, it is defined as

The flow regime can be divided into subcritical flow, Fr < 1, and supercritical flow, Fr > 1. This classification is specially important when defining boundary conditions. In supercritical flows, all characteristics must be specified at inlets and extrapolated from the domain at outlets. In subcritical flows, the characteristics are partially specified from exterior values and partially extrapolated from interior values for both inlets and outlets.