Greens Function of the Linearized de Saint-Venant Equations

We derive and discuss the Greenʹs function of the linearized de Saint-Venant equations (LSVEs) for shallow water waves in channels and rivers. The analysis offers a unified description of previous results on LSVEs regarding, in particular, the existence of three simple linear waves whose interplay determines all the evolution of the solution, the role of the Froude number (F) in all its range of variability (both in subcritical and supercritical conditions), and the physical reason of the instability for F>2 and its and its convective nature.