Shallow water equations
（重定向自Shallow water model）
![Output from a shallow water equation model of water in a bathtub. The water experiences five splashes which generate surface gravity waves that propagate away from the splash locations and reflect off the bathtub walls.](/Images/godic/202502/10/Shallow_water_waves5348.gif")
![Tsunami generation and propagation, as computed with the shallow water equations (red line; without frequency dispersion)), and with a Boussinesq-type model (blue line; with frequency dispersion). Observe that the Boussinesq-type model (blue line) forms a soliton with an oscillatory tail staying behind. The shallow water equations (red line) form a steep front, which will lead to bore formation, later on. The water depth is 100 meters.](/Images/godic/202502/10/Tsunami_with_Boussinesq_and_Shallow_water_equations5348.gif")
The shallow water equations (also called Saint-Venant equations in its unidimensional form, after Adhémar Jean Claude Barré de Saint-Venant) are a set of hyperbolic partial differential equations (or parabolic if viscous shear is considered) that describe the flow below a pressure surface in a fluid (sometimes, but not necessarily, a free surface). The shallow water equations can also be simplified to the commonly used 1-D Saint-Venant equation.