An important qualitative difference between the hydrostatic and nonhydrostatic shallow flows is that the latter supports solitary waves. The figure shows flow vectors and the density contours that represent the position of the free surface of the shallow fluid in numerical simulation of the full Euler equations. Notice a soliton propagating upstream of the ridge. This feature is faithfully reproduced in simulations of the Green-Naghdi equations but absent in simulations of the standard shallow water equations.
