When the horizontal length scale of fluid flow is much greater than its vertical scale, such as during tsunamis or coastal floods, the Navier–Stokes equations can be depth-averaged to yield the shallow-water equationsShallow-water equations that are applicable only to shallow-water waves. These equations rely upon two crucial assumptions, that (1) accelerations in the vertical direction are negligible; and (2) velocities in the horizontal direction are constant throughout the depth. This chapter will employ these two assumptions to modify the Navier–Stokes equations in order to derive specialized continuity and momentum equations for shallow-water wave propagation.