Hierarchy of nonlinear models of the hydrodynamics of long surface waves

The derivation of shallow-water models taking into account the dispersion is based on the Euler equations for an ideal incompressible fluid on a rotating sphere, the mobility of the bottom surface being taken into account, while further passage along the hierarchy from completely nonlinear equations with dispersion towards simplifications proceeds with inheritance of the most important properties, in particular, the laws of conservation. It should be noted that the presence of the consistent balance equation of total energy makes it possible to carry out an additional control of calculations using the numerical methods of the solution instead of only confirming the physical validity of the NLD model.