Conservation laws of shallow water theory and the Galilean relativity principle

Using an example of a model of shallow water theory, we show that the compatibility analysis of Hugoniot conditions for various basic systems of conservation laws in a coordinate system moving together with a strong discontinuity can lead to erroneous results. This is connected with the hierarchy of conservation laws of shallow water theory under a Galilean transformation, by which the law of conservation of the total energy is unconditionally noninvariant under this transformation. As a result, the Hugoniot condition corresponding to this conservation law depends on movement speed of the inertial coordinate system. It is shown that the specified defect of the classical model of shallow water theory is absent in the vortex shallow water model suggested by V. M. Teshukov.