# Isn't Green's law for shallow water waves contradicting the theoretical principles of the hydraulic jump phenomena?

I ask this question in order to qlarify a misunderstanding i have about Green's law. Green's law is a direct consequence of the principle of conservation of energy flux , which implies the amplitude of shallow water waves behaves like $$h^{-1/4}$$ where h is the local mean water depth. On the other hand, Green's law applies to tsunamis, which are manifestation of the moving "version" of the hydraulic jump phenomena. This phenomena is charecterized by loss of energy (non-conservation principle) due to turbulent flow at the transition region. So how can one make these two aspects of the same phenomena (tsunami) not at odd with each other?