Addendum: Hidden symmetries, trivial conservation laws and Casimir invariants in geophysical fluid dynamics (2018 J. Phys. Commun. 2 115018)

Abstract An extension is proposed to the internal symmetry transformations associated with mass, entropy and other Clebsch-related conservation in geophysical fluid dynamics. Those were previously parameterized an arbitrary function  of materially conserved Clebsch potentials. The consists adding potential vorticity q list fields on which a new G mathvariant="italic"> depends. If }=q{ A }(s)$?> = q mathvariant="italic"> ( s stretchy="false">) , where specific s then trivial gives rise law. Otherwise, non-trivial law exists. Moreover, notions Casimir invariants are defined. All symmetries that become hidden following reduction phase space non-canonical Hamiltonian formulation for fluids, while all laws invariants.