Gravitational potential energy is conserved along neutral surfaces in ocean

It is recapitulated that the gravitational potential energy that is conserved along the neutral surfaces needs two terms, one from buoyancy and the other from gravity. I also show a mathematical identity for the time change of this gravitational potential energy which can be interpreted as exchange of energy amongst kinetic, internal, and gravitational potential forms. Movements along the neutral surface conserve the gravitational potential energy and it is shown that not only conversions into and out of the gravitational potential energy balance, but that each of the conversion terms is zero.