The consequences of assuming that density is conserved in the problem of determining absolute velocities are investigated. Two questions are considered: (i) the constraints that the density must satisfy to be compatible with the assumed geostrophic and hydrostatic dynamics and (ii) whether and to what extent the indeterminacy in this dynamics is removed by this additional assumption.
Frenzen, C. L., and Alex C. Warn-Varnas. 1988. "Implications of conservation equations for the determination of absolute velocities." Journal of Marine Research 46, (4). https://elischolar.library.yale.edu/journal_of_marine_research/1909