Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling

John Marshall, Chris Hill, Lev Perelman, Alistair Adcroft

Research output: Contribution to journalArticlepeer-review

1088 Scopus citations


Ocean models based on consistent hydrostatic, quasi-hydrostatic, and nonhydrostatic equation sets are formulated and discussed. The quasi-hydrostatic and nonhydrostatic sets are more accurate than the widely used hydrostatic primitive equations. Quasi-hydrostatic models relax the precise balance between gravity and pressure gradient forces by including in a consistent manner cosine-of-latitude Coriolis terms which are neglected in primitive equation models. Nonhydrostatic models employ the full incompressible Navier Stokes equations; they are required in the study of small-scale phenomena in the ocean which are not in hydrostatic balance. We outline a solution strategy for the Navier Stokes model on the sphere that performs efficiently across the whole range of scales in the ocean, from the convective scale to the global scale, and so leads to a model of great versatility. In the hydrostatic limit the Navier Stokes model involves no more computational effort than those models which assume strict hydrostatic balance on all scales. The strategy is illustrated in simulations of laboratory experiments in rotating convection on scales of a few centimeters, simulations of convective and baroclinic instability of the mixed layer on the 1- to 10-km scale, and simulations of the global circulation of the ocean.

Original languageEnglish (US)
Article number96JC02776
Pages (from-to)5733-5752
Number of pages20
JournalJournal of Geophysical Research: Oceans
Issue numberC3
StatePublished - 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geophysics
  • Oceanography
  • Forestry
  • Aquatic Science
  • Ecology
  • Water Science and Technology
  • Soil Science
  • Geochemistry and Petrology
  • Earth-Surface Processes
  • Atmospheric Science
  • Space and Planetary Science
  • Earth and Planetary Sciences (miscellaneous)
  • Palaeontology


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