## Abstract

This paper provides a primer on the mathematical, physical, and numerical foundations of ocean models that are formulated using finite volume generalized vertical coordinate equations and that use the vertical Lagrangian-remap method to evolve the ocean state. We consider the mathematical structure of the governing ocean equations in both their strong formulation (partial differential equations) and weak formulation (finite volume integral equations), thus enabling an understanding of their physical content and providing a physical-mathematical framework to develop numerical algorithms. A connection is made between the Lagrangian-remap method and the ocean equations as written using finite volume generalized vertical budgets. Thought experiments are offered to exemplify the mechanics of the vertical Lagrangian-remap method and to compare with other methods used for ocean model algorithms.

Original language | English (US) |
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Article number | e2019MS001954 |

Journal | Journal of Advances in Modeling Earth Systems |

Volume | 12 |

Issue number | 10 |

DOIs | |

State | Published - Oct 1 2020 |

## All Science Journal Classification (ASJC) codes

- Global and Planetary Change
- Environmental Chemistry
- General Earth and Planetary Sciences

## Keywords

- finite volume methods
- fluid mechanics
- generalized vertical coordinates
- ocean model equations
- oceanography
- vertical Lagrangian remapping