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.

中文翻译：

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基于有限体积广义垂直坐标的海洋模型中垂直拉格朗日重映射方法入门

本文提供了有关海洋模型的数学，物理和数值基础的入门知识，这些基础是使用有限体积的广义垂直坐标方程式制定的，并使用垂直拉格朗日重映射方法来演化海洋状态。我们在强海洋方程组（偏微分方程）和弱海洋方程组（有限体积积分方程）中都考虑了控制海洋方程的数学结构，从而能够理解其物理内容，并为开发数值算法提供了物理数学框架。拉格朗日重映射方法与使用有限体积广义垂直预算编写的海洋方程之间建立了联系。