Complete derivation of 2D shallow-water model from the primitive equations governing geophysical flows

• Main Authors: Abdul Hadi, Muhammad Salihi, Mustapa, Mohd Zaini, Saad, Shahbudin
• Format: Conference or Workshop Item
• Language: English; English
• Published: 2012
• Subjects: QA Mathematics; TC Hydraulic engineering. Ocean engineering
• Online Access: http://irep.iium.edu.my/27578/1/Full_Derivation_of_2D_Shallowv1.pdf; http://irep.iium.edu.my/27578/4/complete_derivation_of_2d_shallow_water_model_from_the_equations_governing_geophysical_flows.pdf; http://irep.iium.edu.my/27578/; http://martec.umt.edu.my/files/2012/10/list-of-titles-r1.pdf

The fact that the 2D shallow-water model has been used for decades is such a long time that a complete reference on how to derive it from the primitive equations either has likely to become a very rare article or written in a way that is very complicated for the newcomers. Certain physical assumptions and mathematical theorem should be acquired in order to fully understand how the complete 2D shallow-water model is derived which are often being skipped in many recent ocean modelling text books. In this paper, full derivation of the model that consist of momentum conversation in Cartesian coordinates and the continuity equations will be shown in the simplest way to satisfy the curiosity of fresh physical oceanographers.