COMPLETE DERIVATION OF 2D SHALLOW-WATER MODEL FROM THE PRIMITIVE EQUATIONS GOVERNING GEOPHYSICAL FLOWS Muhammad Salihi Bin Abdul Hadi, Mohd Zaini Bin Mustapa & Shahbudin Bin Saad Institute of Oceanography and Maritime Studies (INOCEM), Faculty of Science, International Islamic University Malaysia, Jalan Sultan Ahmad Shah, 25200 Kuantan Pahang DM, Malaysia E-mail: salihi@iium.edu.my ABSTRACT 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. Keywords: 2D shallow water, geophysical flows, primitive equations. 1. INTRODUCTION Consider the respective three momentum conservation equations and the continuity equation out of seven primitive equations governing geophysical flows under Boussinesq, Newtonian-Fluid and Reynolds-Averaged assumptions, in Cartesian coordinate as follows [1] ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) in which where are the three components of velocity, is the Coriolis parameter, is the pressure, is the gravitational acceleration, is the density of the fluid, is the mean density, is the lateral eddy viscosity, is the vertical eddy viscosity and is representing any field variable.