Advanced Ocean Modelling: Using Open-Source Software

Chapter 53D Level ModellingAbstract This chapter introduces the reader to fully three-dimensional hydrodynamiclevel models. Exercises address isolated oceanic eddies, eddy formation ina strait, density-driven exchange flows through a strait, coastal upwelling in threedimensions, the thermohaline deep circulation in the ocean, and, as a highlight,equatorially trapped Kelvin waves accompanying El-Niño events.5.1 The Basic Equations5.1.1 The BasicsThis section outlines the full three-dimensional equations governing the dynamicsof an incompressible fluid with a free surface. This comprises the momentum equations,the continuity equation, and a density-conservation equation, plus boundaryconditions.5.1.2 Conservation of MomentumAs in the vertical-ocean slice model, dynamic pressure is separated into twoparts:P = p + q (5.1)where (lower-case) p refers to the hydrostatic pressure field with reference to anundisturbed (horizontal) sea level, and q includes pressure effects imposed by atilted sea surface and by nonhydrostatic pressure contributions. Again, the first pressurepart p is diagnosed from the hydrostatic balance:∂p∂z =−(ρ − ρ o) g (5.2)J. Kämpf, Advanced Ocean Modelling, DOI 10.1007/978-3-642-10610-1 5,C○ Springer-Verlag Berlin Heidelberg 2010125