Advanced Ocean Modelling: Using Open-Source Software

Contents1 Introduction ................................................... 11.1 Fundamental Physical Laws . . ............................... 11.1.1 CartesianCoordinates ............................... 11.1.2 TheNavier-StokesEquations ......................... 11.1.3 Boundary Fluxes . ................................... 31.1.4 TheHydrostaticApproximation....................... 31.1.5 The Stability Frequency . . . . . . ........................ 41.2 Numerical Methods . . . . . ................................... 41.2.1 Finite Differences ................................... 41.2.2 Requirements for a Finite-Difference Model . . . . . . . ...... 51.3 Modelling with FORTRAN 95 . . . . . . . ........................ 51.3.1 Writing and Compiling Codes ........................ 51.3.2 Modular Source Codes . . . . . . . ........................ 61.4 VisualisationwithSciLab................................... 61.4.1 Writing SciLab Scripts ............................... 61.4.2 GIFAnimations .................................... 71.5 OrganisationofWork ...................................... 81.6 Download of Computer Codes . . . . . . . ........................ 82 1D Models of Ekman Layers .................................... 92.1 Useful Background Knowledge . . . . . . ........................ 92.1.1 Inertial Oscillations . . ............................... 92.1.2 Semi-implicitTreatmentoftheCoriolisForce ........... 102.2 The Surface Ekman Layer . . . ............................... 112.2.1 Boundary-Layer Equations . . . ........................ 112.2.2 Scaling:TheTemporalRossbyNumber ................ 112.2.3 Scaling:TheEkmanNumber ......................... 122.2.4 Solutions of the Boundary-Layer Equations ............. 132.2.5 Finite-Difference Equations . . ........................ 132.2.6 FormulationofDiffusionTerms....................... 142.2.7 Stability Criterion for Diffusion Terms . . . . ............. 14vii