Know the terms and parameters, as well as their meaning, in the equations of motion for a molecular viscous fluid on a rotating planet and characterise the relative importance of different terms in terms of dimensionless numbers (Rossby number, Richardson number).
Be acquainted with the Boussinesq approximation and Reynolds averaging procedure and be able to apply these to given equations of motion.
Be able to find solutions for simplified versions of the equations of motion for geophysical fluids (inertial oscillation, geostrophic flow, flow subject to conservation of potential vorticity, Ekman dynamics near bottom and surface boundary) and interpret the meaning of these solutions.
Be acquainted with the different large-scale waves in geophysical fluids: Kelvin waves, Poincaré waves, Rossby waves (planetary/topographic), be able to derive their dispersion relations and interpret the behaviour of these waves (including role of Rossby radius of deformation).
Know the quantitative effects of density stratification on dynamics of large-scale geophysical fluids: meaning of barotropic/barotropic modes, finding solutions for these modes, as well as for thermal wind and of geostrophic adjustment problems.
Know and understand the equations governing 3D quasi-geostrophic flow, including baroclinic instability and its key control parameters, and be able to find simple solutions of these equations.
The overall aim is to provide students with a solid background in modelling and analysing large-scale fluid motions in atmosphere and ocean.
The two key factors that control these motions are rotation and density stratification. Starting from the full equations of motion on a rotating planet, the so-called primitive equations will be derived by means of Reynolds decomposition and scaling analysis. With this subset, basic concepts and phenomena will be discussed: geostrophic balance, conservation of potential vorticity, Ekman boundary layer, barotropic and baroclinic waves, basic theory of turbulence, geostrophic adjustment and baroclinic instability.
|Complex numbers, methods to solve linear inhomogeneous ordinary differential equations, basic knowledge of linear partial differential equations (wave equation, diffusion equation, Laplace equation).|
Basic knowledge of wave dynamics: dispersion relation, phase velocity, group velocity.
Know the basic equations of motion for a mechanical system in the continuum limit.
Know the concepts of surface/volume forces, stress tensor, stress-strain relations for a Newtonian fluid.
|Verplicht materiaal-Aanbevolen materiaal|
|Cushman Roisin & Becker: Geophysical Fluid Dynamics, ISBN 978-0-12-088759-0|
BeoordelingThe mid-term and final exams will give a maximum of 45 points each. An additional 14 points can be earned by homework/quizzes during tutorials.
Final grade will be the total number of points divided by 10 and rounded to the nearest half grade.