Introduction à la dynamique des fluides géophysiques

Pré-requis nécessaires

Vector calculus, fluid mechanics, partial differential equations

Objectifs

On completing this course, students will be able to build and solve a simplified set of equations of motion applied to a basic atmospheric or oceanic phenomenon. Students will acquire knowledge about the physics of geophysical flows.

Compétences visées

• Relate oceanic phenomena to basic geophysical fluid dynamics processes
• Use mathematical techniques to solve geophysical fluid dynamics problems

Descriptif

Lecture notes (110pp, in English) are available for this course. Topics include

Chap 1. Governing equations

• quick reminder of classical fluid mechanics (Navier-Stokes equations)
• Boussinesq and hydrostatic approximations
• Equations of motion in a rotating frame
• Coriolis and centrifugal forces
• beta plane and f plane approximation

Chap 2. Geostrophic theory

• Geostrophic balance and divergence of geostrophic flow
• Taylor-Proudman theorem and its implications
• Thermal wind balance
• Impact of rotation and stratification on the hydrostatic balance

Chap 3. Shallow water dynamics

• Momentum and mass continuity equations for a single layer
• Potential vorticity in shallow water systems
• Linear wave dynamics
• Inertia-gravity waves
• Kelvin waves
• Barotropic Rossby waves
• Topographic Rossby waves
• Reduced-gravity shallow water system

Chap. 4 Wind-driven ocean circulation

• Reynolds stresses
• The surface and bottom Ekman layers
• Ekman transport and Ekman pumping
• Sverdrup balance
• The intensification of western boundary currents
• Inertial effects