Geological fluid dynamics

(1) Elements of continuum mechanics (stress tensor, mechanical equilibrium, pressure)
(2) The equations of fluid mechanics (fluid, time derivative in fluid mechanics: lagrangian vs eulerian
description of a flow, mass conservation, momentum conservation for an inviscid flow)
(3) The Navier-Stokes equation (viscosity, viscous stress tensor, some exact solutions of the Navier-
Stokes equation)
(4) Dimensional analysis and similarity : Reynolds number, laminar vs turbulent flows
(5) Flows in the mantle (Stream function for 2D flows, Post-glacial rebound, subduction zone)
(6) Volcanic flows (Laminar eruption regime : controls on the eruption rate, spreading of lava
domes,Turbulent and compressible eruption regime : choking)
(7) Thermal convection (heat transport in a fluid, Rayleigh-Benard convection, Plumes and thermals).
(8) Surface and subsurface flows (aquifer and rivers).

Fluids play a major role in numerous geological processes from the core to the Earth surface. The
objective of this class is to introduce the main principles and equations of Fluid mechanics, and to apply them to the description of various geological systems.

The class requires solid bases in mathematics (differential equations) and in continuum mechanics.