Lancaster University

Introduction to continuum mechanics : mass, body force, contact force, global balance laws, decomposition of the contact force into shear and pressure components, particle trajectories, comoving coordinates, local balance laws and the continuity equation.

Static fluids : contact force in static fluids, equations of global and local hydrostatic equilibrium and their solutions in simple scenarios, derivation of Archimedes' principle.

Ideal Fluids : the Euler equation, incompressibility, steady flow and streamlines, Bernoulli's H-theorem and applications, vorticity and irrotational flow, circulation, Kelvin's circulation theorem and its application to tornados, vortex lines, comparison with magnetostatics, potential flow, no-through-flow boundary condition, fluid contact force on rigid bodies and d'Alembert's paradox with examples.

Newtonian fluids : Stress tensor, Newton's law of viscosity, Navier-Stokes equations, no-slip boundary condition, difficulties with solving the Navier-Stokes equations and the importance of computational fluid dynamics, Reynolds' number and hydrodynamic similarity, boundary layers, vortex shedding and resolution of d'Alembert's paradox, Kutta-Joukowski lift formula and flight, vortexinduced vibration.

Waves : compressible fluids, equations of state, linearised solutions to the fluid equations, gravity waves and their dispersion, acoustic waves and the speed of sound.

Fluid mechanics of plasmas : Two-fluid model of plasmas, stationary approximation for the ions, linearisation of the cold plasma equations, Langmuir oscillations and the plasma frequency, electromagnetic waves in plasmas and their dispersion, group velocity of signals in plasmas, application to long-range communication and pulsar distance measurements.

Knowledge and Understanding: on successful completion of the module students should be able to

(i) understand the origin, solution and application of the Navier-Stokes equations;

(ii) understand the wider applications of the Navier-Stokes theory to bio-, geo- and astrophysical systems;

Skills: on successful completion of the module students should be able to

(i) perform simple calculations of physically observable quantities relevant to the subject;

(ii) solve problems based on the application of the general principles of the physics of fluids

(E) Physics of Continuous Matter by B Lautrup