Undergraduate Course

Hydrodynamics and Shocks

Level 4 Physics, 1st term, about 26 lectures
Dr Jerry Chittenden

Have you ever sat on an aeroplane and wondered how it manages to stay in the sky?  
Have you ever thought about why your beer falls out of its glass if you turn it upside down (its not as simple as you think).  
Ever wondered what determines the size of the impact crater when a meteorite hits the Earth?

These and many other questions will be tackled in a new course aimed at improving your understanding of the fundamentals of hydrodynamics and showing you how these are applied within research in shock physics.

Once the basic principles and equations are identified, their application can be illustrated for a number of interesting areas of applied physics which you may be aware of but maybe don't know how physics determines their behaviour, for example supersonic flight, vortexes and turbulence.  By also including shock physics, this opens the course up to include many of the current physics research disciplines which make extensive use of hydrodynamics.  These include the generation of shock waves in astrophysical objects, plasmas, inertial confinement fusion and in material studies experiments.  The course would spend roughly two-thirds on hydrodynamics and one third on shocks.

This is a course which introduces both practical and theoretical concepts in classical physics.  Whilst an applied physics approach will be followed, there should be a sufficient number of mathematical descriptions to avoid a purely descriptive approach.  The topics are largely untouched by other courses, but there are connections with astrophysics, plasma and space physics courses.

Proposed Syllabus

Introduce basic concepts in fluid flow

Sound waves and sound speed.  Standing waves, harmonics and resonance.  Viscosity and the Reynolds number.  Equations of hydrodynamics (Euler's equations, Navier Stokes equation, Bernoulli's equation), solitary waves & solitons. 

Concepts in hydrostatics and hydrodynamics

Displacement, buoyancy and drag.  Whirlpools and vortices.  Cavitation (the Rayleigh bubble problem).  Turbulence.

Principles of flight

Lift.  Supersonics, sonic booms, hypersonics.  lavall nozzles.

Flow driven instabilities

Rayleigh-Taylor, Kelvin-Helmholtz, Richtmeyer-Meshkov.

Shock waves in nature 

Blast waves, supernovae remnants, Sedov-Taylor regime, colliding shocks and Mach stems.

Theoretical model of shocks

Rankine-Hugoniot shock jump conditions, Riemann invariants, the equation of state in compressed solids, isentropic compression.

Shocks in solids and plasmas

Compression, rarefraction and spallation.  Radiative cooling and radiation transport in shocks, sub-critical and super-critical waves, magnetic fields in shocks, shock waves in inertial confinement fusion, the Vishniac instability.

Methods of generating shock waves

Gas-guns, explosives, lasers, pulsed power.