UE Fields and fluids



Hydrodynamics part:
- Review of the fluids hypothesis, complete set of equations (mass, Navier-Stokes, state, energy)
- Vorticity dynamics, Stokeslet
- Concept of boundary layer
- Specific cases: Stokes flow around a cylinder, geostrophic balance, transonic flows (de Laval, Parker's solar wind model)
- Discontinuities and interfaces: Rankine-Hugoniot conditions, entropy and shocks, Sedov-Taylor blast wave solution
- Linear waves and instabilities: acoustic waves, Jeans instability, Rayleigh-Taylor (interface), baroclinity
- Nonlinear waves and instabilities: characteristics of PDEs and Riemann invariants, deep-water and channel waves, solitons, wave modulation
- Dissipative structures: Rayleigh-Benard convection, Landau theory, Lorenz attractor, Poiseuille flow, Kolmogorov turbulence

Magnetohydrodynamics part 
- Fluid description of magnetised plasma: definition, Debye length, plasma pulse, collective effects, Vlasov equation, MHD ordering
- Establishment of MHD mono-fluid equations, generalised Ohm's law, Alfven speed
- MHD effects: force density, two regimes (ideal, resistive MHD), magnetic virial theorem
- Dynamo effect: Cowling's theorem, alpha and omega effects
- Trans-Alfvenic waves (Alfven, magnetosonic) and flows (stellar winds)
- Controlled thermonuclear fusion: history, Lawson criteria, machines, Vlasov-Landau theory (wave-particle resonance), 1D and 2D Tokamak equilibria, instabilities and anomalous transport


Electromagnetism, thermodynamics, continuum mechanics (L3 bachelor course), maths course for Physics bachelor (L3) 


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