Introduction to Transport Phenomena

• Random walk, Binomial distributions, and diffusion
• Transport coefficients, mean-free-paths, collision times
• Scattering and absorption, line escape formalism
• Langevin and Fokker-Planck equations; applications

Introduction to Radiative Transfer

• Definitions (specific intensity, mean intensity, flux moments)
• Equation of transfer limits (pure emission, absorption)
• Source function and formal solution
• Gaussian quadratures, Eddington & two-stream approx.
• Grey atmosphere (Milne solution) and emergent intensity
• Radiative equilibrium; effects of absorption and scattering
• Line formation; redistribution function; escape probability, diffusion approximation
• Mean opacities (flux-weighted, Rosseland, Planck, Absorption means)

Boltzmann Equation and Applications

• Boltzmann Equation and Intro to Kinetic Theory
• Boltzmann H-Theorem, Entropy, Collision Integral
• Applications of the Boltzmann Equation
• Conservation Laws (moments of Boltzmann Equation)

Introduction to Fluid Dynamics

• The continuum model and requirements for a fluid
• Conservation laws, fluid kinematics (Eulerian, Lagrangian)
• Advective Derivative, Vector Fields, Vector Calculus
• Mass and Momentum Equations (Euler and Bernoulli)
• Vorticity, Vorticity Freezing, Vorticity Equation
• Bernoulli Theorem, Kelvin Circulation Theorem, applications

Strain Rate and Viscous Stresses

• Kinematics of Fluid Motion (strain, stress, relative motion)
• Stress-Strain Relations (Stress Tensor and Strain-Rate Tensors)
• Newtonian fluids (compressibility, viscosity coefficients, pressure)
• Derivation of Navier-Stokes Equation
• Reynolds Number and non-dimensional equations of motion
• Mechanical Viscosity (Classic Shear flows, Couette flow, pipe flow)
• Energy Equations (First Law, Reynolds transport theorem, dissipation)
• Heat Equation (conduction, diffusion, entropy, Bernoulli function)

Applications to Accretion Flows

• Spherical Accretion, Outflows, Gravitational Collapse
• Wind Equation (de Laval Nozzle, sonic point, topology)
• Bondi-Hoyle Accretion, Solar Wind critical solutions
• Accretion Disk Theory (Keplerian disks, viscous couples)
• Conservation laws (mass, angular momentum flux)
• Accretion rates, angular momentum distribution, viscosity

Magnetohydrodynamics (MHD)

• Basic assumptions for magnetized fluid
• Conservation laws, Ideal MHD equations
• Magnetic diffusion equation (finite conductivity)
• Hydromagnetic equilibria (pressure, tension)
• Examples (force-free fields, magnetic flux tubes, etc)
• Waves (Alfven waves, Magnetosonic waves)

Shock Waves

• Sound Waves and "signal speeds"
• Steepening to shock waves (PDEs and characteristics)
• Adiabatic (Rankine-Hugoniot) Jump Conditions
• Post-shock conditions, entropy generation
• Oblique shocks
• Similarity solutions (Sedov-Taylor, Wind-driven bubbles)

Fluid Waves and Instabilities

• Surface and Interface waves
• Role of surface and dynamic boundary conditions
• Gravity waves (shallow and deep-water limits)
• Dispersion relations, Stability and instability
• Rayleigh-Taylor and Kelvin-Helmholtz Inatbilities
• Gravitational (Jeans) Instability (perturbation analysis)
• Convective Instability (Schwarzschild criterion, entropy)
• Stable atmospheres (Brunt-Vaisala frequency, buoyancy)

Intro to Turbulence

• Characteristics of turbulent flows
• Chaotic, nonlinear, diffusivity, vorticity cascades. dissipation
• Kolmogoroff spectrum, eddy cascade, scaling relations
• Molecular vs Eddy Viscosities
• Taylor and Kolmogorov microscales
• Introduction to numerical simulations of turbulence