Lecture list
Calculus, undergraduate lecture, Shanghai, fall 2017
Fluid Mechanics, graduate lecture, Shanghai, fall 2017-2018
Numerical Analysis, graduate lecture, Shanghai, fall 2018
Classical Mechanics, undergraduate lecture, Beijing, spring 2020-
Astrophysical Fluid Dynamics, graduate lecture, Beijing, spring 2021-
Information about lectures
Classical Mechanics
This course focuses on analytical mechanics. We start from the least action principle to derive Lagrange's equation and then derive the conservation laws from symmetry. Next we apply Lagrange's equation and conservation laws to some problems: Kepler's problem, oscillation problem, and rigid body motion. Finally we briefly introduce Hamilton's mechanics.
Syllabus
Ch1 Lagrange's mechanics: calculus of variations, least action principle, Lagrange's equation, Lagrangian, some examples
Ch2 Conservation laws: principle of relativity, three symmetries and conservation laws, centre of mass, mechanical similarity, virial theorem
Ch3 Kepler's problem: 1D motion, reduced mass, 2D motion in a central field, effective potential, three orbits, Binet equation, stability of circular orbit
Ch4 Small oscillations: free oscillations, forced oscillations, damped oscillations, forced-damped oscillations, motion in a rapidly oscillating field
Ch5 Rigid body motion: velocity decomposition, angular momentum and moment of inertia, kinetic energy, principal axis, Euler's equations, Eulerian angles, gyroscope, non-inertial frame (rotating frame)
Ch6 Hamilton's mechanics: Hamilton's equations, Poisson brackets, about action, canonical transformation and generating functions, Liouville's Theorem, Hamilton-Jacobi equation
Reference book
Astrophysical Fluid Dynamics
This course is an introduction to fluid dynamics and magnetohydrodynamics that are important for astrophysics, e.g., accretion disk and stellar or planetary atmosphere and interior.
Syllabus
Ch1 Introduction: streamline, material derivative and advection, vorticity, mass conservation
Ch2 Inviscid fluid: Euler equation, Bernoulli's theorem, vorticity equation, Kelvin's theorem
Ch3 Viscous fluid: velocity decomposition, stress and strain, Navier-Stokes equation, vorticity equation, normalisation and Reynolds number, microscopic physics (Boltzmann equation)
Ch4 Applications: plane Poiseuille flow, plane Couette flow, Taylor-Couette flow, rotating flow (Taylor-Proudman theorem), stellar structure (Lane-Emden equation), accretion disk, tide, boundary layer (Prandtl's equation and Blasius solution)
Ch5 Gas dynamics: thermodynamics, acoustic wave, shock, blast wave (Taylor and Sedov), galactic jet (Blandford and Rees), spherical wind (Parker) and accretion (Bondi)
Ch6 Waves: surface gravity wave, internal gravity wave, inertial wave, Kelvin/Poincare/Rossby wave
Ch7 Instabilities: gravitational instability, rotating flow instability, convective instability, shear flow instability
Ch8 Turbulence: energy cascade, turbulent viscosity, scaling laws, Kolmogorov spectrum, turbulent transport in accretion disk
Ch9 MHD: induction equation, Alfven's theorem, Alfven wave, dynamo theory (alpha-omega dynamo)
Reference books
Elementary Fluid Dynamics, Acheson, Oxford University Press, 1990 (Ch1, Ch2, Ch3)
Fluid Mechanics, Landau and Lifshitz, any version (Ch3, Ch8)
The Physics of Fluids and Plasmas, Choudhuri, Cambridge University Press, 1998 (Ch3 microscopic physics)
Astrophysics of Planet Formation, Armitage, Cambridge University Press, 2020, (Ch4 accretion disk)
Tides in Astronomy and Astrophysics, Souchay et, al., Springer, 2013, (Ch4 tide)
恒星物理，黄润乾，中国科学技术出版社，2012 (Ch4 stellar structure)
粘性流体力学，章梓雄和董曾南，清华大学出版社，1998 (Ch4 boundary layer)
Waves in Fluids, Lighthill, Cambridge University Press, 1978 (Ch6 surface gravity wave)
Geophysical Fluid Dynamics, Pedlosky, Springer, 1987 (Ch6 Kelvin/Poincare/Rossby wave)
Hydrodynamic and Hydromagnetic Stability, Chandrasekhar, Oxford University Press, 1961 (Ch7)
An Introduction to Magnetohydrodynamics, Davidson, Cambridge University Press, 2001 (Ch9)
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