The course will meet on Monday, Wednesday and Friday at 330pm in LH2 (usually twice a week).
This is an introductory course on fluid dynamics.
Topics: mechanics of deformable media; fields; Lagrangian and Eulerian descriptions; general remarks on fluid mechanics; fluid element; local thermal equilibrium; aero- and hydrostatics; streamlines, pathlines and streaklines; material derivative; compressibility, incompressibility and divergence of velocity field, relation to sound speed, stream function in two dimensions; local conservation of mass, continuity equation; inviscid flow; stress tensor, pressure; Euler equation; ideal adiabatic flow, entropy advection, equation of state, internal energy equation, homentropic and barotropic flows; Bernoulli's equation (steady and unsteady); sound waves in homentropic flow; vorticity, enstrophy, shear flow, point vortex, vorticity evolution, circulation, vortex tubes, Kelvin and Helmholtz theorems; local conservation laws for inviscid flow: linear momentum, angular momentum, energy (barotropic and incompressible flows), flow helicity; Hamiltonian and Poisson brackets for inviscid (barotropic) flows, Clebsch variables for barotropic flow, Lagrangian for ideal barotropic flow; Fourier's heat diffusion equation, Navier-Stokes equation for incompressible viscous flow, no-slip boundary condition, stress and rate of strain tensors, deviatoric stress and Newton's law for a fluid, isotropic tensors; Poiseuille flow in a pipe; vorticity evolution and diffusion; Reynolds number and similarity principle; Stokes flow past a sphere, drag coefficient; flow past a cylinder, transition from laminar to turbulent flow (qualitative description), flow separation, von Karman vortex street, fully developed turbulence, symmetries: their breaking and statistical restoration.
Some brief lecture notes are here.
Assignment 1 is due by the beginning of the class on Monday Aug 19, 2024
Assignment 2 is due by the beginning of the class on Monday Aug 26, 2024
Assignment 3 is due by the beginning of the class on Monday Sep 9, 2024
Assignment 4 is due by the beginning of the class on Monday Sep 16, 2024
Assignment 5 is due by the beginning of the class on Monday Sep 23, 2024
Assignment 6 is due by the beginning of the class on Monday Oct 7, 2024
Assignment 7 is due by the beginning of the class on Friday Oct 18, 2024
Assignment 8 is due by the beginning of the class on Monday Oct 28, 2024
Assignment 9 is due by the beginning of the class on Monday Nov 4, 2024
Assignment 10 is due by the beginning of the class on Monday Nov 11, 2024
Assignment 11 is due by 5pm on Friday Nov 29, 2024