Primary Text : Kundu & Cohen (= K), Fluid Mechanics (3rd ed., Academic Press)
Topic 1 ( K 1 ) Properties of fluids and statics
Continuum hypothesis. Transport laws. Forces on fluid elements. Equilibrium. Thermodynamics
Topic 2 ( K 3 ) Kinematics
Particle paths, streamlines, streaklines. Eulerian & Lagrangian approaches. Mass conservation and streamfunction. Vorticity, circulation. Relative motion near a point.
Topic 3 ( K 4, 5 ) Dynamics: Conservation laws and equations
Inviscid Euler's equations. Vorticity equation. Bernoulli equation. Stress tensor. Navier-Stokes equations. More vorticity. Rotating frame. Mechanical energy. Thermal energy. Boussinesq equations.
Topic 4 ( K 6, 15 ) INVISCID potential flows, and how to fly
2-D potential flows: inviscid and irrotational. Cauchy-Riemann conditions; Laplace's equation. Complex analytic functions as generators of simple potential flows. Superpose simple flow building blocks. Flow past circular cylinders; circulation added. Forces on bodies; lift and circulation. Conformal mapping: flat plates to circles to wings that fly. Phenomenology of flow separation.
Topic 5 ( K 7 ) Gravity and surface waves
Surface and interfacial gravity waves, irrotational; deep and shallow water waves. Linearization involved in posing the problem. Internal gravity waves. Phase velocity, group velocity and dispersion relations. Wave energy fluxes. Nonlinear wave steepening; hydraulic jumps. Barotropic and baroclinic modes.
Topic 6 ( K 8 ) Dynamic similarity and scaling
Scale analysis; dynamic similarity. Concept of viscous boundary layers and inviscid external flows.
Topic 7 ( K 9 ) Laminar VISCOUS incompressible flows
Exact solutions of steady plane-parallel flows, Couette and Poiseuille. Unsteady impulsive flows. Flow due to oscillating plate.
Topic 8 ( K 10, 14 ) Boundary layers
Boundary-layer concepts; scaling and approximate equations. Self-similar solutions; Blasius boundary layer on a plate; 2-D jets. Separation of boundary layers. Boundary layers as singular perturbation problem. Ekman boundary layers in rotating system. Ekman pumping and spindown.
Topic 9 ( K 16 ) Compressible flows and sound waves
Compressibility effects on flows; thermodynamic relations. 1-D compressible flows; area-velocity relation. Normal shock relations; Rankine-Hugoniot conditions. Weak and strong shocks; Mach cones; oblique shock waves. Sound waves as linear response of stratified compressible systems; using sound waves to probe the inside of a star.
Topic 10 ( K 11 ) Computational fluid dynamics
Discussion of approaches and algorithms used to numerically simulate 2-D and 3-D nonlinear flows. Finite difference and spectral representations; incompressible, anelastic and fully compressible treatments. Examples from current GFD and AFD research simulations.
Topic 11 ( K 12, 13, 14 ) Sampling of instability and turbulence concepts
Instability treated as a linear perturbation, including the effects of rotation. Onset of Rayleigh-Benard convection as an linear instability problem. Kelvin-Helmholtz shear instability. Nonlinear equilibration of motions. Dynamical systems treatment by Lorentz and transitions to chaos. Basic concepts and properties of turbulence.