Syllabus

Primary Text:  Kundu & Cohen (= K), Fluid Mechanics (>3rd ed., Academic Press)

Topic 1 (K1) Properties of fluids and statics

Continuum hypothesis. Transport laws. Forces on fluid elements. Equilibrium. Thermodynamics

Topic 2 (K3) Kinematics

Particle paths, streamlines, streaklines. Eulerian & Lagrangian approaches. Mass conservation and streamfunction. Vorticity, circulation. Relative motion near a point.

Topic 3 (K4,5) 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 (K6,15) 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 (K7) Gravity and surface waves (and how to surf!)

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 (K8) Dynamic similarity and scaling

Scale analysis; dynamic similarity. Concept of viscous boundary layers and inviscid external flows.

Topic 7 (K9) Laminar VISCOUS incompressible flows

Exact solutions of steady plane-parallel flows, Couette and Poiseuille. Unsteady impulsive flows. Flow due to oscillating plate.

Topic 8 (K10,14) 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 (if time) (K12,13,14) 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.