astr/atoc 5400 Syllabus

SYLLABUS - ASTR 5400 Introduction to Fluid Dynamics - Spring 2016 Toomre

MWF 11:00-11:50am Duane E126 + optional video/demo sessions

Primary Text : Kundu, Cohen & Dowling (= K), Fluid Mechanics (2016, 6th ed., Academic Press)

Topic A ( Chap 1 = K: 1; and K: 3 ) Kinematics and dynamics of fluids

Continuum hypothesis; fluid model. Eulerian and Lagrangian formulations; material derivative. Simplest dynamical equations (conserve mass, momentum): inviscid Euler's equations. Kinematics; relative motion near a point. Streamfunction; streamlines, streaklines, pathlines.

Topic B ( K: 4, 13 ) Navier-Stokes (+ rotation) and simple Bernoulli equations

Stress-strain relations; stress tensor; viscous forces. Navier-Stokes equations: continuity and momentum equations. Thermal energy equation. Equations in noninertial rotating frame (thus with Coriolis forces). Bernoulli equations; simplest examples of inviscid flows.

Topic C ( K: 5 ) Vorticity concepts

Vorticity dynamics; vortex lines and tubes. Kelvin's circulation theorem. Vorticity equation in inertial and rotating frames. Taylor-Proudman theorem. Potential vorticity.

Topic D ( K: 4.11 ) Dynamic similarity and scaling

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

Topic E ( K: 7, 14 ) INVISCID potential (irrotational) flows

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 F ( K: 8 ) Gravity waves and linearization concepts

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 G ( 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 H ( K: 6 ) 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 I ( K: 10, 13 ) 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 J ( K: 15 ) Compressible flows and acoustic 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. Acoustic and gravity waves as linear response of stratified compressible medium; using these waves to probe the inside of a star.

Topic K ( K: 11, 12) Sampling of instability and turbulence concepts

Instability treated as a linear perturbation, including the effects of rotation. Onset of Rayleigh-Benard convection as a linear instability problem. Kelvin-Helmholtz shear instability. Nonlinear equilibration of motions. Basic concepts and properties of turbulence.