Fabian Waleffe -- Math 801 -- U. of Wisconsin

Math 801: Fall 2016
Hydrodynamic instabilities and bifurcations

Fabian Waleffe

Day  Time  Place 
TR  1:00-2:30pm B325 Van Vleck Hall
File:Vortex-street-animation.gif

Current Course description (This is a Topics course, content may change every semester)

References

Grading

Homework will be assigned (see below). Research papers will be studied and presented.

Lectures and assigned reading

date DRAZIN topic
9/6 1.1–3, 10.2 General intro, Navier-Stokes equations, Linearization, Stability, Bifurcations. Flow behind a cylinder.
9/8 5.3 Diffusion equation, damping. Derivation of perturbation energy equation.
9/13 5.3 Read J. Serrin's 1959 `On the Stability of viscous fluid motions'
9/14 Homework 1
9/15 Variational Calculus, Helmholtz
9/20 Diffusion: Fourier + Gaussian fundamental solutions. Enhanced diffusion in a shear flow.
9/22 Stability of unbounded uniform shear flow, Kelvin modes
9/27 Transient growth: venitian blind and lift-up. Jordan matrices, non normal matrices. Relevance to hydrodynamics.
9/28 Homework 2
9/29 Instabilities of hyperbolic and elliptic flows.
10/4 Rigid body rotation. Inertial waves.
10/6 Kelvin-Helmholtz
10/11 K-H Analysis, Rayleigh-Taylor, gravity waves
10/6 Kelvin Ship Waves: see Ship Wakes: Kelvin or Mach Angle? (PRL 2013)
but see also Commentary in Physics World but see also Kelvin's original drawings , a pretty nice photo of Kelvin's pattern!