Spatiotemporal and Turbulent Dynamics

Catalog description

Advanced graduate course on the dynamics of spatiotemporal patterns in nonlinear time-dependent partial differential equations. Topics include bifurcations and symmetry, equilibria, traveling waves, periodic orbits of nonlinear ordinary and partial differential equations, and unstable coherent structures in turbulence. Example systems include 1d and 2d Swift-Hohenberg equations, the 1d Kuramoto-Sivashinsky equation, Rayleigh-Bénard convection, and Navier-Stokes dynamics in plane Couette and pipe flows.