The phenomenology and mathematical foundations of fluid turbulence theories are surveyed, with an emphasis on statistical models.
Tel: 492-0532 Email: firstname.lastname@example.org WWW: http://www.math.ualberta.ca/~bowman/m655
Frisch, U. Turbulence, The Legacy of A.N. Kolmogorov, Cambridge, 1995 ISBN 0-521-45713-0.
George, William K., Lectures in Turbulence for the 21st Century, http://www.turbulence-online.com/Publications/Lecture_Notes/Turbulence_Lille/TB_16January2013.pdf, 2013.
Grades will be based on a number of equally weighted homework assignments distributed during the term.
* Symmetries and conservation laws.
* Navier-Stokes equation as a dynamical system.
* Inviscid statistical equipartition.
* Kolmogorov's 1941 theory of a self-similar turbulent cascade.
* Intermittency; refined self-similarity hypothesis; multi-fractal models.
* Burgers turbulence.
* Statistical theories of turbulence: the closure problem; Langevin models; statistical closures: the direct-interaction approximation and Markovian closures; realizability.
* Reduced descriptions of turbulence: renormalization group theory, shell models, decimation, spectral reduction.
* Numerical simulations of turbulence: the pseudospectral method, subgrid models, and large-eddy simulations.
* Coherent structures; vortex statistics in two-dimensional fluid turbulence.
* Passive scalar advection; chaotic mixing; multiscale methods.