Fall, 2015 John Bowman

*The phenomenology and mathematical foundations of fluid
turbulence theories are surveyed, with an emphasis on statistical models.*

- Lectures:
M W F 1600-1650 CAB 563
- Office hours and contact information:
TBA
Tel: 492-0532 Email: bowman@math.ualberta.ca WWW: http://www.math.ualberta.ca/~bowman/m655

- Text:
Frisch, U.

**Turbulence, The Legacy of A.N. Kolmogorov,**Cambridge, 1995 ISBN 0-521-45713-0. - Supplemental reference (optional):
George, William K.,

**Lectures in Turbulence for the 21st Century**,`http://www.turbulence-online.com/Publications/Lecture_Notes/Turbulence_Lille/TB_16January2013.pdf`, 2013. - Evaluation:
Grades will be based on a number of equally weighted homework assignments distributed during the term.

- Topics:
* 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.

* Applications.

- Prerequisites: Facility with the use of Fourier transforms in solving
partial differential equations is assumed.

John Bowman 2015-09-02