Instructor: Stamatis Dostoglou

Description: The course will be an introduction to Fluid Mechanics and the prevailing mathematical theories of turbulence.

The course will examine at first Newtonian incompressible fluids (described by the Navier-Stokes equations), but also more general fluids (for example, compressible). It will then concentrate on the Kolmogorov theory of turbulence.

Topics will include: Equations of motion, vorticity, convection, viscocity, dynamic similarity,coherent structures (eddies), universal laws, specific flow problems.

Prerequisites: The course should be accessible to everybody with a good grasp of multi-variable calculus.

Bibliography:

• Kolmogorov, A. N.
  Selected works of A. N. Kolmogorov. Vol. I. Mathematics and mechanics.
  Kluwer Academic Publishers Group, Dordrecht, 1991.
• Davidson, P. A.
  Turbulence. An introduction for scientists and engineers.
  Oxford University Press, Oxford, 2004.
  
• Foias, C.; Manley, O.; Rosa, R.; Temam, R.
  Navier-Stokes equations and turbulence. Encyclopedia of Mathematics and its Applications, 83. Cambridge University Press, Cambridge, 2001.
• Serrin, J.
  Mathematical principles of classical fluid mechanics. 1959
  Handbuch der Physik, Bd. 8/1, Strömungsmechanik I,
  pp. 125--263
  Springer-Verlag, Berlin-Gottingen-Heidelberg.
  (In English.)
• Majda, A.; Bertozzi, A.:
  Vorticity and incompressible flow.
  Cambridge Texts in Applied Mathematics, 27.
  Cambridge University Press, Cambridge, 2002.
  

(Course description also available as pdf file)