Selected topics in Fluid Mechanics

Whether on the scale of a planet, or a pinhead, happening over centuries or over miliseconds, flows of different fluids are all described by the famous Navier-Stokes equations. The course builds on the basic and general tools of continuum mechanics, to look in detail into a collection of phenomena relevant to various systems ranging from protein dynamics, through our everyday kitchen and bathroom experience, to atmospheric dynamics. Relevant approximations leading to the solution of flow equations are discussed.

Knowledge of classical continuum mechanics or basic hydrodynamics (e.g. covered by "Hydrodynamics and Elasticity" course) is a suggested prerequisite.

1. Hydrodynamic instabilities.

Boussinesq approximation. Thermal (Rayleigh-Benard) instability. Convection cells. Convection patterns in nature. Wind-generation of waves (Kelvin-Helmholtz instability). Centrifugal (Taylor-Couette) instability. Surface tension and Rayleigh-Plateau instability.

1. Boundary layer theory.

Prandtl's theory. Asymptotic expansions. Why does a plane fly?

3. Microscale flows.

What does dripping honey have in common with glacier flows and swimming bacteria? Why are microscale flows dominated by viscosity? Stokes equations. Microfluidics.

4. Geophysical fluid flows.

Equations of motion in a rotating frame. Rossby number. Geostrophic balance. Vorticity and potential vorticity. Quasi-geostrophic approximation. Internal gravity waves. Planetary (Rossby) waves. Baroclinic instability. Elements of magnetohydrodynamics (MHD).

5. Bits and pieces of interests to the attendees.

Interested in a particular aspect of fluid flows? We will happily discuss it further.

1. Acheson, D. J., Elementary Fluid Dynamics, Clarendon (1990).

2. Batchelor, G. K. Introduction to Fluid Dynamics, Cambridge University Press (1967).

3. Landau and Lifshitz, Fluid Mechanics (2nd Ed.), Pergamon Press (1987).

4. Pedlosky, J. Geophysical Fluid Dynamics, Springer (1986).

5. Lautrup, B. Physics of Continuous Matter.

After completing the course the student will be able to formulate problems in fluid mechanics and understand the underlying hypotheses. Familiarity with the methods of linear stability theory and differential equations is assumed.

Exercises, colloquia and oral exam.