Hydrodynamics and elasticity

fizyka
matematyka

w sali

The theoretical framework known as hydrodynamics and elasticity provides a powerful and complete description of our world at macroscopic scales (i.e, at large scales and long times compared to the molecular scales). The macroscopic dynamics of a variety of complex systems, such as biological and soft materials, atmospheric clouds, and the crust of the Earth, poses a formidable challenge for theoretical modeling, in which knowledge of classical hydrodynamics and elasticity is a major prerequisite.

This course introduces the basic equations of hydrodynamics and elasticity and

methods of their solution.

• We discuss the physics of everyday phenomena

• We provide a uniform mathematical framework to describe flow and deformation

• We show numerous real-life applications and examples

The course will cover a range of topics, such as:

1. Continuum description of matter, conservation laws and fundamental equations - Navier-Stokes and friends;

2. Hydrostatics: pressure, lift force, stability, ships and balloons

3. Inviscid flows: Euler equations, potential flows, lift force, d'Alembert paradox

4. Viscous flows: Why do planes fly? Boundary layer and explanation of aerodynamic lift. Low-Reynolds numbers and the Aristotelian world. Swimming of microorganisms;

5. Flows with a twist: Vortices – bathtub vortex versus tornado.

6. Elasticity theory: Stress and deformation, bending and twisting of shafts rods, microtubules, and DNA.

7. Waves: Shallow- and deep-water, capillary waves and tsunamis; seismic waves.

1. B. Lautrup, Physics of Continuous Matter: Exotic and Everyday Phenomena in the Macroscopic World.

2. D.J. Acheson, Elementary fluid dynamics.

3. L. D. Landau and E. M. Lifshitz, Fluid mechanics.

4. L. D. Landau, L. P. Pitaevskii, A. M. Kosevich, and E.M. Lifshitz, Theory of elasticity.

5. S. C. Hunter, Mechanics of continuous media.

During the semester there will be two mid term exams and homework assignments (every week). The final exam will be given during the final exam period.