Hydrodynamics and Elasticity

The theoretical framework known as hydrodynamics and elasticity provides a powerful and complete description of our world at macroscopic scales (i.e., at large spatial and time scales compared to the molecular ones). 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 gives an introduction to the derivation of the basic equations of hydrodynamics and elasticity as well as common methods for their solutions in simple applications.

Due to the COVID-19 pandemic, both lectures and tutorials will be online. We will meet weekly via Google Meet according to the schedule published in USOS.

• Lecture: Tuesdays, 14:15 - 17:00 (Gustavo Abade)
• Tutorials: Thursdays, 9:15 - 12:00 (Daniel Albuquerque)

Program:

1. The fundamental equations of continuum mechanics;
2. Inviscid flows: Euler equation, sound waves, potential flow, lift and drag forces exerted by moving fluid on immersed bodies;
3. Viscous flows: Navier-Stokes equations, boundary layer and explanation of aerodynamic lift. Micro-hydrodynamics and swimming motion of flagellated microorganisms;
4. Waves: shallow- and deep-water, capillary waves;
5. Elasticity theory: Stress and deformation, bending and twisting of shafts rods.

Bibliography:

1. D. J. Acheson, Elementary fluid dynamics.
2. B. Lautrup, Physics of continuous matter: exotic and everyday phenomena in the macroscopic world.
3. G. K. Batchelor, An introduction to fluid dynamics.
4. L. D. Landau and E. M. Lifshitz, Fluid mechanics.
5. A. R. Patterson, A first course in fluid dynamics.

Assessment:

The final assessment will be based on one test (during the semester) and a written exam (during the exam session). A tentative schedule for examinations is:

• Test: Thu 10 December 2020 (9:15 - 12:00)
• Exam: Thu 4 February 2021 (9:15 - 12:00)