The course is based on relevant chapters from the book “Modern Classical Physics” by Roger D. Blandford and Kip S. Thorne, as well as the recommended textbook “Fluid Dynamics” by N. Vlakhakis. Additional useful bibliography includes the recommended textbook by I. D. Chatzidimitriou and G. D. Bozis, titled “Introduction to Continuum Mechanics”, which covers part of the course material.
Course Syllabus (Indicative):
- Introduction: General concepts and definitions of fluid-related quantities (Stress tensor, material and local derivatives).
- Fluid Statics: Elements of statics (force densities, pressure, momentum fluxes).
- Fluid Kinematics: Analysis of fluid motion. Incompressible and irrotational flows (potential flows), velocity potential, and stream functions. Streamlines, streaklines, trajectories (pathlines), and their visualization.
- Ideal Fluids: Conservation equations and equations of motion; first integrals (Bernoulli’s equation). Applications in ideal fluids. Geostrophic flows, absolute and potential vorticity.
- Real Fluids: Equations of motion and applications (solutions for fundamental flows, low Reynolds number flows, high Reynolds number flows). Introduction to Computational Fluid Dynamics (CFD).
- Fluid Perturbations and Waves: Surface and internal gravity waves, Rossby waves, inertial waves. Acoustic waves. Shock waves.
- Fluid Instabilities: Jeans, Kelvin-Helmholtz, Rayleigh-Taylor, Rayleigh-Bénard, and the Rayleigh criterion.
- Turbulence: Introduction to turbulent flow.
Instructional Material & Methods
The teaching of the syllabus is supplemented by five problem sets (mandatory or optional), consisting of either theoretical reinforcement exercises or practical applications. Additional resources include supplementary notes, a series of recorded past lectures, and other educational materials such as the National Committee for Fluid Mechanics Films (NCFMF) collection from the MIT archives, demonstration videos, and Python-based computational notebooks.