ACM 40890 Advanced Fluid Mechanics

Description: In Spring 2025, I will be teaching a module on Advanced Fluid Dynamics. This module will introduce students to advanced topics in hydrodynamic stability theory, turbulence modelling, and experimental techniques.

 

 

These are the main topics we will study:

  • Canonical examples of fluid instability: Eigenvalue analysis of linear instability in the Rayleigh-Benard, Rayleigh-Taylor, and Kelvin-Helmholtz systems. Eigenvalue analysis of parallel flow instability leading to the Orr-Sommerfeld equation.
  • Parallel flow instability beyond the temporal theory: Absolute and convective instability, transient growth
  • Turbulence: Problems in turbulence. Kolmogorov spectra. Wall-bounded turbulence and Reynolds averaging. Closure models. Discussion of direct numerical simulation and large-eddy simulation. The notion of wall-functions in large-eddy simulation.
  • Introduction to High-Performance computing: Solving sparse linear problems iteratively. Applications of such methods to Computational Fluid Dynamics. Introduction to multithread and multicore programming in Fortran.
  • Experimental fluid dynamics, involving droplets and water waves.

Lecture Notes:

  • A full set of lecture notes will be provided to the students via email in the first week.

Course Documents:

Group Projects:

Examinable Results:

  • Week 1: Longwave Theory, Section 5.6
  • Week 1: Exercises 5.1, 5.2, and 5.3
  • Week 2: Exercises 3.1 and 3.2
  • Week 3: All calculations to do with the piston wavemaker, but paying special attention to the height-to-stroke ratio
  • Week 4: Von Neumann Stability Analysis, Section 10.5
  • Week 5: Theorem 11.3, Theorem 11.4, and pseudocode for SOR method
  • Week 6: Exercise 12.1
  • Week 7: Derivation of turbulence intensity transport equation, Section 12.7
  • End of list!

Computer code