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.
Course documents:
- Introduction
- A full set of lecture notes will be provided to the students via email in the first week.
- Project Handbook
Computer code
- Rayleigh-Benard convection
- Introduction to Spectral Methods
- Viscous Rayleigh-Taylor instability
- Eigenvalue solver for plane Couette flow
- Eigenvalue solver for plane Poiseuille flow
- Eigenvalue solver for the study of Absolute Instability
- Transient Growth
- Weakly Nonlinear Theory
- Diffusion models for CFD (matlab version)
- Turbulence modelling codes