MATH5453 Foundations of Fluid Dynamics
Part 1: Fluids Equations
Lecture 1: Continuum hypothesis and kinematics
The continuum hypothesis: video, notes
Lecture 2: Mass conservation and streamfunctions
Index notation: video, notes 1/3, notes 2/3, notes 3/3
Mass conservation: video, notes 1/2, notes 2/2
Lecture 3: The Navier–Stokes equation
The Navier–Stokes equation: video, notes 1/4, notes 2/4, notes 3/4, notes 4/4
Different kinds of pressures: video, notes
Boundary conditions: video, notes 1/2, notes 2/2
Lecture 4: Some exact solutions of the Navier–Stokes equation
Plane Poiseuille flow: video, notes 1/2, notes 2/2
Flow down an inclined plane: video, notes 1/3, notes 2/3, notes 3/3
Stokes first problem: video, notes 1/2, notes 2/2
Plane Couette flow startup: video, notes 1/3, notes 2/3, notes 3/3
Lecture 5: Vorticity
The vorticity equation: video, notes 1/2, notes 2/2
Lecture 6: Dynamical similarity and the Reynolds number
The Reynolds number: video, notes
Lecture 7: Potential flows and the Bernoulli equation
The Bernoulli equation: video, notes 1/2, notes 2/2
Part 2: Topics in Fluid Dynamics
Part delivered by Prof. Oliver Harlen.
Lecture 8: Energy and thermodynamics
Lecture 9: Applications of thermodynamics and the heat equation
Lecture 10: Thermal convection
Lecture 11: Waves: Linear theory of sound waves
Lecture 12: Water waves
Lecture 13: Energy transport in deep water waves
Lecture 14: Internal gravity waves
Lecture 15: Nonlinear waves
Lecture 16: Bore formation and energy loss
Lecture 17: Low Reynolds number flows
Lecture 18: Lubrication theory
Part 3: Introduction to Turbulence
Lecture 19: High Reynolds number flows and boundary layers
The Blasius boundary layer: video, notes 1/4, notes 2/4, notes 3/4, notes 4/4
Lecture 20: From laminar to turbulence
Lecture 21: Introduction to turbulence modelling
Lecture 22: Computational models for turbulent flows