Unit of study_

# MATH4074: Fluid Dynamics

Fluid Dynamics is the study of systems which allow for a macroscopic description in some continuum limit. It is not limited to the study of liquids such as water but includes our atmosphere and even car traffic. Whether a system can be treated as a fluid, depends on the spatial scales involved. Fluid dynamics presents a cornerstone of applied mathematics and comprises a whole gamut of different mathematical techniques, depending on the question we ask of the system under consideration. The course will discuss applications from engineering, physics and mathematics: How and in what situations a system which is not necessarily liquid can be described as a fluid? The link between an Eulerian description of a fluid and a Lagrangian description of a fluid, the basic variables used to describe flows, the need for continuity, momentum and energy equations, simple forms of these equations, geometric and physical simplifying assumptions, streamlines and stream functions, incompressibility and irrotationality and simple examples of irrotational flows. By the end of this unit, students will have received a basic understanding into fluid mechanics and have acquired general methodology which they can apply in their further studies in mathematics and/or in their chosen discipline.

Code MATH4074 Mathematics and Statistics Academic Operations 6
 Prerequisites: ? (A mark of 65 or above in 12cp of MATH2XXX ) or (12cp of MATH3XXX ) None MATH3974 (MATH2961 and MATH2965) or (MATH2921 and MATH2922)

At the completion of this unit, you should be able to:

• LO1. Explain and apply the fundamentals of fluid mechanics
• LO2. Explain how and in what situations a system which is not necessarily liquid can be described as a fluid
• LO3. Explain and apply the link between an Eulerian description of a fluid and a Lagrangian description of a fluid.
• LO4. Explain the general framework of asymptotics - simplifying equations by exploiting small parameters and scaling regimes and geometric as well as physical assumptions
• LO5. Describe kinematic and dynamic flows using complex analysis, PDE theory and perturbation theory.
• LO6. Recall and explain the basic definitions of stream function, velocity potential, incompressibility, irrotationality and other fundamental quantities to describe fluids
• LO7. Synthesis ideas about with added circulation; and apply to Laplace's equation and the use of complex variable methods for its solution in two dimensions; airfoil theory and the derivation of the formula for life; basic understanding of how aircraft fly.
• LO8. Explain the distinction of high and low Reynolds number flows
• LO9. Explain ideas of hydrodynamic stability and give examples of calculations; and transitions to turbulence via a sequence of bifurcations; the turbulent closure problem and other difficulties; Kolmogorov's theory for the spectrum of turbulent eddies.
• LO10. Explain the fundamental theory of water waves

## Unit outlines

Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.