MTH3360 - Fluid dynamics

Leader(s): Dr Simon Clarke

Offered

Clayton First semester 2009 (Day)

Synopsis

The basic equations of fluid dynamics; Cartesian tensors, the viscous stress tensor; equations of state; linearisation, sound and internal gravity waves; phase and group velocity; non-linear evolution; shocks; computational methods; Bernoulli's equation; vorticity and circulation; Kelvin's circulation theorem; rotational and irrotational flow; two dimensional homogenous incompressible flow; viscous effects and boundary layers; separation from a ball, with applications to cricket, golf and baseball; flow in a rotating reference frame, geostrophic flow.

Objectives

On completion of this unit, students will: understand the scope of fluid dynamics in the physical sciences; understand the method of linearisation, and its application to waves in fluids; understand the physical reasons why waves may shock, and the nature of the developed shocks after they do; be familiar with the blast wave solutions, and the method of similarity; be aware of several basic numerical methods for one dimensional gas dynamics, as well as their strengths and limitations; understand how the fluid equations can be simplified for the case of an inviscid incompressible flow and be able to determine some simple irrotational flows; understand the effects of viscosity on high-speed flow, including the formation and behaviour of boundary layers; be familiar with the properties of rotating flows and the importance of the geostrophic approximation to flows on the surface of the Earth.

Assessment

Examination (3 hours): 60%
Assignments: 20%
Tests: 20%

Contact hours

Three 1-hour lectures and an average of two 1-hour support classes per week

Prerequisites

MTH2010 and MTH2032 or equivalent

Prohibitions

ASP3021, ASP3062, ATM3062, MAT3121, MAT2102, MAT3102, ATM3132, ATM3172, MTH3362