# PHSI426 Fluids, Instability and Turbulence

## Paper description

This paper provides an introduction to the mechanics of fluids with an emphasis on the physical and mathematical underpinnings of the subject. At the conclusion of this paper students should be able to access the fluid mechanics literature at a level appropriate for a beginning graduate student.

Prerequisites:
MATH 203

This paper consists of 15 lectures and 6 tutorials. There are 3 assignments.

Assesment:
Final Exam 70%, Assignments 30%

Important information about assessment for PHSI426

Course Co-ordinator:
Associate Professor Inga Smith

After completing this paper students are expected to have achieved the following major learning objectives:

• Know the difference between Lagrangian and Eulerian frames of reference in the description of the movement of fluids;
• Understand the conservation of mass, momentum and energy in fluid flow, leading to the derivation of the Navier-Stokes equations;
• Be able to approximate and manipulate the Navier-Stokes equations into forms suitable for particular situations;
• Understand some fundamental theorems of fluids, e.g. Kelvin’s circulation theorem;
• Understand the implications of space and time for the equations governing boundary layer flow;
• Apply the equations governing basic wave motion in fluids;
• Derive equations for the growth/decay of linear perturbations in a simple flow;
• Be able to outline how small perturbations evolve to fully developed turbulence;
• Understand the arguments introduced in a basic quantification of turbulence.

Topics:

• Flow of ideal fluids & kinematics & conservation laws
• Viscous fluids, dimensionless numbers and similarity
• Waves & instabilities
• Turbulence
• Boundary layer flow
• Convective transport

# Formal University Information

The following information is from the University’s corporate web site.

## Details

Fluid mechanics is introduced through vector calculus and tensors approaches to the Navier-Stokes equations. These equations are applied to real-world examples (for example from Antarctica), instabilities and turbulence.

Paper title Fluids, Instability and Turbulence PHSI426 Physics 0.0833 10 points Semester 2 (On campus) \$704.22 Tuition Fees for international students are elsewhere on this website.
Limited to
BSc(Hons), PGDipSci, MSc
Eligibility

Non-physics majors should consult the course coordinator before enrolling in this paper.

Contact
inga.smith@otago.ac.nz
Teaching staff
Course Co-ordinator: Dr Inga Smith
Textbooks
Textbooks are not required for this paper.
Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Information literacy, Self-motivation, Teamwork.
Learning Outcomes
After completing this paper students are expected to:
1. Know the difference between Lagrangian and Eulerian frames of reference in the description of the movement of fluids
2. Understand the conservation of mass, momentum and energy in fluid flow, leading to the derivation of the Navier-Stokes equations
3. Be able to approximate and manipulate the Navier-Stokes equations into forms suitable for particular situations
4. Understand some fundamental theorems of fluids (e.g. Kelvin's circulation theorem)
5. Understand the implications of space and time for the equations governing boundary layer flow
6. Apply the equations governing basic wave motion in fluids
7. Derive equations for the growth/decay of linear perturbations in a simple flow
8. Be able to outline how small perturbations evolve to fully developed turbulence
9. Understand the arguments introduced in a basic quantification of turbulence

## Timetable

### Semester 2

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None