Study information

# Fluid Dynamics in Physics and Astronomy - 2023 entry

MODULE TITLE CREDIT VALUE Fluid Dynamics in Physics and Astronomy 15 PHY3220 Prof Matthew Browning (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
 Number of Students Taking Module (anticipated) 30
DESCRIPTION - summary of the module content
Many systems of both everyday and astrophysical importance can be studied using the equations and concepts of fluid dynamics.  The cup of coffee you drink in the morning, the waves you see at the beach, the blood pumping through your body -- but also the interiors of stars and planets, and the disks in which they form – are all governed by some version of these equations.

In this module, you will learn the fundamental concepts of fluid mechanics and apply them to a variety of problems in physics, everyday life, and astronomy. You will learn how to solve the Navier-Stokes equations (which govern the flow) in simple cases, and how to describe some aspects of fluid dynamical phenomena even in cases where no analytical solution is possible.

AIMS - intentions of the module

This module aims to provide students with an understanding of the basic concepts of fluid dynamics, and practice in using these to solve problems of interest.  It also aims to highlight some of the many important applications of fluid dynamics in physics and astronomy, and to develop some physical intuition for the many problems in which no complete solution for the flow can be obtained.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge

1. Explain the basic concepts and equations of fluid dynamics;
2. Use the Navier-Stokes (and/or Euler, as appropriate) equations to solve or constrain the fluid flow in simple geometries;
3. Identify and describe non-dimensional parameters that frequently govern the flow;
4. Interpret solutions of partial differential equations in physical terms.

Discipline Specific Skills and Knowledge

5. Describe astronomical and physical phenomena whose behaviour is governed by fluid flow;
6. Translate a complex physical problem into an approximate problem that can be solved or constrained.

Personal and Key Transferable / Employment Skills and Knowledge

7. Develop problem-solving skills;
8. Develop self-study skills.

SYLLABUS PLAN - summary of the structure and academic content of the module
I. Fundamental ideas and equations of fluid dynamics
1. Continuity equation; mass conservation
2. Euler equation; momentum conservation
3. Navier-Stokes equation
4. Governing non-dimensional parameters
5. Laminar flow and other limiting states
6. Energetics and Bernoulli’s principle
7. Boundary layers
II. Vorticity and rotating fluids
1. Vorticity equation
2. Kelvin’s circulation theorem
3. Irrotational flow
4. Flow in rotating reference frames
III. Waves and instabilities
1. Linearisation
2. Examples of classic waves (including inertial and gravity waves)
3. Classic instabilities (including Rayleigh-Taylor, convection)
IV. Compressible fluid dynamics
1. The speed of sound and the Mach number
2. Shock waves
3. Effects of stratification
V. Applications to problems in physics, geophysics, and astronomy:
(Examples to be chosen at instructor’s discretion; below list is illustrative)
1. Convection in stars and planets
2. Accretion and accretion disks
3. Planetary winds
4. Aerodynamics
5. Biophysical fluids
VI. Survey of advanced topics (as time permits)
1. Introduction to magnetohydrodynamics (MHD)
2. Non-Newtonian fluids
3. Turbulence

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 22 128 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 22 x 1 hour lectures In class lectures / problems classes. Guided Independent Study Approx. 8 hours Problems sets discussed in class. Guided Independent Study Approx. 30 hours Self-Study material Guided Independent Study Approx. 16 hours Individual project work Guided Independent Study Approx. 74 hours Personal private revision.

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Problem sets  4 hours per set 1-8 Discussion in class

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams Practical Exams 40 60 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework (mini-projects) 40% 8 hours per project 1-8 Written Feedback
Examination 60% 2 hours and 30 minutes 1-8
Mark via MyExeter, feedback via ELE and solutions (Newton).

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
Coursework (mini-projects) Examination (defer only) (40%) 1-8 August/September assessment period
Examination Examination (60%) 1-8 August/September assessment period

RE-ASSESSMENT NOTES

Coursework is not referrable, but deferral assessment is via ref/def written examination

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener