Course details
A specialist MAGIC course
Semester
 Spring 2021
 Monday, January 25th to Friday, March 19th; Monday, April 26th to Friday, May 7th
Hours
 Live lecture hours
 10
 Recorded lecture hours
 0
 Total advised study hours
 40
Timetable
 Wednesdays
 14:05  14:55 (UK)
Announcements
Apologies for another change of time, but I've had to move the final 10th lecture of this module to avoid a clash with some other teaching I have to do at UEA. It will now be on the same day, but now start an hour earlier at 1pm. The 9th lecture will take place at the usual time. So the last two lectures will now be as follows:
 Lecture 9: Wednesday 28th April, 2pm3pm
 Lecture 10: Wednesday 5th May, 1pm2pm
The Magic timetable has been updated to reflect this.
Description
The Reynolds number gives the ratio of inertial to viscous effects in a fluid flow.
When the Reynolds number is small, inertial effects are negligible and the Du/Dt term in the NavierStokes equations may be neglected.
This simplifies the NavierStokes equations, making them linear and instantaneous.
These simplifications make solving lowReynoldsnumber flow problems much easier than high Reynolds number flows.
This module will consider the circumstances under which the Reynolds number will be small and examine the basic properties of lowReynoldsnumber flows.
We shall present a number of solution techniques, and show how they can be applied to a range of problems.
In the course of this, students will meet various useful applied mathematics methods, including solution by potentials, boundary integral methods, and asymptotic approximations.
When the Reynolds number is small, inertial effects are negligible and the Du/Dt term in the NavierStokes equations may be neglected.
This simplifies the NavierStokes equations, making them linear and instantaneous.
These simplifications make solving lowReynoldsnumber flow problems much easier than high Reynolds number flows.
This module will consider the circumstances under which the Reynolds number will be small and examine the basic properties of lowReynoldsnumber flows.
We shall present a number of solution techniques, and show how they can be applied to a range of problems.
In the course of this, students will meet various useful applied mathematics methods, including solution by potentials, boundary integral methods, and asymptotic approximations.
Prerequisites
Essential
 Vector Calculus (div, grad, curl, line,surface/volume integrals, divergence theorem)
 Differential Equations (methods for firstorder ordinary differential equations)
 Basic Fluid Mechanics (introductory course in inviscid fluid mechanics)
 Further Fluid mechanics (introductory course in viscous fluid mechanics)
 Tensors and the Einstein Summation Convention (some previous experience useful)
 Nondimensionalisation / scaling analysis
Syllabus
 Introduction to lowReynoldsnumber flow (3 lectures) The Stokes equations and boundary conditions. Basic properties, uniqueness theorem, reciprocal theorem, minimum dissipation theorem. Oscillating Couette flow and Poiseuille flow.
 Fundamental solutions and representation by potentials (4 lectures) Solution using potentials. PapkovichNeuber potentials, flow past a rigid sphere. Boundary integrals and the multipole expansion.
 Slenderbody theory (3 lectures) Basic derivation. Applications to sedimenting slender objects and swimming microorganisms.
Lecturer

Dr Robert Whittaker
 University
 University of East Anglia
Bibliography
Follow the link for a book to take you to the relevant Google Book Search page
You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library'  this sometimes works well, but not always  you will need to enter your location, but it will be saved after you do that for the first time.
 Elementary Fluid Dynamics (Acheson, D. J., )
 Viscous Flow (Ockendon & Ockendon, )
 An Introduction to Fluid Dynamics (Batchelor, G. K., )
 Low Reynolds Number Hydrodynamics (Happel & Brenner, )
 Boundary Integral and Singularity Methods for Linearised Viscous Flow (Pozrikidis, C., )
 Microhydrodynamics (Kim & Karrila, )
Assessment
The assessment for this course will be released on Monday 10th May 2021 at 00:00 and is due in before Monday 24th May 2021 at 11:00.
The assessment for this course will be via a single takehome paper in the Semester 2 Magic Assessment Period. There will be one question on each of the three topics, and all three questions should be attempted.
Please note that you are not registered for assessment on this course.
Files
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Lectures
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