Course details
Semester
 Autumn 2021
 Monday, October 4th to Friday, December 10th
Hours
 Live lecture hours
 10
 Recorded lecture hours
 0
 Total advised study hours
 40
Timetable
 Mondays
 13:05  13:55 (UK)
Description
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
 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.
 An Introduction to Fluid Dynamics (C. K. Batchelor and G. K. Batchelor, book)
 Boundary Integral and Singularity Methods for Linearized Viscous Flow (C. Pozrikidis and Professor of Fluid Mechanics C Pozrikidis, book)
 Elementary Fluid Dynamics (D. J. Acheson, book)
 Low Reynolds number hydrodynamics (J. Happel and H. Brenner, book)
 Microhydrodynamics (Sangtae Kim and Seppo J. Karrila, book)
 Viscous Flow (H. Ockendon and J. R. Ockendon, book)
Assessment
The assessment for this course will be released on Monday 10th January 2022 at 00:00 and is due in before Sunday 23rd January 2022 at 23:59.
Assessment for all MAGIC courses is via takehome exam which will be made available at the release date (the start of the exam period).
You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).
If you have kept uptodate with the course, the expectation is it should take at most 3 hoursâ€™ work to attain the pass mark, which is 50%.
Please note that you are not registered for assessment on this course.
Files
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Lectures
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