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Classical & Biological Fluid Dynamics - MAT00054M

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  • Department: Mathematics
  • Module co-ordinator: Prof. Martin Bees
  • Credit value: 10 credits
  • Credit level: M
  • Academic year of delivery: 2022-23

Related modules

Co-requisite modules

  • None

Additional information

Prerequisite information:

  • Natural Science students must have taken Vector Calculus (MAT00030I) and Fundamentals of Fluid Dynamics (MAT00012H) 
  • MSc students must have taken a first course in fluid dynamics.

Module will run

Occurrence Teaching cycle
A Spring Term 2022-23

Module aims

To develop further the theoretical understanding and mathematical techniques necessary for analysing fluid flows and their biological applications.

Module learning outcomes

  • Analyse and understand different flow regimes

  • Understand theories underlying fluid flow dynamics

  • Be able to carry out exact and approximate calculations for important types of fluid flows


Module content


  • Two dimensional inviscid flows and the complex variables formalism.

  • Very viscous (Stokes) flows: basic equations and boundary conditions. Reversibility.

  • The Stokes drag for a sphere and its generalisations to bodies of complex shapes.

  • The far-field flow approximation for bodies in very viscous flows. The Oseen tensor.

  • Calculate the swimming velocity of a wavy sheet and relate this to swimming by ciliates.

  • Use resistive force theory to analyse the swimming of bacteria and spermatozoa.

  • Thin film flows. 

Academic and graduate skills

  • Academic skills: The skills taught are used in many areas of applied mathematics and mathematical physics and are essential for modern applications of fluid dynamics. Students on this module will analyse two important topics of mathematical biology in addition to the material of the H-level variant of the module.

  • Graduate skills: students will develop their ability to assimilate, process and engage with new material quickly and efficiently. They will develop problem-solving skills and learn to analyse critically different approaches. Students on this module will learn to work more independently than those on the H-level variant.


Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Classical & Biological Fluid Dynamics
2 hours 100

Special assessment rules



Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Classical & Biological Fluid Dynamics
2 hours 100

Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

  • D J Acheson. Elementary Fluid Dynamics, OUP.
  • L. M. Milne-Thompson, Theoretical Hydrodynamics, Dover.
  • J. Lighthill, Flagellar hydrodynamics, SIAM Review, 18, pp. 161-230, 1976.
  • S. Childress, Mechanics of swimming and flying, Cambridge Studies in Mathematical Biology (2), C.U.P., 1981.
  • G K Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press.
  • L D Landau and E M Lifshitz, Fluid Mechanics, Butterworth-Heinemann.

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.