MAGIC092: Introduction to superfluids and turbulence

Course details

A specialist MAGIC course


Spring 2023
Monday, January 23rd to Friday, March 31st


Live lecture hours
Recorded lecture hours
Total advised study hours


09:05 - 09:55 (UK)


The aim of the course is to give a mathematical introduction to superfluids and superfluid turbulence.

Some of the existing mathematical models used to describe superfluid liquid Helium and Bose-Einstein condensates of dilute gases will be devised.

Experimental and numerical experiments will also complement the course as examples.

More details on the course topics are given in the Syllabus. 


Calculus, partial differential equation, general concepts of mechanics and fluid mechanics.

A basic knowledge of quantum mechanics would be preferable. 


  • brief history of superfluidity, introduction to different types of superfluids 
  • Landau's two-fluid model 
  • the Biot-Savart model and the Euler equation 
  • the local induction approximation limit 
  • Hasimoto's transformations and some of the nonlinear Schroedinger equation solutions 
  • Bose-Einstein condensates and the Gross-Pitaevskii equation 
  • Bogoliubov excitations and quantised vortices 
  • vortex reconnections 
  • introduction to classical turbulence and Kolmogorov's -5/3 law 
  • superfluid turbulence phenomenology 


  • DP

    Dr Davide Proment

    University of East Anglia


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The assessment for this course will be released on Monday 1st May 2023 at 00:00 and is due in before Monday 15th May 2023 at 11:00.

Assessment for all MAGIC courses is via take-home 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 up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.


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