Uploaded June 2024 | Updated September 2026, 2 weeks ago
Oxford Mathematician Dr Tom Crawford derives a mathematical model for the flow of ice in glaciers, which leads to the nonlinear wave equation. Featuring footage of glaciers filmed on location in Svalbard.
The model begins by considering the mass flux through a small 2D segment of the glacier. Taking the limit as the size of the segment tends to zero, we arrive at the conservation of mass equation given in terms of the glacier height, the mass flux of ice, and the accumulation rate.
To determine an equation for the mass flux we use at the Navier-Stokes momentum equation and apply conditions for a non-Newtonian fluid. Due to the small Reynolds Number we are able to neglect the inertial terms, and solve the resulting system for the stress.
Finally, we apply Glen's Flow Law to obtain the flux in terms of the glacier height. Substituting this back into the mass equation gives the final governing equation in the form of a nonlinear wave equation.
Produced by Dr Tom Crawford at the University of Oxford. Tom is Public Engagement Lead at the Oxford University Department of Continuing Education: conted.ox.ac.uk/profiles/tom-crawford
Check out more in the 'Maths on Tour' series at the links below.
Ancient Egypt: youtube.com/watch?v=lX_f5oB83YI
Jantar Mantar Jaipur: youtube.com/watch?v=q84DUrXJ3xE
Dinosaurs: youtube.com/watch?v=yj5UQCRFbp4
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here: beautifulequation.com/collections/tom-rocks-maths
With thanks to
Ian Hewitt's lecture notes
Oxford University
Oxford University Department for Continuing Education
CADARN: youtube.com/watch?v=IRrcaHQZi5I
Oxford Mathematician Dr Tom Crawford derives a mathematical model for the flow of ice in glaciers, which leads to the nonlinear wave equation. Featuring footage of glaciers filmed on location in Svalbard.
The model begins by considering the mass flux through a small 2D segment of the glacier. Taking the limit as the size of the segment tends to zero, we arrive at the conservation of mass equation given in terms of the glacier height, the mass flux of ice, and the accumulation rate.
To determine an equation for the mass flux we use at the Navier-Stokes momentum equation and apply conditions for a non-Newtonian fluid. Due to the small Reynolds Number we are able to neglect the inertial terms, and solve the resulting system for the stress.
Finally, we apply Glen's Flow Law to obtain the flux in terms of the glacier height. Substituting this back into the mass equation gives the final governing equation in the form of a nonlinear wave equation.
Produced by Dr Tom Crawford at the University of Oxford. Tom is Public Engagement Lead at the Oxford University Department of Continuing Education: conted.ox.ac.uk/profiles/tom-crawford
Check out more in the 'Maths on Tour' series at the links below.
Ancient Egypt: youtube.com/watch?v=lX_f5oB83YI
Jantar Mantar Jaipur: youtube.com/watch?v=q84DUrXJ3xE
Dinosaurs: youtube.com/watch?v=yj5UQCRFbp4
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here: beautifulequation.com/collections/tom-rocks-maths
With thanks to
Ian Hewitt's lecture notes
Oxford University
Oxford University Department for Continuing Education
CADARN: youtube.com/watch?v=IRrcaHQZi5I
