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Maths of Glaciers - Svalbard and Nonlinear Wave Equations

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: https://www.conted.ox.ac.uk/profiles/... Check out more in the 'Maths on Tour' series at the links below. Ancient Egypt:    • The Maths of Ancient Egypt: Numbers, ...   Jantar Mantar Jaipur:    • The Maths of the Solar System - Arist...   Dinosaurs:    • Which Dinosaur is the Fastest? The Ma...   For more maths content check out Tom's website https://tomrocksmaths.com/ You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.   / tomrocksmaths     / tomrocksmaths     / tomrocksmaths   Get your Tom Rocks Maths merchandise here: https://www.beautifulequation.com/col... With thanks to Ian Hewitt's lecture notes Oxford University Oxford University Department for Continuing Education CADARN:    • Animated Graphic of Glacial Growth an...