Mathematical Modeling of Glacier Flow - Deriving the Nonlinear Wave Equation

Explore the mathematical modeling of glacier flow in this 49-minute video featuring Oxford Mathematician Dr Tom Crawford. Derive a mathematical model for ice flow in glaciers, leading to the nonlinear wave equation, while viewing stunning footage of glaciers filmed in Svalbard. Begin with mass flux through a 2D glacier segment, arriving at the conservation of mass equation. Apply the Navier-Stokes momentum equation and conditions for non-Newtonian fluids to determine mass flux. Neglect inertial terms due to small Reynolds Number and solve for stress. Use Glen's Flow Law to express flux in terms of glacier height, ultimately obtaining the governing equation as a nonlinear wave equation. Gain insights into the 'Maths on Tour' series and access additional mathematical content through provided links to Tom's website and social media platforms.