Applications of mathematics to environmental problems involving the use of models with ordinary differential equations, first order partial differential equations, and nonlinear diffusion equations. Examples to be considered are : river flow and sediment transport; glacier dynamics, glacier outburst floods (jökulhlaups); plate tectonics and the convection of planetary mantles.

Lecture Synopsis

Rivers

1. Chézy and Manning flow laws.
2. Slowly varying flow; flood hydrograph.
3. Rapidly varying flow, St. Venant equations.
4. Scaling; the Froude number. Waves and instability.
5. Sediment transport; bedforms.
6. Bedload transport; the Exner equation. Suspended sediment.
7. Anti-dunes and dunes.

   Glacier dynamics

8. Waves, surges, floods.
9. Glacier dynamics, surface waves.
10. Subglacial sliding and drainage.
11. Linked cavity systems and surges.
12. Jökulhlaups.

    Mantle convection

13. Plate tectonics.
14. Rayleigh-Bénard convection.
15. Boundary layer theory.
16. Temperature-dependent viscosity, subduction; Venus.

Reading List

• A. C. Fowler, Mathematics and the environment, Mathematical Institute lecture notes, 1998

• K. Richards, Rivers, Methuen, 1982

• G. B. Whitham, Linear and nonlinear waves Wiley, New York, 1974

• W. S. B. Paterson, The physics of glaciers, 3rd edition. Pergamon Press, 1994

• D. L. Turcotte and G. Schubert, Geodynamics, John Wiley,1982

• G. F. Davies, Dynamic Earth. Plates, plumes and mantle convection, C. U. P., Cambridge, 1999