Glaciological research

Glacier flow

Possibly the most interesting dynamical phenomenon is the glacier surge, a relaxation oscillation typified by the behaviour of the Variegated glacier (see the description in Paterson's book, The Physics of Glaciers). Normally, people say surging is unexplained, but this is not quite right. You can explain surging behaviour via a multi-valued sliding law, and it is possible to obtain such laws from realistic theories of hard bed sliding (see my 1987 JGR paper, cited below). The outstanding problem here is to describe how the drainage transition is effected in a three-dimensional geometry. I think this is a major control on the size of the surge. For the other `type' of surging glacier, the sub-polar (or polythermal) Trapridge, thermally controlled and sliding over till, the overall mechanism may be similar, though the details would be very different. The situation looks a bit like the ice sheet surge theory developed by Doug MacAyeal (see also Fowler and Johnson 1995, etc.).

Ice sheet dynamics

At the large scale, ice sheet modelling is probably in quite good shape. At the small to medium scale, however, this is less obviously true. The apparent occurrence of massive surges of the Hudson Strait ice stream of the Laurentide ice sheet in the last ice age (causing Heinrich events) must depend on the interplay between basal sliding and basal drainage, and modelling this is still at a rudimentary stage. Nor is it clear how such drainage theories will be included in the next generation of large ice sheet models.

At a smaller scale, the formation of ice streams may well be caused by the same positive feedback between sliding and drainage. Clare Johnson's thesis showed this to be feasible, though further work remains to be done.

Basal sliding

Sliding theory itself is rather dead, though it is certainly true that it is starved of data. For deformable tills, rheology is the main issue, but there are also interesting problems to do with erosion, for example the formation of drumlins. The main interest of sliding in terms of dynamics is through its dependence on the basal water pressure. Another weakly perceived point is that under cold ice, there should usually be a region between the frozen parts of the bed, and those where excess water is produced. In this `subtemperate' region, one has two thermal conditions and the sliding rate is indeterminate. I've been preaching this particular point for nearly 20 years.

Subglacial hydrology

This is full of interesting problems. The theory of jökulhlaups is simply stated, but still needs development in terms of describing sediment transport and erosion. Indeed, time dependent drainage and sediment transport theories (and their interaction) hardly exist, and in view of the (relative) ease with which data can be gathered, there is a lot of scope for developing theories which can use such data as a diagnostic tool for describing basal conditions.

Relevant publications

  1. Fowler, A.C. and D.A. Larson 1978 On the flow of polythermal glaciers, part I: Model and preliminary analysis. Proc. R. Soc. Lond. A363, 217-242.

  2. Fowler, A.C. 1979 The use of a rational model in the mathematical analysis of a polythermal glacier. J. Glaciol. 24, 443-456.

  3. Fowler, A.C. 1979 A mathematical approach to the theory of glacier sliding. J. Glaciol. 23, 131-141.

  4. Fowler, A.C. 1980 The existence of multiple steady states in the flow of large ice masses. J. Glaciol. 25, 183-184.

  5. Fowler, A.C. and D.A. Larson 1980 On the flow of polythermal glaciers II: Surface wave analysis. Proc. R. Soc. Lond. A370, 155-171.

  6. Fowler, A.C. and D.A. Larson 1980 The uniqueness of steady state flows of glaciers and ice sheets. Geophys. J. R. Astr. Soc. 63, 333-345.

  7. Fowler, A.C. and D.A. Larson 1980 Thermal stability properties of a model of glacier flow. Geophys. J. R. Astr. Soc. 63, 347-359.

  8. Fowler, A.C. 1981 A theoretical treatment of the sliding of glaciers in the absence of cavitation. Phil. Trans. R. Soc. Lond. Ser. A298, 637-685.

  9. Fowler, A.C. 1982 Waves on glaciers. J. Fluid Mech. 120, 283-321.

  10. Fowler, A.C. 1984 On the transport of moisture in polythermal glaciers. Geophys. Astrophys. Fluid Dynamics 28, 99-140.

  11. Fowler, A.C. 1986 A sliding law for glaciers of constant viscosity in the presence of subglacial cavitation. Proc. R. Soc. Lond. A407, 147-170.

  12. Fowler, A.C. 1986 Subtemperate basal sliding. J. Glaciol. 32, 3-5.

  13. Fowler, A.C. 1987 Sliding with cavity formation. J. Glaciol. 33, 255-267.

  14. Fowler, A.C. 1987 A theory of glacier surges. J. Geophys. Res. 92, 9111-9120.

  15. Fowler, A.C. 1989 A mathematical analysis of glacier surges. SIAM J. Appl. Math. 49, 246-262.

  16. Fowler, A.C. 1989 A mathematical analysis of glacier surges. SIAM J. Appl. Math. 49, 246-262.

  17. Fowler, A.C. 1992 Modelling ice sheet dynamics. Geophys. Astrophys. Fluid Dyn. 63, 29-65.

  18. Fowler, A.C. and J.S. Walder 1993 Creep closure of channels in deforming subglacial till. Proc. Roy. Soc. A, 441, 17-31.

  19. Walder, J.S. and A. Fowler 1994 Channelised subglacial drainage over a deformable bed. J. Glaciol. 40, 3-15.

  20. Fowler, A.C. and C. Johnson 1995 Hydraulic runaway: a mechanism for thermally regulated surges of ice sheets. J. Glaciol. 41, 554-561.

  21. Fowler, A.C. and F.S.L. Ng 1996 The rôle of sediment transport in the mechanics of jökulhlaups. Ann. Glaciol. 22, 255-259.

  22. Fowler, A.C. 1996 Glaciers and ice sheets. In: The mathematics of models for climatology and environment. NATO ASI Series I, Global Environmental Change, No. 48, ed. J.I. Diaz, pp. 301-335. Springer-Verlag, Berlin.

  23. Fowler, A.C. and C. Johnson 1996 Ice sheet surging and ice stream formation. Ann. Glaciol. 23, 68-73.

  24. Fowler, A.C. and E. Schiavi 1998 A theory of ice sheet surges. J. Glaciol. 44, 104-118.

  25. Fowler, A.C. 1999 Breaking the seal at Grímsvötn. J. Glaciol. 45, 506-516.

  26. Fowler, A.C. 2000 An instability mechanism for drumlin formation. Deformation of glacial materials, eds. A. Maltman, M.J. Hambrey and B. Hubbard, Spec. Pub. Geol. Soc. 176, 307-319.

  27. Fowler, A.C. 2001 Modelling the flow of glaciers and ice sheets. In: Continuum mechanics and applications in geophysics and the environment, eds. B. Straughan, R. Greve, H. Ehrentraut, and Y. Wang, Springer-Verlag, Berlin, pp. 201-221.

  28. Fowler, A.C. 2001 Dunes and drumlins. In: Geomorphological fluid mechanics, eds. A. Provenzale and N. Balmforth, pp. 430-454, Springer-Verlag, Berlin.

  29. Fowler, A.C., Tavi Murray and F.S.L. Ng 2001 Thermally controlled glacier surges. J. Glaciol. 47, 527-538.

  30. Fowler, A.C. 2002 Evolution equations for dunes and drumlins. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, Serie A. Mat. 96 (3), 377-387.

  31. Fowler, A.C. 2003 Rheology of subglacial till [letter]. J. Glaciol. 48 (163), 631-632.

  32. Fowler, A.C. 2003 On the rheology of till. Ann. Glaciol. 37, 55-59.