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Über dieses Buch

The purpose and scope of this book on theoretical glaciology is outlined in the Introduction. Its aim is to study the theoretical aspects of'ice mechanics' and the 'dynamics of ice masses in a geophysical environment. For the mature reader, the book can serve as an introduction to glaciology. How­ ever, this is not what I would regard as advisible. Glaciology is an inter­ disciplinary science in which many special scientific disciplines play their part, from descriptive geography to fairly abstract mathematics. Advance­ ment will evolve from a merger of two or more branches of scientific specialization. In the last 20 years, several researchers in different fields of glaciology have written books emphasizing the aspects of their specialities and I have listed some which are known to me at the end of the Introduction. When glancing through these books, one recognizes that the mathematical aspects of glaciology are generally glossed over and, to date, there seems to be nothing available which concentrates on these. Therefore, I have written this book in an effort to close the gap and no apologies are offered for the mathematical emphasis. Rather, I believe that this neglect has, to a certain extent, aggra­ vated progress in the modelling of glaciology problems.

Inhaltsverzeichnis

Frontmatter

Fundamental Physics and Materials Technology of Ice

Frontmatter

Chapter 1. General Concepts

Abstract
Basic to ice mechanics — be it the theory of glacier flow, the response of floating ice plates to external loading, ice drifting and ice ridging, or the very practical questions of ice forces on structures — are the fundamental laws of continuum physics. These consist of the balance laws of mass, momentum, angular momentum, and energy, and indeed, there is no essential problem in glaciology in which use of one or more of these laws is not made. Not all of them would necessarily be used for answering the questions in mind. For instance, in the so-called ‘mass balance’ of a glacier, one only makes use of the law of conservation of mass. A similar situation prevails when one is investigating the response of a glacier to changes in climate. Of course, in such situations the true picture is oversimplified, and the neglect of certain physical laws might have to be bought at the expense of accuracy, or must be compensated by introducing phenomenological statements which replace the neglected balance laws. However, the simplifications in the physical picture and the replacement of certain basic balance laws by phenomenological statements often leads to drastic mathematical reductions yielding detailed physical insight that could not otherwise be obtained. As an example we mention that the distribution of stress and velocity in an ice sheet is often determinable without simultaneously searching for the temperature distribution. Alternatively, the temperature distribution may be determined independently from that of velocity. In either case, some assumptions about the neglected fields must be made, assumptions motivated by experimental observations or by some sort of plausibility arguments.
Kolumban Hutter

Chapter 2. A Brief Summary of Constitutive Relations for Ice

Abstract
In Chapter 1 the constitutive theory was treated from a rather general point of view and no specific details were given about ice as a material. Here, we give a brief summary of its constitutive response from a view-point of material science. No claim of completeness will be made, however.
Kolumban Hutter

The Deformation of an Ice Mass under Its Own Weight

Frontmatter

Chapter 3. A Mathematical Ice-Flow Model and Its Application to Parallel-Sided Ice Slabs

Abstract
The previous chapters were devoted to the derivation of the basic principles and to the material properties of ice with no particular intention of applying the collected information to a physical problem. Here, in this chapter, attention will be focussed on a first simple application of the knowledge gained so far. In particular, an attempt is made to shed some light on the deformation mechanism and thermal conditions of glaciers and ice sheets.
Kolumban Hutter

Chapter 4. Thermo-Mechanical Response of Nearly Parallel-Sided Ice Slabs Sliding over Their Bed

Abstract
In Chapter 3, the strictly parallel-sided ice slab was analysed. Solutions to the flow and temperature problem were constructed for which stresses did not vary with the coordinate along the glacier axis. Two solutions were found which satisfied these conditions. In the first, apart from stresses, velocities and temperature are also independent of the coordinate along the ice slab. For this solution to be consistent with the boundary conditions of the general model, both accumulation and ablation had to be neglected. To account for the inclusion of the latter, and for floating ice shelves, in order to properly allow for mass flux from the grounded portion of the ice sheet, the velocity field had to be assumed to vary with the length coordinate. On the basis that stress and temperature are still independent of this coordinate, it was found that the longitudinal velocity components vary linearly along the ice sheet axis, whereas transverse velocities remain independent of the length coordinate and vary linearly with depth. Longitudinal and transverse stretchings are equal and constant in this case, and the constant transverse surface velocity gives the possibility of including a constant accumulation rate. For a grounded ice slab, it was shown that this solution is in violation with a stress-dependent sliding law. For an ice shelf, on the other hand, the solution is meaningful, provided that the drag from the ocean current is neglected; in this case, the flow parameters can be related to the thermal conditions in the atmosphere. It is clear from the above that for ice slabs resting on a rockbed, a more general solution to the flow problem should be sought which is free from the defects mentioned above. This is one reason why one should search for a solution, in which longitudinal stretching effects are consistently taken into account. A second reason is the fact that glaciers and ice sheets are only very nearly parallel-sided. Generally, the rockbed and free surface undulate about a mean plane surface. Rockbed protuberances force the ice to flow around them. Together with the spatially-dependent accumulation rate, they cause (also in the steady state) surface undulations and are thus responsible for the longitudinal stretching effects occurring in ice slopes. It is evident in these instances that stresses can no longer be independent of the longitudinal coordinate.
Kolumban Hutter

Chapter 5. The Application of the Shallow-Ice Approximation

Abstract
In the previous chapter, the nearly parallel-sided ice slab was thoroughly analysed; in particular, its steady-state response was treated, and it was shown how small-amplitude bottom protuberances affect surface topography, basal stresses and surface velocities. Attention was restricted to plane motion and to ice slabs for which the mean bed and mean surface were plane and strictly parallel so that the mean ice thickness was constant. In reality, this is only approximately correct as it is well known that ice-sheet thicknesses may vary from up to 3000 m inland or more to zero thickness at the snout. On length scales which are comparable with the extension of the ice sheet, the assumption of small variations about a parallel-sided ice slab is thus unrealistic. On the other hand, calculations, as those performed in Chapter 4, must be limited to length scales for which ice-sheet thicknesses do not deviate appreciably from a layer with a constant thickness.
Kolumban Hutter

Chapter 6. The Response of a Glacier or an Ice Sheet to Seasonal and Climatic Changes

Abstract
In the preceding chapters, attention was focused on the development of a mathematical model of glacier flow and on first flow applications under plane motion. Except for the surface-wave stability analysis in a parallel-sided ice strip in Chapter 4, most questions were concerned with the response of a glacier and ice sheet to steady-state conditions, or at least conditions close to such a steady state.
Kolumban Hutter

Chapter 7. Three-Dimensional and Local Flow Effects in Glaciers and Ice Sheets

Abstract
The investigations of ice-flow problems which have been undertaken in this book so far, have been rather qualitative and thus theoretical because only plane flow was considered and, furthermore, very simple glacier geometries were assumed. Either conditions near the strictly parallel-sided ice slab were analysed or the top and bottom surfaces were assumed to vary slowly in the horizontal directions. Three important problems, however, remained untouched; they are:
(i)
Valley glaciers are bounded by mountain sides. These flanks affect the flow and their influence is all the greater, the narrower the valley. Hence, ice flow in a channel of a finite cross-section should be analysed. As a first approximation, flow in a cylindrical channel provides sufficient indications as to the order of magnitude of the boundedness effect of the valley.
 
(ii)
The analyses of ice sheets were performed in Chapters 5 and 6 for plane motion, and it was shown that real ice sheets spread in both horizontal directions. In order to be able to predict real ice-sheet geometries, the solution procedures of Chapters 5 and 6 should, therefore, be generalized to include both horizontal dimensions.
 
(iii)
Most ice-flow problems in glaciers that are relevant in engineering, are of a local nature and so the simplifications of a nearly-parallelsided ice slab or the shallow-ice approximation do not apply. Under these circumstances, the full two- or three-dimensional boundary-value problem must be solved, but the complexity of these problems is generally so immense that no analytic solutions can be found. Numerical techniques, of which finite differences and finite elements are two alternatives, must then be resorted to. The latter profits from the existence of variational principles.
 
Kolumban Hutter

Backmatter

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