Theoretical Glaciology

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August 1983



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.


I. Fundamental Physics and Materials Technology of Ice.- 1, General Concepts.- 1. Introduction.- 2. Equations of Balance.- 3. Material Response.- (a) General constitutive relations, simple materials.- (b) The rule of material objectivity.- (c) Material symmetry.- (d) Constitutive response for isotropic bodies.- (e) Materials with bounded memory - some constitutive representations.- (f) Incompressibility.- (g) Some representations of isotropic functions.- 4. The Entropy Principle.- (a) The viscous heat-conducting compressible fluid.- (b) The viscous heat-conducting incompressible fluid.- (c) Pressure and extra stress as independent variables.- (d) Thermoelastic solid.- (e) Final remarks.- 5. Phase Changes.- (a) Phase changes for a viscous compressible heat-conducting fluid.- (b) Phase changes for a viscous incompressible heat-conducting fluid.- References.- 2. A Brief Summary of Constitutive Relations for Ice.- 1. Preliminary Remarks.- 2. The Mechanical Properties of Hexagonal Ice.- (a) The crystal structure of ordinary ice.- (b) The elastic behavior of hexagonal ice.- (c) The inelastic behavior of single-crystal ice.- 3. The Mechanical Properties of Polycrystalline Ice.- (a) The elastic behavior of polycrystalline ice.- (b) Linear viscoelastic properties of polycrystalline ice.- (?) General theory.- (?) Experimental results.- (c) Non-linear viscous deformation and creep.- (?) Results of creep tests.- (?) Generalization to a three-dimensional flow law.- (?) Other flow laws.- 4. The Mechanical Properties of Sea Ice.- (a) The phase diagram of standard sea ice and its brine content.- (b) Elastic properties.- (c) Other material properties.- References.- II. The Deformation of an Ice Mass Under Its Own Weight.- 3. A Mathematical Ice-flow Model and its Application to Parallel-sided Ice Slabs.- 1. Motivation and Physical Description.- 2. The Basic Model - Its Field Equations and Boundary Conditions.- (a) The field equations.- (?) Cold ice region.- (?) Temperate ice region.- (b) Boundary conditions.- (?) At the free surface.- (?) Along the ice-water interface.- (?) Along the bedrock surface.- (?) Along the melting surface.- 3. The Response of a Parallel-sided Ice Slab to Steady Conditions.- (a) Dimensionless forms of the field equations.- (b) Parallel-sided ice slab, a first approximation to glacier and ice-shelf flow dynamics.- (?) Velocity and temperature fields.7V-independent.- (?) Extending and compressing flow.- (?) Floating ice shelves.- 4. Concluding Remarks.- References.- 4. Thermo-mechanical Response of Nearly Parallel-sided Ice Slabs Sliding over their Bed.- 1. Motivation.- 2. The Basic Boundary-value Problem and its Reduction to Linear Form.- 3. The Solution of the Boundary-value Problems.- (a) Zeroth-order problem.- (b) First-order problem.- (?) Harmonic perturbation from uniform flow for a zero accumulation rate.- (?) Analytic solution for a Newtonian fluid.- (?) Numerical solution for non-linear rheology.- (?) Effect of a steady accumulation rate.- (?) A historical note on a previous approach.- (?) The first-order temperature problem.- (c) Numerical results for steady state.- (?) Transfer of bottom protuberances to the surface.- (?) Basal stresses.- (?) Surface velocities.- (?) Effect of a steady accumulation rate.- 4. Remarks on Response to a Time-dependent Accumulation Rate.- 5. Surface-wave Stability Analysis.- (a) The eigenvalue problem.- (b) Discussion of results.- 6. Final Remarks.- References.- 5, The Application of the Shallow-ice Approximation.- 1. Background and Previous Work.- 2. Derivation of the Basal Shear-stress Formula by Integrating the Momentum Equations over Ice Thickness.- (a) Derivation.- (b) The use of the basal shear-stress formula in applied glaciology.- 3. Solution of the Ice-flow Problem using the Shallow-ice Approximation.- (a) Governing equations.- (b) Shallow-ice approximation.- (c) Construction of the perturbation solution.- (d) Results.- (e) Temperature field.- 4. Theoretical Steady-state Profiles.- (a) Earlier theories and their limitations.- (b) Surface profiles determined by using the shallow-ice approximation.- 5. An Alternative Scaling - a Proper Analysis of Dynamics of Ice Sheets with Ice Divides.- (a) Finite-bed inclination.- (b) Small-bed inclination.- (c) Illustrations.- References.- 6. The Response of a Glacier or an Ice Sheet to Seasonal and Climatic Changes.- 1. Statement of the Problem.- 2. Development of the Kinematic Wave Theory.- (a) Full non-linear theory.- (b) Perturbation expansion - linear theory.- (c) An estimate for the coefficients C and D.- (d) Boundary and initial conditions.- 3. Theoretical Solutions for a Model Glacier.- (a) Solutions neglecting diffusion.- (b) Theoretical solutions for a diffusive model.- (?) Coefficient functions for the special model.- (?) Solution for a step function.- (?) General solution for uniform accumulation rate.- (?) The inverse problem - calculation of climate from variations of the snout.- 4. General Treatment for an Arbitrary Valley Glacier.- (a) Fourier analysis in time.- (?) Low-frequency response.- (?) High-frequency response.- (?) Use of the results.- (b) Direct integration methods.- 5. Derivation of the Surface-wave Equation from First Principles - Non-linear Theory.- (a) Surface waves in the shallow-ice approximation.- (?) Integration by the methods of characteristics.- (?) An illustrative example.- (?) A remark on linearization.- (?) Effects of diffusion.- (b) Remarks regarding time-dependent surface profiles in ice sheets.- (c) Long waves in an infinite ice slab - Is accounting for diffusion enough?.- (?) Basic equations.- (?) Construction of perturbation solutions.- (?) Numerical results.- 6. Concluding Remarks.- References.- 7. Three-dimensional and Local Flow Effects in Glaciers and Ice Sheets.- 1. Introduction.- 2. Effect of Valley Sides on the Motion of a Glacier.- (a) Solutions in special cases.- (?) Exact solutions for the limiting cases.- (?) Solution for a slightly off-circular channel.- (?) A note on very deep and wide channels.- (b) A useful result for symmetrical channels with no boundary slip.- (c) Numerical solution - discussion of results.- 3. Three-dimensional Flow Effects in Ice Sheets.- (a) Basic equations.- (b) Decoupling of the stress-velocity problem from the problem of surface profile.- (c) The equation describing the surface geometry.- (d) The margin conditions.- 4. Variational Principles.- (a) Fundamental variational theorem.- (b) Variational principle for velocities.- (c) Reciprocal variational theorem.- (d) Maximum and minimum principles.- (e) Adoption of the variational principles to ice problems.- 5. Discussion of Some Finite-element Solutions.- References.- Appendix. Detailed Calculations Pertaining to Higher-order Stresses in the Shallow-ice Approximation.- Author Index.



`...a remarkable book of high quality and of great importance to anybody who is interested in the mechanics of ice and glaciers. It has the advantage of being clearly written and it contains all the necessary background material.'
Pageoph, 123 (1985)
`...the book provides a very detailed mathematical treatment of natural ice flows, and will stand as a reference text for noth the practitioner seeking valid models for correlation and prediction, and the theoretician embarking on further developments.'
Journal of Fluid Mechanics, 150 (1985)

EAN: 9789027714732
ISBN: 9027714738
Untertitel: Material Science of Ice and the Mechanics of Glaciers and Ice Sheets. 1983. Auflage. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: August 1983
Seitenanzahl: 546 Seiten
Format: gebunden
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