ALBERT

Note: TABLE OF CONTENTS: ACKNOWLEDGEMENTS. - PREFACE. - INTRODUCTION. - SYMBOLS AND NOTATION. - PART 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 isotropie 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. - (α) General theory. - (β) Experimental results. - (c) Non-linear viscous deformation and creep. - (α) Results of creep tests. - (β) Generalization to a three-dimensional flow law. - (γ) Other flow laws. - 4. The Mechanical Properties of Sea Ice. - (a) The phase diagram of standard sea ice and its brine conten. - (b) Elastic properties. - (c) Other material properties. - References. - PART 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. - (α) Cold ice region. - (β) Temperate ice region. - (b) Boundary conditions. - (α) At the free surface. - (β) Along the ice-water interface. - (γ) Along the bedrock surface. - (δ) 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. - (α) Velocity and temperature fields x-independent. - (β) Extending and compressing flow. - (γ) Floating ice shelves 4. Concluding Remark. - 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. - (α) Harmonic perturbation from uniform flow for a zero accumulation rate. - (β) Analytic solution for a Newtonian fluid. - (γ) Numerical solution for non-linear rheology. - (δ) Effect of a steady accumulation rate. - (ε) A historical note on a previous approach. - (η) The first-order temperature problem. - (c) Numerical results for steady state. - (α) Transfer of bottom protuberances to the surface. - (β) Basal stresses. - (γ) Surface velocities. - (δ) 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. - (α) Coefficient functions for the special model. - (β) Solution for a step function. - (γ) General solution for uniform accumulation rate. - (δ) The inverse problem - calculation of climate from variations of the snout. - 4. General Treatment for an Arbitrary Valley Glacier. - (a) Fourier analysis in time. - (α) Low-frequency response. - (β) High-frequency response. - (γ) 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. - (α) Integration by the methods of characteristics. - (β) An illustrative example. - (γ) A remark on linearization. - (δ) 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?. - (α) Basic equations. - (β) Construction of perturbation solutions. - (γ) 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. - (α) Exact solutions for the limiting cases. - (β) Solution for a slightly off-circular channel. - (γ) 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. - SUBJECT INDEX.