Theoretical glaciology: material science of ice and the mechanics of glaciers and ice sheets
A comprehensive 'mathematical' introduction to the science and behaviour of glaciers and ice sheets in their geophysical environment. In two parts: Part I. Fundamental physics and materials technology of ice. Part II. The deformation of an ice mass under its own weight.
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Reidel [u.a.]
1983
|
| Series: | Mathematical approaches to geophysics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | A comprehensive 'mathematical' introduction to the science and behaviour of glaciers and ice sheets in their geophysical environment. In two parts: Part I. Fundamental physics and materials technology of ice. Part II. The deformation of an ice mass under its own weight. |
| Physical Description: | XXXII, 510 S. Ill., graph. Darst. |
| ISBN: | 9027714738 |
Staff View
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| 520 | 3 | |a A comprehensive 'mathematical' introduction to the science and behaviour of glaciers and ice sheets in their geophysical environment. In two parts: Part I. Fundamental physics and materials technology of ice. Part II. The deformation of an ice mass under its own weight. | |
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Record in the Search Index
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| adam_text |
Titel: Theoretical glaciology
Autor: Hutter, Kolumban
Jahr: 1983
TABLE OF CONTENTS
Acknowledgements õ³³³
Preface xv
Introduction õ³õ
Symbols and Notation xxvii
Part I. Fundamental Physics and Materials Technology
of Ice
Chapter 1. General Concepts 3
1. Introduction 3
2. Equations of Balance 4
3. Material Response 18
(a) General constitutive relations, simple materials 18
(b) The rule of material objectivity 20
(c) Material symmetry 22
(d) Constitutive response for isotropie bodies 25
(e) Materials with bounded memory-some constitutive
representations 27
(f) Incompressibility 30
(g) Some representations of isotropie functions 30
4. The Entropy Principle 33
(a) The viscous heat-conducting compressible fluid 34
(b) The viscous heat-conducting incompressible fluid 37
(c) Pressure and extra stress as independent variables 38
(d) Thermoelastie solid 39
(e) Final remarks 40
5. Phase Changes 41
(a) Phase changes for a viscous compressible heat-conducting
fluid 42
viii TABLE OF CONTENTS
(b) Phase changes for a viscous incompressible heat-conducting
fluid 46
References 46
Chapter 2. A Brief Summary of Constitutive Relations for Ice 48
1. Preliminary Remarks 48
2. The Mechanical Properties of Hexagonal Ice 49
(a) The crystal structure of ordinary ice 49
(b) The elastic behavior of hexagonal ice 52
(c) The inelastic behavior of single-crystal ice 56
3. The Mechanical Properties of Polycrystalline Ice 60
(a) The elastic behavior of polycrystalline ice 60
(b) Linear viscoelastic properties of polycrystalline ice 63
( a) General theory 63
(ß) Experimental results 77
(c) Non-linear viscous deformation and creep 81
(a) Results of creep tests 81
iß) Generalization to a three-dimensional flow law 85
(-;) Other flow laws 91
4. The Mechanical Properties of Sea Ice 99
(a) The phase diagram of standard sea ice and its brine content 100
(b) Elastic properties 103
(c) Other material properties 105
References 110
Part II. The Deformation of an Ice Mass under its own
Weight
Chapter 3. A Mathematical Ice-flow Model and its Application to
Parallel-sided Ice Slabs 119
1. Motivation and Physical Description 119
2. The Basic Model - Its Field Equations and Boundary Conditions 122
(a) The field equations 124
(a) Cold ice region 124
(ß) Temperate ice region 126
(b) Boundary conditions 131
(a) At the free surface 132
(ß) Along the ice-water interface 136
(¦/) Along the bedrock surface 138
(?) Along the melting surface 143
3. The Response of a Parallel-sided Ice Slab to Steady Conditions 145
(a) Dimensionless forms of the field equations 148
(b) Parallel-sided ice slab, a first approximation to glacier and
ice-shelf flow dynamics 154
(a) Velocity and temperature fields ?-independent 155
TABLE OF CONTENTS ix
(â) Extending and compressing flow 166
(ã) Floating ice shelves 179
4. Concluding Remarks 183
References 184
Chapter 4. Thermo-mechanical Response of Nearly Parallel-sided Ice
Slabs Sliding over their Bed 188
1. Motivation 188
2. The Basic Boundary-value Problem and its Reduction to Linear
Form 190
3. The Solution of the Boundary-value Problems 199
(a) Zeroth-order problem 199
(b) First-order problem 200
(a) Harmonic perturbation from uniform flow for a zero
accumulation rate 202
(â) Analytic solution for a Newtonian fluid 204
(7) Numerical solution for non-linear rheology 208
(ä) Effect of a steady accumulation rate 212
(å) A historical note on a previous approach 214
(ç) The first-order temperature problem 215
(c) Numerical results for steady state 218
(a) Transfer of bottom protuberances to the surface 220
(â) Basal stresses 230
(y) Surface velocities 236
( 5) Effect of a steady accumulation rate 240
4. Remarks on Response to a Time-dependent Accumulation Rate 242
5. Surface-wave Stability Analysis 243
(a) The eigenvalue problem 244
(b) Discussion of results 249
6. Final Remarks 252
References 253
Chapter 5. The Application of the Shallow-ice Approximation 256
1. Background and Previous Work 256
2. Derivation of the Basal Shear-stress Formula by Integrating the
Momentum Equations over Ice Thickness 260
(a) Derivation 260
(b) The use of the basal shear-stress formula in applied
glaciology 264
3. Solution of the Ice-flow Problem using the Shallow-ice
Approximation 268
(a) Governing equations 268
(b) Shallow-ice approximation 270
(c) Construction of the perturbation solution 274
x TABLE OF CONTENTS
(d) Results 282
(e) Temperature field 289
4. Theoretical Steady-state Profiles 292
(a) Earlier theories and their limitations 292
(b) Surface profiles determined by using the shallow-ice
approximation 298
5. An Alternative Scaling - a Proper Analysis of Dynamics of Ice
Sheets with Ice Divides 309
(a) Finite-bed inclination 314
(b) Small-bed inclination 316
(c) Illustrations 321
References 330
Chapter 6. The Response of a Glacier or an Ice Sheet to Seasonal
and Climatic Changes 333
1. Statement of the Problem 333
2. Development of the Kinematic Wave Theory 336
(a) Full non-linear theory 336
(b) Perturbation expansion-linear theory 341
(c) An estimate for the coefficients C and D 342
(d) Boundary and initial conditions 346
3. Theoretical Solutions for a Model Glacier 346
(a) Solutions neglecting diffusion 347
(b) Theoretical solutions for a diffusive model 353
(a) Coefficient functions for the special model 353
(ß) Solution for a step function 355
(/) General solution for uniform accumulation rate 363
(()) The inverse problem -calculation of climate from
variations of the snout 367
4. General Treatment for an Arbitrary Valley Glacier 369
(a) Fourier analysis in time 370
(t) Low-frequency response 371
(ß) High-frequency response 373
(¦/) Use of the results 374
(b) Direct integration methods 375
5. Derivation of the Surface-wave Equation from First Principles
Non-linear Theory 377
(a) Surface waves in the shallow-ice approximation 379
(a) Integration by the methods of characteristics 382
(ß) An illustrative example 392
(¦/) A remark on linearization 398
(e)) Effects of diffusion 400
(b) Remarks regarding time-dependent surface profiles in ice
sheets 403
TABLE OF CONTENTS ֎
(c) Long waves in an infinite ice slab - Is accounting for
diffusion enough? 404
(a) Basic equations 405
(â) Construction of perturbation solutions 407
(y) Numerical results 416
6. Concluding Remarks 420
References 421
Chapter 7. Three-dimensional and Local Flow Effects in
Glaciers and Ice Sheets 424
1. Introduction 424
2. Effect of Valley Sides on the Motion of a Glacier 425
(a) Solutions in special cases 428
(a) Exact solutions for the limiting cases 428
(â) Solution for a slightly off-circular channel 431
(7) A note on very deep and wide channels 434
(b) A useful result for symmetrical channels with no boundary
slip 438
(c) Numerical solution discussion of results 441
3. Three-dimensional Flow Effects in Ice Sheets 450
(a) Basic equations 451
(b) Decoupling of the stress-velocity problem from the problem
of surface profile 455
(c) The equation describing the surface geometry 460
(d) The margin conditions 461
4. Variational Principles 462
(a) Fundamental variational theorem 463
(b) Variational principle for velocities 467
(c) Reciprocal variational theorem 468
(d) Maximum and minimum principles 471
(e) Adoption of the variational principles to ice problems 474
5. Discussion of Some Finite-element Solutions 476
References 482
Appendix. Detailed Calculations Pertaining to Higher-order
Stresses in the Shallow-ice Approximation 484
Author Index 490
Subject Index 494 |
| any_adam_object | 1 |
| author | Hutter, Kolumban 1941-2024 |
| author_GND | (DE-588)121218694 |
| author_facet | Hutter, Kolumban 1941-2024 |
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| author_sort | Hutter, Kolumban 1941-2024 |
| author_variant | k h kh |
| building | Verbundindex |
| bvnumber | BV001204775 |
| callnumber-first | G - Geography, Anthropology, Recreation |
| callnumber-label | GB2403 |
| callnumber-raw | GB2403.2 |
| callnumber-search | GB2403.2 |
| callnumber-sort | GB 42403.2 |
| callnumber-subject | GB - Physical Geography |
| classification_rvk | RB 10368 RB 10369 SK 950 TI 4000 |
| ctrlnum | (OCoLC)9394238 (DE-599)BVBBV001204775 |
| dewey-full | 551.3/1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 551 - Geology, hydrology, meteorology |
| dewey-raw | 551.3/1 |
| dewey-search | 551.3/1 |
| dewey-sort | 3551.3 11 |
| dewey-tens | 550 - Earth sciences |
| discipline | Geologie / Paläontologie Mathematik Geographie |
| format | Book |
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| isbn | 9027714738 |
| language | English |
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| spelling | Hutter, Kolumban 1941-2024 Verfasser (DE-588)121218694 aut Theoretical glaciology material science of ice and the mechanics of glaciers and ice sheets Kolumban Hutter Dordrecht [u.a.] Reidel [u.a.] 1983 XXXII, 510 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical approaches to geophysics A comprehensive 'mathematical' introduction to the science and behaviour of glaciers and ice sheets in their geophysical environment. In two parts: Part I. Fundamental physics and materials technology of ice. Part II. The deformation of an ice mass under its own weight. Glaciologie Glaciologie gtt Glaciology Glaziologie (DE-588)4205614-7 gnd rswk-swf Gletscherkunde (DE-588)4157593-3 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Gletscherkunde (DE-588)4157593-3 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Glaziologie (DE-588)4205614-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000727553&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hutter, Kolumban 1941-2024 Theoretical glaciology material science of ice and the mechanics of glaciers and ice sheets Glaciologie Glaciologie gtt Glaciology Glaziologie (DE-588)4205614-7 gnd Gletscherkunde (DE-588)4157593-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4205614-7 (DE-588)4157593-3 (DE-588)4114528-8 |
| title | Theoretical glaciology material science of ice and the mechanics of glaciers and ice sheets |
| title_auth | Theoretical glaciology material science of ice and the mechanics of glaciers and ice sheets |
| title_exact_search | Theoretical glaciology material science of ice and the mechanics of glaciers and ice sheets |
| title_full | Theoretical glaciology material science of ice and the mechanics of glaciers and ice sheets Kolumban Hutter |
| title_fullStr | Theoretical glaciology material science of ice and the mechanics of glaciers and ice sheets Kolumban Hutter |
| title_full_unstemmed | Theoretical glaciology material science of ice and the mechanics of glaciers and ice sheets Kolumban Hutter |
| title_short | Theoretical glaciology |
| title_sort | theoretical glaciology material science of ice and the mechanics of glaciers and ice sheets |
| title_sub | material science of ice and the mechanics of glaciers and ice sheets |
| topic | Glaciologie Glaciologie gtt Glaciology Glaziologie (DE-588)4205614-7 gnd Gletscherkunde (DE-588)4157593-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Glaciologie Glaciology Glaziologie Gletscherkunde Mathematisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000727553&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hutterkolumban theoreticalglaciologymaterialscienceoficeandthemechanicsofglaciersandicesheets |