Pattern formation in viscous flows: the Taylor-Couette problem and Rayleigh-Bénard convection
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1999
|
| Series: | International series of numerical mathematics
128 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008359773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturverz. S. 191 - 204 |
| Physical Description: | XI, 209 S. Ill., graph. Darst. |
| ISBN: | 376436047X 081766047X |
Staff View
MARC
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| 100 | 1 | |a Meyer-Spasche, Rita |e Verfasser |0 (DE-588)108581705 |4 aut | |
| 245 | 1 | 0 | |a Pattern formation in viscous flows |b the Taylor-Couette problem and Rayleigh-Bénard convection |c Rita Meyer-Spasche |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1999 | |
| 300 | |a XI, 209 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series of numerical mathematics |v 128 | |
| 500 | |a Literaturverz. S. 191 - 204 | ||
| 650 | 4 | |a Analyse numérique | |
| 650 | 4 | |a Bifurcation | |
| 650 | 4 | |a Convection | |
| 650 | 4 | |a Expérience Taylor | |
| 650 | 4 | |a Fluide visqueux | |
| 650 | 4 | |a Motif | |
| 650 | 7 | |a Taylor, Tourbillons de |2 ram | |
| 650 | 4 | |a Tourbillon | |
| 650 | 7 | |a Écoulement visqueux |2 ram | |
| 650 | 4 | |a Pattern formation (Physical sciences) | |
| 650 | 4 | |a Rayleigh-Bénard convection | |
| 650 | 4 | |a Taylor vortices | |
| 650 | 4 | |a Viscous flow | |
| 650 | 0 | 7 | |a Taylor-Couette-Strömung |0 (DE-588)4249869-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Bénard-Effekt |0 (DE-588)4144456-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Taylor-Couette-Strömung |0 (DE-588)4249869-7 |D s |
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| 830 | 0 | |a International series of numerical mathematics |v 128 |w (DE-604)BV035415862 |9 128 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008359773 | |
Record in the Search Index
| DE-BY-TUM_call_number | 0102 MAT 650f 2001 A 892-128 |
|---|---|
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| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010588928 |
| _version_ | 1821931842332262401 |
| adam_text | Contents
1 The Taylor Experiment
1.1 Modeling of the experiment 1
1.1.1 Introduction 1
1.1.2 Mathematical description of the experiment 6
1.1.3 Narrow gap limit and Rayleigh Benard problem ... 8
1.1.4 End effects 11
1.2 Flows between rotating cylinders 13
1.3 Stability of Couette flow 17
1.3.1 Equations of motion for axisymmetric
perturbations 19
1.3.2 Computation of marginal curves 23
1.3.3 Validity of the principle of exchange of stability ... 27
2 Details of a Numerical Method
2.1 Introduction 29
2.1.1 Numerical model 29
2.1.2 Numerical methods 32
2.1.3 Validity of the model 33
2.1.4 Stability 35
2.2 The discretized system 36
2.2.1 Discretization in the axial z direction 36
2.2.2 Discretization in the radial r direction 40
2.2.3 Boundary conditions 40
2.2.4 Final version of the equations 42
2.3 Computation of solutions 45
2.3.1 Pseudo arclength continuation and
Newton iterations 45
2.3.2 Continuation in the Reynolds number Re 48
ix
x Contents
2.3.3 Continuation in the wave number k 50
2.3.4 Simple continuation 51
2.3.5 Switching branches 52
2.4 Computation of flow parameters 55
2.4.1 Periodicity 56
2.4.2 Computation of um := u(rm, zm; A)
at rm := 1 + 6/2, zm = 0 58
2.4.3 Computation of the torque 59
2.4.4 Computation of kinetic energies 60
2.4.5 Computation of the stream function 64
2.5 Numerical accuracy 66
2.5.1 Finite Differences 67
2.5.2 Truncation of the Fourier Series 71
2.5.3 Conclusions 76
3 Stationary Taylor Vortex Flows
3.1 Introduction 77
3.2 Computations with fixed period A rs 2 81
3.2.1 A narrow gap problem, r] = 0.95 82
3.2.2 A wide gap problem, r — 0.5 84
3.3 Variation of flows with period A 85
3.3.1 Previous results on flows with wavelengths A ^ 2 . . 85
3.3.2 Continuous change of period 88
3.3.3 Flows near Re = VU Recr 91
3.3.4 Flows for Re = 800 « 3.65 Recr 101
3.4 Interactions of secondary branches 106
3.4.1 A neighborhood of (Re24, A24)
and the basic (2,4) fold 106
3.4.2 Connections to the Rayleigh Benard problem .... 110
3.4.3 The basic (n, 2n) fold for higher
Reynolds numbers 113
3.4.4 The basic 2 vortex surface 117
3.5 Re = 2 Recr and the (n,pn) double points 121
3.6 Stability of the stationary vortices 133
3.6.1 Wavy vortices 133
3.6.2 Eckhaus and short wavelength instabilities 136
Contents xi
4 Secondary Bifurcations on Convection Rolls
4.1 Introduction 143
4.2 The Rayleigh Benard problem 148
4.2.1 Convection in fluids 148
4.2.2 Boussinesq approximation 150
4.2.3 The Rayleigh Benard problem as limiting case
of the Taylor problem 154
4.3 Stationary convection rolls 160
4.3.1 The basic equations 160
4.3.2 Critical curves of the primary solution 164
4.3.3 Pure mode solutions 167
4.4 The (2,4) interaction in a model problem 169
4.4.1 The model problem 169
4.4.2 Calculation of secondary bifurcation points
on the 2 roll solutions 170
4.4.3 Calculation of secondary bifurcation points
on the 4 roll solutions 172
4.4.4 The perturbation approach 175
4.5 The (2,6) interaction in a model problem 179
4.5.1 Calculation of secondary bifurcation points
on the 2 roll solutions 179
4.5.2 Calculation of secondary bifurcation points
on the 6 roll solutions 181
4.5.3 Nonlinear interactions between
the bifurcating branches 182
4.6 Generalisations and consequences 184
4.6.1 Other interactions 184
4.6.2 Linear superpositions of pure mode solutions .... 185
4.6.3 Secondary bifurcations in the
Taylor problem revisited 188
Bibliography 191
Index 205
|
| any_adam_object | 1 |
| author | Meyer-Spasche, Rita |
| author_GND | (DE-588)108581705 |
| author_facet | Meyer-Spasche, Rita |
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| ctrlnum | (OCoLC)41271964 (DE-599)BVBBV012329062 |
| dewey-full | 532/.0533 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.0533 |
| dewey-search | 532/.0533 |
| dewey-sort | 3532 3533 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV012329062 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:28:21Z |
| institution | BVB |
| isbn | 376436047X 081766047X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008359773 |
| oclc_num | 41271964 |
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| owner | DE-703 DE-91G DE-BY-TUM DE-29T DE-634 DE-11 DE-188 |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-29T DE-634 DE-11 DE-188 |
| physical | XI, 209 S. Ill., graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Birkhäuser |
| record_format | marc |
| series | International series of numerical mathematics |
| series2 | International series of numerical mathematics |
| spellingShingle | Meyer-Spasche, Rita Pattern formation in viscous flows the Taylor-Couette problem and Rayleigh-Bénard convection International series of numerical mathematics Analyse numérique Bifurcation Convection Expérience Taylor Fluide visqueux Motif Taylor, Tourbillons de ram Tourbillon Écoulement visqueux ram Pattern formation (Physical sciences) Rayleigh-Bénard convection Taylor vortices Viscous flow Taylor-Couette-Strömung (DE-588)4249869-7 gnd Bénard-Effekt (DE-588)4144456-5 gnd |
| subject_GND | (DE-588)4249869-7 (DE-588)4144456-5 |
| title | Pattern formation in viscous flows the Taylor-Couette problem and Rayleigh-Bénard convection |
| title_auth | Pattern formation in viscous flows the Taylor-Couette problem and Rayleigh-Bénard convection |
| title_exact_search | Pattern formation in viscous flows the Taylor-Couette problem and Rayleigh-Bénard convection |
| title_full | Pattern formation in viscous flows the Taylor-Couette problem and Rayleigh-Bénard convection Rita Meyer-Spasche |
| title_fullStr | Pattern formation in viscous flows the Taylor-Couette problem and Rayleigh-Bénard convection Rita Meyer-Spasche |
| title_full_unstemmed | Pattern formation in viscous flows the Taylor-Couette problem and Rayleigh-Bénard convection Rita Meyer-Spasche |
| title_short | Pattern formation in viscous flows |
| title_sort | pattern formation in viscous flows the taylor couette problem and rayleigh benard convection |
| title_sub | the Taylor-Couette problem and Rayleigh-Bénard convection |
| topic | Analyse numérique Bifurcation Convection Expérience Taylor Fluide visqueux Motif Taylor, Tourbillons de ram Tourbillon Écoulement visqueux ram Pattern formation (Physical sciences) Rayleigh-Bénard convection Taylor vortices Viscous flow Taylor-Couette-Strömung (DE-588)4249869-7 gnd Bénard-Effekt (DE-588)4144456-5 gnd |
| topic_facet | Analyse numérique Bifurcation Convection Expérience Taylor Fluide visqueux Motif Taylor, Tourbillons de Tourbillon Écoulement visqueux Pattern formation (Physical sciences) Rayleigh-Bénard convection Taylor vortices Viscous flow Taylor-Couette-Strömung Bénard-Effekt |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008359773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035415862 |
| work_keys_str_mv | AT meyerspascherita patternformationinviscousflowsthetaylorcouetteproblemandrayleighbenardconvection |
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| Call Number: |
0102 MAT 650f 2001 A 892-128
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