Bifurcations in flow patterns: some applications of the qualitative theory of differential equations in fluid dynamics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1991
|
| Schriftenreihe: | Nonlinear topics in the mathematical sciences
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 209 S. graph. Darst. |
| ISBN: | 079231428X |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV005153013 | ||
| 003 | DE-604 | ||
| 005 | 20020806 | ||
| 007 | t | ||
| 008 | 920610s1991 d||| |||| 00||| eng d | ||
| 020 | |a 079231428X |9 0-7923-1428-X | ||
| 035 | |a (OCoLC)24215662 | ||
| 035 | |a (DE-599)BVBBV005153013 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-703 |a DE-83 |a DE-11 |a DE-91G | ||
| 050 | 0 | |a QA911 | |
| 082 | 0 | |a 532/.05/0151535 |2 20 | |
| 084 | |a SK 560 |0 (DE-625)143246: |2 rvk | ||
| 084 | |a UG 3900 |0 (DE-625)145629: |2 rvk | ||
| 084 | |a PHY 220f |2 stub | ||
| 084 | |a PHY 229f |2 stub | ||
| 084 | |a MAT 587f |2 stub | ||
| 100 | 1 | |a Bakker, P. G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Bifurcations in flow patterns |b some applications of the qualitative theory of differential equations in fluid dynamics |c by P. G. Bakker |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1991 | |
| 300 | |a XI, 209 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Nonlinear topics in the mathematical sciences |v 2 | |
| 650 | 4 | |a Bifurcation | |
| 650 | 7 | |a Bifurcation, théorie de la |2 ram | |
| 650 | 4 | |a Dynamique fluide | |
| 650 | 7 | |a Equations différentielles - Solutions numériques |2 ram | |
| 650 | 4 | |a Flot conique | |
| 650 | 7 | |a Fluides, dynamique des |2 ram | |
| 650 | 4 | |a Singularité | |
| 650 | 4 | |a Système dynamique | |
| 650 | 4 | |a Théorie qualitative équation différentielle | |
| 650 | 4 | |a Viscosité | |
| 650 | 4 | |a Bifurcation theory | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Fluid dynamics | |
| 650 | 0 | 7 | |a Strömungsmechanik |0 (DE-588)4077970-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Verzweigung |g Mathematik |0 (DE-588)4078889-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Differentialgleichung |0 (DE-588)4205536-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Differentialgleichung |0 (DE-588)4205536-2 |D s |
| 689 | 0 | 1 | |a Verzweigung |g Mathematik |0 (DE-588)4078889-1 |D s |
| 689 | 0 | 2 | |a Strömungsmechanik |0 (DE-588)4077970-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Nonlinear topics in the mathematical sciences |v 2 |w (DE-604)BV004223528 |9 2 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003176914&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-003176914 | ||
Datensatz im Suchindex
| _version_ | 1804119296313393152 |
|---|---|
| adam_text | CONTENTS
Preface ix
CHAPTER I SOME ELEMENTS OF THE QUALITATIVE THEORY
OF DIFFERENTIAL EQUATIONS
1. Phase space representation of a dynamical system 1
2. Phase portraits near singular points 5
3. Topological structure of phase portraits, structural stability, bifurcation 9
3.1. Topological structure of phase portraits 9
3.2. Structural stability, bifurcation 10
3.3. Saddle connections 14
3.4. Multiple limit cycle 14
4. Higher order singularities in R2 16
4.1. Higher order singular points with one zero eigenvalue 16
4.2. Higher order singular points having both eigenvalues zero; p = 0 20
5. Bifurcation of vector fields, unfoldings 24
6. Center manifolds 30
7. An approach to physical unfoldings in flow patterns 39
8. References 40
CHAPTER II TOPOLOGY OF CONICAL FLOW PATTERNS
1. Introduction 42
1.1. Concepts and definitions 42
1.2. A survey of conital flow theory 43
1.3. Conical streamlines, conical stagnation points 45
1.4. Transition phenomena in conical flow patterns 48
2. Local conical stagnation point solutions in irrotational flow 52
2.1. Conical potential equation 52
2.2. Conical stagnation point solutions 54
3. Classification of conical stagnation points in conical flows 59
3.1. First order conical stagnation points 59
3.2. Irrotational attachments and separations 65
3.3. Higher order conical stagnation points 70
vi TABLE OF CONTENTS
4. Analytical unfoldings in conical flows 76
4.1. Bifurcation parameters 76
4.2. Approximate solutions near regular points 77
4.3. Saddle node bifurcation 81
4.4. Bifurcation of topological saddle point 85
4.5. Bifurcation of topological node 93
5. External corner flow; a nonanalytical unfolding of a starlike node 95 ,
5.1. The flow around an external corner 95
5.2. Boundary conditions and bifurcation modes 99
5.3. Bifurcations of the starlike node 102
5.4. Symmetrical external corners 109
5.5. Transition of oblique saddle to starlike node 115
6. References 120
CHAPTER III TOPOLOGICAL ASPECTS OF STEADY VISCOUS
FLOWS NEAR PLANE WALLS
1. A way to obtain local solutions of the Navier Stokes equations 123
2. Steady viscous flow near a plane wall, elementary singular points in
the flow patterns 126
2.1. Approximate solutions near a plane wall 126
2.2. Elementary singular points located at the wall (on wall singularities) 130
2.3. Elementary singular points in the flow (free singularities) 131
3. Higher order singularities in the flow pattern 132
3.1. Higher order singular points in the flow field 132
3.2. Higher order singular points on the wall 134
4. Unfolding of the topological saddle point of the third order 145
4.1. Local phase portraits of the unfolding 145
4.2. Incipient bubble separation 149
4.3. Separation along a moving wall 150
4.4. MRS criterion for separations in flows along a moving wall 156
4.5. Unfolding model for moving wall separations 158
5. Unfolding of a topological saddle point of the fifth order 163
5.1. Description of the unfolding 163
5.2. Bubble capturing by a secondary separation 167
6. Unfolding of a saddle point with three hyperbolic sectors in a half plane, txx ^ 0 169
6.1. Universal physical unfolding 170
6.2. Movement principle 171
6.3. Bifurcation sets, flow patterns 173
TABLE OF CONTENTS vii
7. Unfolding of a saddle point with two or four hyperbolic sectors
in a half plane, nxx *¦ 0 178
7.1. Universal physical unfolding 178
7.2. Determination of codimension 179
7.3. Neighbouring singular points, local bifurcation sets Bs and Bc 180
7.4. Flow patterns and global bifurcation sets B j and Bg2 184
8. Viscous flow near a circular cylinder at low Reynolds numbers 194
8.1. Description of flow topology 194
8.2. Symmetrical bifurcations 195
8.3. Asymmetrical bifurcations, transition scenario s 198
9. References 203
Index of subjects 205
|
| any_adam_object | 1 |
| author | Bakker, P. G. |
| author_facet | Bakker, P. G. |
| author_role | aut |
| author_sort | Bakker, P. G. |
| author_variant | p g b pg pgb |
| building | Verbundindex |
| bvnumber | BV005153013 |
| callnumber-first | Q - Science |
| callnumber-label | QA911 |
| callnumber-raw | QA911 |
| callnumber-search | QA911 |
| callnumber-sort | QA 3911 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 560 UG 3900 |
| classification_tum | PHY 220f PHY 229f MAT 587f |
| ctrlnum | (OCoLC)24215662 (DE-599)BVBBV005153013 |
| dewey-full | 532/.05/0151535 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.05/0151535 |
| dewey-search | 532/.05/0151535 |
| dewey-sort | 3532 15 6151535 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02435nam a2200613 cb4500</leader><controlfield tag="001">BV005153013</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20020806 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">920610s1991 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">079231428X</subfield><subfield code="9">0-7923-1428-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)24215662</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV005153013</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-91G</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA911</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">532/.05/0151535</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 560</subfield><subfield code="0">(DE-625)143246:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UG 3900</subfield><subfield code="0">(DE-625)145629:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 220f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 229f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 587f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bakker, P. G.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Bifurcations in flow patterns</subfield><subfield code="b">some applications of the qualitative theory of differential equations in fluid dynamics</subfield><subfield code="c">by P. G. Bakker</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht [u.a.]</subfield><subfield code="b">Kluwer</subfield><subfield code="c">1991</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 209 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Nonlinear topics in the mathematical sciences</subfield><subfield code="v">2</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bifurcation</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Bifurcation, théorie de la</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dynamique fluide</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Equations différentielles - Solutions numériques</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Flot conique</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Fluides, dynamique des</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Singularité</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Système dynamique</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Théorie qualitative équation différentielle</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Viscosité</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bifurcation theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations</subfield><subfield code="x">Numerical solutions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fluid dynamics</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Strömungsmechanik</subfield><subfield code="0">(DE-588)4077970-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Verzweigung</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4078889-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare Differentialgleichung</subfield><subfield code="0">(DE-588)4205536-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare Differentialgleichung</subfield><subfield code="0">(DE-588)4205536-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Verzweigung</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4078889-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Strömungsmechanik</subfield><subfield code="0">(DE-588)4077970-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Nonlinear topics in the mathematical sciences</subfield><subfield code="v">2</subfield><subfield code="w">(DE-604)BV004223528</subfield><subfield code="9">2</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003176914&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-003176914</subfield></datafield></record></collection> |
| id | DE-604.BV005153013 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:23:56Z |
| institution | BVB |
| isbn | 079231428X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003176914 |
| oclc_num | 24215662 |
| open_access_boolean | |
| owner | DE-12 DE-703 DE-83 DE-11 DE-91G DE-BY-TUM |
| owner_facet | DE-12 DE-703 DE-83 DE-11 DE-91G DE-BY-TUM |
| physical | XI, 209 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Kluwer |
| record_format | marc |
| series | Nonlinear topics in the mathematical sciences |
| series2 | Nonlinear topics in the mathematical sciences |
| spelling | Bakker, P. G. Verfasser aut Bifurcations in flow patterns some applications of the qualitative theory of differential equations in fluid dynamics by P. G. Bakker Dordrecht [u.a.] Kluwer 1991 XI, 209 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonlinear topics in the mathematical sciences 2 Bifurcation Bifurcation, théorie de la ram Dynamique fluide Equations différentielles - Solutions numériques ram Flot conique Fluides, dynamique des ram Singularité Système dynamique Théorie qualitative équation différentielle Viscosité Bifurcation theory Differential equations Numerical solutions Fluid dynamics Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 s Verzweigung Mathematik (DE-588)4078889-1 s Strömungsmechanik (DE-588)4077970-1 s DE-604 Nonlinear topics in the mathematical sciences 2 (DE-604)BV004223528 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003176914&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bakker, P. G. Bifurcations in flow patterns some applications of the qualitative theory of differential equations in fluid dynamics Nonlinear topics in the mathematical sciences Bifurcation Bifurcation, théorie de la ram Dynamique fluide Equations différentielles - Solutions numériques ram Flot conique Fluides, dynamique des ram Singularité Système dynamique Théorie qualitative équation différentielle Viscosité Bifurcation theory Differential equations Numerical solutions Fluid dynamics Strömungsmechanik (DE-588)4077970-1 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4078889-1 (DE-588)4205536-2 |
| title | Bifurcations in flow patterns some applications of the qualitative theory of differential equations in fluid dynamics |
| title_auth | Bifurcations in flow patterns some applications of the qualitative theory of differential equations in fluid dynamics |
| title_exact_search | Bifurcations in flow patterns some applications of the qualitative theory of differential equations in fluid dynamics |
| title_full | Bifurcations in flow patterns some applications of the qualitative theory of differential equations in fluid dynamics by P. G. Bakker |
| title_fullStr | Bifurcations in flow patterns some applications of the qualitative theory of differential equations in fluid dynamics by P. G. Bakker |
| title_full_unstemmed | Bifurcations in flow patterns some applications of the qualitative theory of differential equations in fluid dynamics by P. G. Bakker |
| title_short | Bifurcations in flow patterns |
| title_sort | bifurcations in flow patterns some applications of the qualitative theory of differential equations in fluid dynamics |
| title_sub | some applications of the qualitative theory of differential equations in fluid dynamics |
| topic | Bifurcation Bifurcation, théorie de la ram Dynamique fluide Equations différentielles - Solutions numériques ram Flot conique Fluides, dynamique des ram Singularité Système dynamique Théorie qualitative équation différentielle Viscosité Bifurcation theory Differential equations Numerical solutions Fluid dynamics Strömungsmechanik (DE-588)4077970-1 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | Bifurcation Bifurcation, théorie de la Dynamique fluide Equations différentielles - Solutions numériques Flot conique Fluides, dynamique des Singularité Système dynamique Théorie qualitative équation différentielle Viscosité Bifurcation theory Differential equations Numerical solutions Fluid dynamics Strömungsmechanik Verzweigung Mathematik Nichtlineare Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003176914&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004223528 |
| work_keys_str_mv | AT bakkerpg bifurcationsinflowpatternssomeapplicationsofthequalitativetheoryofdifferentialequationsinfluiddynamics |