Vortex dominated flows: analysis and computation for multiple scale phenomena
Gespeichert in:
| Vorheriger Titel: | Ting, Lu Viscous vortical flows |
|---|---|
| Beteiligte Personen: | , , |
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
[2007]
|
| Schriftenreihe: | Applied mathematical sciences
161 |
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=2877229&prov=M&dok_var=1&dok_ext=htm http://www.gbv.de/dms/bs/toc/522152791.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016273338&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Enthält Literaturverzeichnis Seite 489 - 499 und Index |
| Umfang: | XIII, 506 Seiten Illustrationen, Diagramme |
| ISBN: | 9783540685814 3540685812 |
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| 245 | 1 | 0 | |a Vortex dominated flows |b analysis and computation for multiple scale phenomena |c Lu Ting ; Rupert Klein ; Omar M. Knio |
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| 500 | |a Enthält Literaturverzeichnis Seite 489 - 499 und Index | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Viscous flow |x Mathematical models | |
| 650 | 4 | |a Viscous flow |x Mathematics | |
| 650 | 4 | |a Vortex-motion |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1819270128331653120 |
|---|---|
| adam_text | LU TING RUPERT KLEIN OMAR M. KNIO VORTEX DOMINATED FLOWS ANALYSIS AND
COMPUTATION FOR MULTIPLE SCALE PHENOMENA WITH 139 FIGURES 4Y SPRINGER
CONTENTS 1. INTRODUCTION 1 2. VORTEX-DOMINATED FLOWS AND GENERAL THEORY
7 2.1 GOVERNING EQUATIONS FOR COMPRESSIBLE VISCOUS VORTICAL FLOWS 9 2.2
THE CONSISTENCY CONDITIONS AND TIME INVARIANTS 13 2.2.1 DERIVATION OF
THE CONSISTENCY CONDITIONS 14 2.2.2 DERIVATION OF THE TIME INVARIANTS 16
2.2.3 AXISYMMETRIC FLOWS 18 2.2.4 TWO-DIMENSIONAL FLOWS 19 2.3
INCOMPRESSIBLE VORTICAL FLOWS 23 2.3.1 FAR-FIELD VECTOR VELOCITY
POTENTIAL 26 2.3.2 REDUCTION OF THE VECTOR VELOCITY POTENTIAL IN THE FAR
FIELD TO THE CORRESPONDING SCALAR POTENTIAL 28 2.3.3 RELATING THE
COEFFICIENTS IN THE SCALAR POTENTIALS OF NTH ORDER DIRECTLY TO NTH
MOMENTS OF VORTICITY.... 32 3. MOTION AND DECAY OF VORTEX FILAMENTS *
MATCHED ASYMPTOTICS 35 3.1 INVISCID THEORIES OF VORTICAL FLOWS AND THEIR
DEFICIENCIES 40 3.1.1 POTENTIAL FLOWS AROUND A SPINNING DISC AND A
RANKINE VORTEX 43 3.1.2 POTENTIAL FLOW INDUCED BY A VORTEX LINE 53 3.2
PLANAR MOTION OF VORTEX SPOTS AND THEIR CORE STRUCTURES 58 3.2.1 THE
INNER SOLUTION ^ 62 3.2.2 LEADING-ORDER CORE STRUCTURE 69 3.2.3
ASYMMETRIC FIRST ORDER SOLUTION IN THE NORMAL TIME SCALE AND THE
VELOCITY OF THE VORTEX 72 3.2.4 ASYMMETRIC FIRST ORDER TWO-TIME SOLUTION
AND THE OSCILLATORY MOTION OF THE VORTEX CENTER 74 3.3 MOTION OF SLENDER
VORTEX FILAMENTS AND EVOLUTION OF THEIR CORE STRUCTURES 81 3.3.1 THE
EXPANSION SCHEME 87 X CONTENTS 3.3.2 THE LEADING-ORDER EQUATIONS 89
3.3.3 THE FIRST ORDER EQUATIONS AND THE ASYMMETRIC SOLUTIONS 91 3.3.4
ALTERNATIVE DERIVATION: VORTICITY-BASED ANALYSIS 98 3.3.5 ASYMPTOTIC
SOLUTION OF THE VORTICITY TRANSPORT EQUATION 106 3.3.6 THE SECOND-ORDER
EQUATIONS AND THE EVOLUTION OF THE CORE STRUCTURE 108 3.3.7 FILAMENT
WITH AXIAL CORE STRUCTURE VARIATION 121 3.3.8 VORTICES IN A BACKGROUND
FLOW WITH ORDER ONE VORTICITYL24 3.3.9 MOTION AND CORE STRUCTURE OF A
GEOSTROPHIC VORTEX . . 129 3.4 VORTEX FILAMENTS WITH COMPRESSIBLE CORE
STRUCTURE 134 3.4.1 EVOLUTION EQUATIONS FOR COMPRESSIBLE VORTEX
FILAMENTS 135 3.4.2 OUTER SOLUTION FOR A COMPRESSIBLE FILAMENT 136 3.4.3
INNER SOLUTION FOR A COMPRESSIBLE FILAMENT 138 3.4.4 THE LEADING-ORDER
EQUATIONS 143 3.4.5 THE FIRST ORDER EQUATIONS AND THE VELOCITY OF THE
FILAMENT 144 3.4.6 THE SECOND-ORDER EQUATIONS AND THE EVOLUTION OF THE
CORE STRUCTURE 150 3.4.7 EVOLUTION EQUATIONS FOR THE COMPRESSIBLE CORE
STRUCTURE 151 4. NONLINEAR DYNAMICS OF NEARLY STRAIGHT VORTEX FILAMENTS
. 155 4.1 SELF-STRETCHING AND CURVATURE NONLINEARITY 158 4.1.1 THE
KLEIN-MAJDA REGIME 158 4.1.2 LINEARIZATION OF NONLOCAL SELF-INDUCTION IN
THE KLEIN-MAJDA REGIME 159 4.1.3 HASIMOTO S TRANSFORMATION 161 4.1.4
INTERACTION OF CURVATURE AND SELF-INDUCTION EFFECTS . . . 168 4.1.5
STRUCTURE OF SOLUTIONS 175 4.2 LINEAR AND NONLINEAR STABILITY OF A
FILAMENT IN AN IMPOSED STRAINING FIELD 179 4.2.1 DERIVATION OF THE
FILAMENT EQUATION WITH EXTERNAL STRAIN 182 4.2.2 RIGOROUS NONLINEAR
STABILITY THEORY 5 . 183 4.2.3 LINEAR STABILITY THEORY 185 4.2.4
NUMERICAL SOLUTIONS FOR THE FILAMENT EQUATION WITH EXTERNAL STRAIN 187
4.3 NONLINEAR VORTEX PAIR INSTABILITY 191 4.3.1 DERIVATION OF THE
FILAMENT PAIR EQUATIONS 196 4.3.2 LINEAR STABILITY OF PARALLEL VORTICES
OF OPPOSITE STRENGTH AND CROW S THEORY 203 4.3.3 NUMERICAL SOLUTIONS FOR
AN ANTISYMMETRIC VORTEX PAIR 206 CONTENTS XI 4.4 LARGE AMPLITUDE AND
LONG WAVELENGTH DISPLACEMENTS OF A FILAMENT PAIR 212 4.4.1
AMPLITUDE-WAVELENGTH SCALINGS 213 4.4.2 NONLINEAR CURVATURE - POTENTIAL
FLOW INTERACTIONS .... 214 4.4.3 MATHEMATICAL PROPERTIES 216 4.4.4
LONG-WAVE INTERACTIONS OF FILAMENT PAIRS 218 5. NUMERICAL SIMULATION OF
SLENDER VORTEX FILAMENTS 227 5.1 VALIDITY OF THE SLENDER VORTEX
ASYMPTOTICS AND APPLICATIONS . 229 5.1.1 COAXIAL VORTEX RINGS IN AN
AXISYMMETRIC FLOW 229 5.1.2 INTERACTIONS OF VORTEX FILAMENTS 234 5.2
VORTEX ELEMENT METHODS FOR SLENDER VORTEX FILAMENTS 242 5.2.1 THIN-TUBE
MODELS FOR WEAKLY STRETCHED VORTICES 244 5.2.2 PERFORMANCE IN THE
KLEIN-MAJDA REGIME 249 5.2.3 REPRESENTATION OF CORE DYNAMICS IN
THIN-TUBE SIMULATIONS 262 5.2.4 ENHANCEMENT OF PERFORMANCE 271 6.
NUMERICAL SIMULATIONS OF THE MERGING OF VORTICES OR FILAMENTS 285 6.1
CLASSIFICATION OF MERGING PROBLEMS AND EFFICIENT NUMERICAL SCHEMES 287
6.1.1 CLASSIFICATION OF MERGING PROBLEMS 288 6.1.2 EFFICIENT NUMERICAL
SCHEME AND COMPUTATIONAL DOMAIN 290 6.1.3 LONG-TIME BEHAVIOR 294 6.2
MERGING OF TWO-DIMENSIONAL VORTICES 296 6.2.1 NUMERICAL SIMULATION OF
VORTEX MERGING AND THE ROLL-UP OF THIN SHEAR LAYERS 299 6.2.2 RULES OF
MERGING OF VORTICES 309 6.2.3 APPROXIMATE SOLUTION OF NAVIER-STOKES
EQUATIONS USING SUPERPOSITION OF LAMB VORTICES 316 6.3 MERGING OR
INTERSECTION OF VORTEX FILAMENTS 328 6.3.1 MERGING OF COAXIAL VORTEX
RINGS 329 6.3.2 NUMERICAL MODELING OF MERGING OF VORTEX FILAMENTS . .
339 7. FLOW GENERATED 347 7.1 SOUND GENERATION BY AN UNSTEADY VORTICAL
FLOW 349 7.1.1 EXPANSION SCHEMES AND THE GOVERNING EQUATIONS .... 351
7.1.2 THE VORTICAL FLOW FIELD 353 7.1.3 THE ACOUSTIC FIELD 358 7.1.4
SOUND GENERATION DUE TO TURBULENCE 359 7.1.5 SOUND GENERATION BY VORTEX
FILAMENTS 360 7.2 VORTICAL FLOW OUTSIDE A SPHERE AND SOUND GENERATION
362 XII CONTENTS 7.2.1 THE IMAGE OF A ROTATIONAL FLOW DUE TO THE
PRESENCE OF A SPHERE 362 7.2.2- SOUND GENERATION DUE TO THE PRESENCE OF
A SPHERE.... 365 7.2.3 A SLENDER VORTEX FILAMENT OUTSIDE A SPHERE 367
7.2.4 COMPUTATIONAL EXAMPLES 370 8. SOUND GENERATED FLOW 383 8.1 SINGLE
TIME SCALE, LOW MACH NUMBER LIMITS 384 8.1.1 EXPANSIONS IN A SINGLE TIME
AND MULTIPLE SPACIAL SCALES384 8.1.2 A SINGLE SPATIAL SCALE: ZERO MACH
NUMBER FLOW IN ACOUSTICALLY COMPACT DOMAINS 388 8.1.3 MULTIPLE SPATIAL
SCALES: LONG-WAVE ACOUSTICS AND BAROCLINIC SMALL-SCALE FLOW 390 8.1.4
LOCALIZED SMALL-SCALE FLOW AND MULTIPLE TIME SCALES: THERMOACOUSTICS 394
8.2 COMPUTATIONAL SCHEMES FOR LOW MACH NUMBER FLOWS 399 8.2.1 A ZERO
MACH NUMBER GODUNOV-TYPE SCHEME 400 8.2.2 VORTICITY-BASED FORMULATION
407 8.3 APPLICATION TO THERMOACOUSTIC REFRIGERATION 412 8.3.1
CONVERGENCE PROPERTIES AND MODELING APPROXIMATIONS 413 8.3.2 TEMPERATURE
DIFFERENCE ACROSS A THERMOACOUSTIC COUPLE 421 8.3.3 QUANTITATIVE
VISUALIZATION OF THE FLOW AROUND A THERMOACOUSTIC COUPLE 427 8.3.4
ANALYSIS OF PERFORMANCE 431 9. EPILOGUE 455 9.1 NUMERICAL STRATEGIES FOR
EXTENDED SLENDER VORTEX SIMULATIONS 455 9.2 A MULTIPLE SCALES ASYMPTOTIC
FRAMEWORK FOR METEOROLOGICAL MODELING 457 9.2.1 UNIVERSAL PARAMETERS AND
DISTINGUISHED LIMITS 457 9.2.2 NONDIMENSIONALIZATION AND GENERAL
MULTISCALE ANSATZ 459 9.2.3 DISTINGUISHED LIMITS VERSUS MULTIPARAMETER
EXPANSIONS 461 9.2.4 PERSPECTIVES 461 APPENDICES 463 A. GOVERNING
EQUATIONS FOR HIGHER-ORDER SOLUTIONS 465 B. SECOND-ORDER -TWO-TIME
SOLUTIONS 469 CONTENTS XIII C. EQUATIONS OF MOTION OF FILAMENTS 475 D.
FORMULAE FOR THE COEFFICIENTS IN (6.2.74) AND (6.2.75) 479 E.
TRANSFORMATIONS TO FILAMENT ATTACHED COORDINATES 481 E.I CONSERVATION
LAWS IN ORTHOGONAL COORDINATES 481 E.2 SCALAR TRANSPORT EQUATIONS IN
ORTHOGONAL COORDINATES . 482 E.3 COMPRESSIBLE FLOW EQUATIONS IN
FILAMENT ATTACHED COORDINATES 483 E.4 FORMULAS FOR THE COORDINATE SYSTEM
ATTACHED TO C 485 REFERENCES 488 INDEX 501
|
| any_adam_object | 1 |
| author | Ting, Lu Klein, Rupert 1959- Knio, Omar M. |
| author_GND | (DE-588)1055745009 (DE-588)172188717 (DE-588)133394913 |
| author_facet | Ting, Lu Klein, Rupert 1959- Knio, Omar M. |
| author_role | aut aut aut |
| author_sort | Ting, Lu |
| author_variant | l t lt r k rk o m k om omk |
| building | Verbundindex |
| bvnumber | BV023070181 |
| callnumber-first | Q - Science |
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| callnumber-search | QA1 TA357.5.V56 |
| callnumber-sort | QA 11 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | UF 4300 |
| ctrlnum | (OCoLC)78989785 (DE-599)DNB982031602 |
| dewey-full | 532.0595 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532.0595 |
| dewey-search | 532.0595 |
| dewey-sort | 3532.0595 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV023070181 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:07:57Z |
| institution | BVB |
| isbn | 9783540685814 3540685812 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016273338 |
| oclc_num | 78989785 |
| open_access_boolean | |
| owner | DE-29T DE-634 DE-83 DE-188 DE-19 DE-BY-UBM |
| owner_facet | DE-29T DE-634 DE-83 DE-188 DE-19 DE-BY-UBM |
| physical | XIII, 506 Seiten Illustrationen, Diagramme |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spellingShingle | Ting, Lu Klein, Rupert 1959- Knio, Omar M. Vortex dominated flows analysis and computation for multiple scale phenomena Applied mathematical sciences Mathematik Mathematisches Modell Viscous flow Mathematical models Viscous flow Mathematics Vortex-motion Mathematical models Vortex-motion Mathematics Wirbelströmung (DE-588)4190007-8 gnd Viskose Strömung (DE-588)4226965-9 gnd Numerische Strömungssimulation (DE-588)4690080-9 gnd |
| subject_GND | (DE-588)4190007-8 (DE-588)4226965-9 (DE-588)4690080-9 (DE-588)4113937-9 |
| title | Vortex dominated flows analysis and computation for multiple scale phenomena |
| title_auth | Vortex dominated flows analysis and computation for multiple scale phenomena |
| title_exact_search | Vortex dominated flows analysis and computation for multiple scale phenomena |
| title_full | Vortex dominated flows analysis and computation for multiple scale phenomena Lu Ting ; Rupert Klein ; Omar M. Knio |
| title_fullStr | Vortex dominated flows analysis and computation for multiple scale phenomena Lu Ting ; Rupert Klein ; Omar M. Knio |
| title_full_unstemmed | Vortex dominated flows analysis and computation for multiple scale phenomena Lu Ting ; Rupert Klein ; Omar M. Knio |
| title_old | Ting, Lu Viscous vortical flows |
| title_short | Vortex dominated flows |
| title_sort | vortex dominated flows analysis and computation for multiple scale phenomena |
| title_sub | analysis and computation for multiple scale phenomena |
| topic | Mathematik Mathematisches Modell Viscous flow Mathematical models Viscous flow Mathematics Vortex-motion Mathematical models Vortex-motion Mathematics Wirbelströmung (DE-588)4190007-8 gnd Viskose Strömung (DE-588)4226965-9 gnd Numerische Strömungssimulation (DE-588)4690080-9 gnd |
| topic_facet | Mathematik Mathematisches Modell Viscous flow Mathematical models Viscous flow Mathematics Vortex-motion Mathematical models Vortex-motion Mathematics Wirbelströmung Viskose Strömung Numerische Strömungssimulation Hochschulschrift |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2877229&prov=M&dok_var=1&dok_ext=htm http://www.gbv.de/dms/bs/toc/522152791.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016273338&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT tinglu vortexdominatedflowsanalysisandcomputationformultiplescalephenomena AT kleinrupert vortexdominatedflowsanalysisandcomputationformultiplescalephenomena AT knioomarm vortexdominatedflowsanalysisandcomputationformultiplescalephenomena |