Mathematical study of degenerate boundary layers: a large scale ocean circulation problem
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
May 2018
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
volume 253, number 1206 (first of 7 numbers) |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | vi, 105, 4 ungezählte Seiten Illustrationen |
| ISBN: | 9781470428358 |
Internformat
MARC
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| 100 | 1 | |a Dalibard, Anne-Laure |d 1982- |0 (DE-588)1160505977 |4 aut | |
| 245 | 1 | 0 | |a Mathematical study of degenerate boundary layers |b a large scale ocean circulation problem |c Anne-Laure Dalibard, Laure Saint-Raymond |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c May 2018 | |
| 264 | 4 | |c © 2018 | |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 253, number 1206 (first of 7 numbers) | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-030486506 | ||
Datensatz im Suchindex
| _version_ | 1804178723523526656 |
|---|---|
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Contents
1. Introduction
Munk boundary layers
State of the art
Boundary layer degeneracies
Stability of the stationary Munk equation
Geometrical preliminaries
Regularity and flatness assumptions
Singularity lines
Domains with islands
Periodic domains and domains with corners
Main approximation results
General case
Periodic and rectangle cases
Outline of the paper
2. Multiscale analysis
Local coordinates and the boundary layer equation
East and West boundary layers
The scaled equation
Domain of validity
North and South boundary layers
The scaled equation
Study of the boundary layer equation (2.11):
Boundary conditions for s G
Connection with East and West boundary layers
Discontinuity zones
Lifting the discontinuity
The interior singular layer
The case of islands
North and South periodic boundary layers
3. Construction of the approximate solution
The interior term
Lifting the East boundary conditions
Traces of the East boundary layers
Definition of the East corrector
North and South boundary layers
Definition of the initial boundary value problem
Estimates for Vhv,s
Extinction and truncation
IV
CONTENTS
3.4. The interface layer 59
3.4.1. The lifting term 59
3.4.2. The interior singular layer 60
3.4.3. Connection with the West boundary 64
3.5. Lifting the West boundary conditions 67
3.6. Approximate solution in the periodic and rectangle case 69
3.6.1. In the periodic case 69
3.6.2. In the rectangle case 69
Chapter 4. Proof of convergence 71
4.1. Remainders stemming from the interior term ripint = ^ + t/jhh 71
4.1.1. Error terms due to the truncation X£- 71
4.1.2. Error terms due to the lifting term 0ilft 75
4.2. Remainders coming from the boundary terms 76
4.2.1. Laplacian in curvilinear coordinates 76
4.2.2. Error terms associated with North and South layers 79
4.2.3. Error terms associated with East and West boundary layers 82
4.2.4. Error terms associated with discontinuity layers 88
4.3. Remainders in the periodic and rectangular cases 88
Chapter 5. Discussion: Physical relevance of the model 91
Acknowledgments 93
Appendix 95
Appendix A: The case of islands: derivation of the compatibility condition
(1.15) and proof of Lemma 1.2.1 95
Appendix B: Equivalents for the coordinates of boundary points near
horizontal parts 96
Appendix C: Estimates on the coefficients a and b. 97
Appendix D: Proof of Lemma 3.4.3 100
Notations 101
Sizes of parameters and terms 103
Bibliography
105
|
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| id | DE-604.BV045095841 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:08:30Z |
| institution | BVB |
| isbn | 9781470428358 |
| language | English |
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| physical | vi, 105, 4 ungezählte Seiten Illustrationen |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Dalibard, Anne-Laure 1982- (DE-588)1160505977 aut Mathematical study of degenerate boundary layers a large scale ocean circulation problem Anne-Laure Dalibard, Laure Saint-Raymond Providence, Rhode Island American Mathematical Society May 2018 © 2018 vi, 105, 4 ungezählte Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 253, number 1206 (first of 7 numbers) Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Meereswelle (DE-588)4038334-9 gnd rswk-swf Grenzschicht (DE-588)4022005-9 gnd rswk-swf Meereswelle (DE-588)4038334-9 s Grenzschicht (DE-588)4022005-9 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Saint-Raymond, Laure (DE-588)135780594 aut Memoirs of the American Mathematical Society volume 253, number 1206 (first of 7 numbers) (DE-604)BV008000141 1206 V:DE-605;X:Imageware application/pdf http://digitale-objekte.hbz-nrw.de/storage2/2018/06/11/file_70/7897772.pdf Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030486506&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dalibard, Anne-Laure 1982- Saint-Raymond, Laure Mathematical study of degenerate boundary layers a large scale ocean circulation problem Memoirs of the American Mathematical Society Mathematisches Modell (DE-588)4114528-8 gnd Meereswelle (DE-588)4038334-9 gnd Grenzschicht (DE-588)4022005-9 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4038334-9 (DE-588)4022005-9 |
| title | Mathematical study of degenerate boundary layers a large scale ocean circulation problem |
| title_auth | Mathematical study of degenerate boundary layers a large scale ocean circulation problem |
| title_exact_search | Mathematical study of degenerate boundary layers a large scale ocean circulation problem |
| title_full | Mathematical study of degenerate boundary layers a large scale ocean circulation problem Anne-Laure Dalibard, Laure Saint-Raymond |
| title_fullStr | Mathematical study of degenerate boundary layers a large scale ocean circulation problem Anne-Laure Dalibard, Laure Saint-Raymond |
| title_full_unstemmed | Mathematical study of degenerate boundary layers a large scale ocean circulation problem Anne-Laure Dalibard, Laure Saint-Raymond |
| title_short | Mathematical study of degenerate boundary layers |
| title_sort | mathematical study of degenerate boundary layers a large scale ocean circulation problem |
| title_sub | a large scale ocean circulation problem |
| topic | Mathematisches Modell (DE-588)4114528-8 gnd Meereswelle (DE-588)4038334-9 gnd Grenzschicht (DE-588)4022005-9 gnd |
| topic_facet | Mathematisches Modell Meereswelle Grenzschicht |
| url | http://digitale-objekte.hbz-nrw.de/storage2/2018/06/11/file_70/7897772.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030486506&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT dalibardannelaure mathematicalstudyofdegenerateboundarylayersalargescaleoceancirculationproblem AT saintraymondlaure mathematicalstudyofdegenerateboundarylayersalargescaleoceancirculationproblem |
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