Developments in the theory of turbulence:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Pr.
1983
|
| Edition: | 1. issued in paperback (with corrections) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 368 S. |
| ISBN: | 019856161X |
Staff View
MARC
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| 100 | 1 | |a Leslie, David C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Developments in the theory of turbulence |c D. C. Leslie |
| 250 | |a 1. issued in paperback (with corrections) | ||
| 264 | 1 | |a Oxford |b Clarendon Pr. |c 1983 | |
| 300 | |a IX, 368 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Statistische mechanica |2 gtt | |
| 650 | 7 | |a Turbulentie |2 gtt | |
| 650 | 4 | |a Turbulence | |
| 650 | 0 | 7 | |a Turbulente Strömung |0 (DE-588)4117265-6 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | ntents
RODUCTORY MATERIAL 1
torical note 1
Tensor notation 1
The equations of motion 2
^Survey of statistical questions 5
Stability theory 8
Reynolds’ equation and the turbulent energy equation 8
The impracticability of solving the turbulence equations on a
»•computer 12
OGENEOUS ISOTROPIC TURBULENCE 15
eral description of this type of turbulence 15
Fourier transformation of the Navier-Stokes equations 16
•A compressed notation 20
rProperties of the correlation tensor 20
The Fourier-transformed energy equation 23
- Role of the inertial term; the Kolmogorov hypothesis 25
, A simple form for the spectrum in the dissipation range 26
■( The size of a typical dissipation eddy 28
Intermittency 30
? E PROBLEM OF CLOSURE 37
The nature of the problem 37
The series method 38
, Gaussian probability distributions 39
*• The quasi-normality approximation 41
E DIRECT INTERACTION APPROXIMATION ; 47
1 The importance of the time-dependence 47
, The infinitesimal response function 47
, The formal statement of Direct Interaction 51
An alternative deduction of the DI equations 55
; DI for the scalar equation • 56
E JUSTIFICATION OF DIRECT INTERACTION 59
The difficulty of providing a justification 59
A simple one-dimensional model 60
5 211 Statement of the model 60
522 Application of various methods to the model 61
, The generalization to time-dependent b 65
A collective model 67
Diagram expansion of the solution 72
The random coupling model 80
Higher-order approximations and future prospects 83
p
Contents
xii
6 THE CONSEQUENCES OF EULERIAN DIRECT
INTERACTION 88
6 1 Statement of the equations 88
6 2 Simplification of the equations using an assumed time-dependence 91
6 3 Inertial range forms: divergence of the response integral 95
6 4 Calculation of the energy flow 98
6 5 Reconsideration of the response integral 106
7 ALTERNATIVE METHODS OF CLOSURE 109
7 1 Introduction 109
7 2 Phase space and the Liouville equation 109
7 3 An expansion solution of the Liouville equation 111
7 4 Eigenfunctions, adjoints, and Green functions of the Fokker-Planck
equation 114
7 5 The Fokker-Planck energy equation j 117
751 Another explanation of the breakdown of quasi-normality 122
7 6 The response equation in the Fokker-Planck method 123
761 The response function method 124
762 The correlation function method 129 •
763 The method of the first excited state 130
764 The entropy method 131
7 7 Closure by using a self-consistent field 135
7 8 The method of Phythian 140
7 9 An alternative model representation for DI 144
79!A model representation for Edward’s FP equations 147
7 10 The Wiener-Hermite expansion 150
7 11 Concluding discussion 153
8 CONVECTION OF A PASSIVE SCALAR IN AN
EULERIAN FRAMEWORK 156
8 1 Introduction 156
8 2 General consideration of the temperature problem 158
8 3 Scalar diffusion for (Pr) « 1 162
8 4 Scalar diffusion for (Pr) » 1 165
841 Batchelor’s model of a turbulent fluid 165 -
842 Batchelor’s calculation of the viscous-convection spectrum 167
843 Kraichnan’s extensions of Batchelor’s analysis 172
8 5 The diffusion of a single particle 173
8 6 Relative diffusion of two particles 179
9 THE NEED FOR A LAGRANGIAN TREATMENT 186
9 1 The failure of Eulerian DI under Galilean transformation 1861
92A new treatment of Lagrangian fluid mechanics 188 -
9 3 The continuity condition 193
9 4 Infinitesimal response functions for the scalar field 193
9 5 Infinitesimal response functions for the velocity field 196
9 6 The complementary equations of motion 198,
9 7 Statistically-averaged functions 202
Contents
THE CONSEQUENCES OF EULERIAN DIRECT
INTERACTION 88
6 1 Statement of the equations 88
6 2 Simplification of the equations using an assumed time-dependence 91
6 3 Inertial range forms: divergence of the response integral 95 •
6 4 Calculation of the energy flow 98 ‘
6 5 Reconsideration of the response integral 106
ALTERNATIVE METHODS OF CLOSURE 109
7 1 Introduction 109
7 2 Phase space and the Liouville equation 109 ’
7 3 An expansion solution of the Liouville equation 111
7 4 Eigenfunctions, adjoints, and Green functions of the Fokker-Planck 4
equation 114;
7 5 The Fokker-Planck energy equation I 117
751 Another explanation of the breakdown of quasi-normality 122
7 6 The response equation in the Fokker-Planck method 123
761 The response function method 124
762 The correlation function method 129
763 The method of the first excited state 130
764 The entropy method 131
7 7 Closure by using a self-consistent field 135
7 8 The method of Phythian 140
7 9 An alternative model representation for DI 144
79!A model representation for Edward’s FP equations 147
7 10 The Wiener-Hermite expansion 150
7 11 Concluding discussion 153
CONVECTION OF A PASSIVE SCALAR IN AN
EULERI AN FRAMEWORK 156
8 1 Introduction 156 ’
8 2 General consideration of the temperature problem 158
8 3 Scalar diffusion for (Pr) « 1 162
8 4 Scalar diffusion for (Pr) »1 165
841 Batchelor’s model of a turbulent fluid 165
842 Batchelor’s calculation of the viscous-convection spectrum 167
843 Kraichnan’s extensions of Batchelor’s analysis 172
8 5 The diffusion of a single particle 173 *
8 6 Relative diffusion of two particles 179
THE NEED FOR A LAGRANGIAN TREATMENT 186
9 1 The failure of Eulerian DI under Galilean transformation 186
92A new treatment of Lagrangian fluid mechanics 188
9 3 The continuity condition 193
9 4 Infinitesimal response functions for the scalar field 193
9 5 Infinitesimal response functions for the velocity field 196,
9 6 The complementary equations of motion 198
9 7 Statistically-averaged functions 202f
Contents xiii
jjCT INTERACTION IN A LAGRANGIAN
MEWORK 204
,: Introductory note 204
, Unmodified DI for the scalar field 204
The Lagrangian History Direct Interaction approximation for the scalar
Afield 209
Abridgement of the LHDI equations 213
% The Abridged Lagrangian Interaction for the velocity field 216
The ALI equations for homogeneous isotropic turbulence 221
LILEAN-INVARIANT CALCULATIONS OF THE
RTIAL RANGE VELOCITY FIELD 227
1 Calculations with assumed time-dependences 227
2 Calculation of the time-dependences 230
, Detailed comparison of ALI with experiments on the turbulent velocity
field 236
Detailed consideration of distant energy transfers 242
^ Structure functions of the velocity field 249
•*6 Another type of Galilean-invariant closure 257
11 6 1 Introduction 257
■ 11 6 2 Statement of the model 257
11 6 3 Inertial range calculations with the test-field model 262
11 6 4 Appraisal of the test-field model 262
v7 Numerical comparison of various methods of closure 264
IFFUSION OF A PASSIVE SCALAR IN THE ALI
PROXIMATION 267
1 The spectrum of passive temperature fluctuations 267
2 The diffusion of a pair of marked particles 277
$ Scalar diffusion in the test-field model 282
4 Interim appraisal of the ALI model * 283
Description of a particular real flow 285
1 Introduction - 285
2 Selection of a typical problem 286
3 Structure of the mean flow 286
■4 Characteristics of the turbulence in a parallel-sided channel 291
,5 Further reading 298
ISTING METHODS OF CALCULATION FOR
GINEERING FLOWS 300
•L Introduction 300
•2 The eddy viscosity and mixing length methods 300
r? One-point calculation of the pair correlations 303
xiv Contents
15 THE APPLICATION OF THE THEORY TO REAL
FLOWS 312
15 1 Introduction 312
15 2 The formal application of DI to shear flows -312
15 2 1 Restatement of the Navier-Stokes equations and closure by
Eulerian DI 312
15 2 2 The difficulty of the computational approach 316
15 3 Homogeneous anisotropic flows 317
15 3 1 Solution by formal expansion 319
15 3 2 Justification of the expansion 324
15 4 The asumption of constant spectral shape 326
15 5 An approximation for inhomogeneous turbulence 332
15 5 1 Choice and nature of the equations 332
15 5 2 Detailed deduction of the energy equation 335
15 5 3 The other two equations of motion 342
15 5 4 Summary of the assumptions 346
15 6 Standard spectra from the logarithmic flow 347
15 7 Concluding remarks 354
APPENDIX 356
INDEX
|
| any_adam_object | 1 |
| author | Leslie, David C. |
| author_facet | Leslie, David C. |
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| author_sort | Leslie, David C. |
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| ctrlnum | (OCoLC)9620908 (DE-599)BVBBV000107648 |
| dewey-full | 532/.0527 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.0527 |
| dewey-search | 532/.0527 |
| dewey-sort | 3532 3527 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. issued in paperback (with corrections) |
| format | Book |
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| id | DE-604.BV000107648 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:08:44Z |
| institution | BVB |
| isbn | 019856161X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000056146 |
| oclc_num | 9620908 |
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| owner | DE-12 DE-29T DE-188 |
| owner_facet | DE-12 DE-29T DE-188 |
| physical | IX, 368 S. |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Clarendon Pr. |
| record_format | marc |
| spelling | Leslie, David C. Verfasser aut Developments in the theory of turbulence D. C. Leslie 1. issued in paperback (with corrections) Oxford Clarendon Pr. 1983 IX, 368 S. txt rdacontent n rdamedia nc rdacarrier Statistische mechanica gtt Turbulentie gtt Turbulence Turbulente Strömung (DE-588)4117265-6 gnd rswk-swf Turbulenztheorie (DE-588)4186472-4 gnd rswk-swf Turbulente Strömung (DE-588)4117265-6 s DE-604 Turbulenztheorie (DE-588)4186472-4 s HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000056146&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Leslie, David C. Developments in the theory of turbulence Statistische mechanica gtt Turbulentie gtt Turbulence Turbulente Strömung (DE-588)4117265-6 gnd Turbulenztheorie (DE-588)4186472-4 gnd |
| subject_GND | (DE-588)4117265-6 (DE-588)4186472-4 |
| title | Developments in the theory of turbulence |
| title_auth | Developments in the theory of turbulence |
| title_exact_search | Developments in the theory of turbulence |
| title_full | Developments in the theory of turbulence D. C. Leslie |
| title_fullStr | Developments in the theory of turbulence D. C. Leslie |
| title_full_unstemmed | Developments in the theory of turbulence D. C. Leslie |
| title_short | Developments in the theory of turbulence |
| title_sort | developments in the theory of turbulence |
| topic | Statistische mechanica gtt Turbulentie gtt Turbulence Turbulente Strömung (DE-588)4117265-6 gnd Turbulenztheorie (DE-588)4186472-4 gnd |
| topic_facet | Statistische mechanica Turbulentie Turbulence Turbulente Strömung Turbulenztheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000056146&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lesliedavidc developmentsinthetheoryofturbulence |