Modeling in fluid mechanics: instabilities and turbulence
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
[2018]
|
| Series: | A Chapman & Hall book
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xiv, 495 Seiten Illustrationen, Diagramme |
| ISBN: | 9781138506831 |
Staff View
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Record in the Search Index
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| adam_text | Contents
fit
Foreword xi
Preface xiii
1 Mathematical Background 1
1.1 Dynamical systems ........................................................ 1
1.1.1 Vector fields and dynamical systems................................ 1
1.1.2 Critical points in phase space..................................... 6
1.1.3 Higher-order autonomous systems................................... 12
1.1.4 Dirac delta function.............................................. 17
1.1.5 Special functions................................................. 21
1.1.6 Green’s function.................................................. 25
1.1.7 Boundary and initial value problems............................... 29
1.2 Asymptotic behavior and stability........................................ 38
1.2.1 Asymptotic expansions............................................. 38
1.2.2 Asymptotic behavior of autonomous systems......................... 46
1.2.3 Stability of autonomous systems................................... 53
1.2.4 More on stability................................................. 57
1.3 Bifurcations ............................................................ 62
1.3.1 Instability and bifurcations...................................... 63
1.3.2 Saddle-node bifurcation........................................... 66
1.3.3 Transcritical and pitchfork bifurcations ......................... 69
1.3.4 Hopf bifurcation.................................................. 70
1.3.5 Saddle-node bifurcation of a periodic orbit....................... 72
1.3.6 Global bifurcation................................................ 72
1.4 Attractors .............................................................. 75
1.4.1 Chaotic motion and symbolic dynamics.............................. 75
1.4.2 Homoclinic tangles and Smale’s horseshoe map...................... 81
1.4.3 Poincare return map............................................... 83
1.4.4 Lyapunov’s exponents and entropy.................................. 85
1.4.5 Attracting sets and attractors.................................... 87
1.5 Fractals................................................................. 94
1.5.1 Local structure of fractals....................................... 94
1.5.2 Operations with fractals......................................... 102
1.5.3 Fractal attractors in dynamical systems.......................... 110
1.6 Perturbations .......................................................... 120
1.6.1 Regular perturbation theory...................................... 120
1.6.2 Singular perturbation theory..................................... 143
1.7 Elements of tensor analysis............................................. 154
1.7.1 Transformations of coordinate systems............................ 154
1.7.2 Covariant and contravariant derivatives.......................... 156
vii
viii Contents
1.7.3 Christoffel symbols and curvature tensor......................... 157
1.7.4 Integral formulas................................................... 158
1.8 Navier-Stokes equations for nonequilibrium gas mixture.................... 159
1.8.1 Continuity, momentum and energy equations........................ 159
1.8.2 Closing relations and transport coefficients .................... 167
1.8.3 Boundary conditions................................................. 168
1.8.4 Deducing Navier-Stokes equation..................................... 169
1.8.5 Existence and uniqueness of solutions of the Navier-Stokes equation 171
1.8.6 Relativistic Navier-Stokes equation................................. 179
1.9 Exercises ................................................................ 183
Bibliography 199
2 Models for Hydrodynamic Instabilities 203
2.1 Stability concepts ....................................................... 203
2.1.1 Boundary conditions................................................. 204
2.1.2 Inviscid and high-Reynolds-number flow.............................. 205
2.1.3 Basic definitions................................................... 206
2.2 Rayleigh-Taylor instability .............................................. 207
2.2.1 Potential flow...................................................... 207
2.2.2 Plane boundaries.................................................... 212
2.2.3 Spherical boundaries................................................ 216
2.2.4 Nonlinear perturbation theory ...................................... 224
2.2.5 Inhomogeneous fluids ............................................... 235
2.2.6 Viscous fluids...................................................... 241
2.3 Kelvin-Helmholtz instability ............................................. 246
2.3.1 Instability of annular incompressible jet........................... 248
2.3.2 Rotating jets....................................................... 255
2.3.3 Supersonic viscous jet.............................................. 267
2.3.4 Supersonic viscous jet with Gaussian sound velocity distribution . . 277
2.3.5 Relativistic jet.................................................... 296
2.4 Exercises ................................................................ 306
Bibliography 307
3 Models for Turbulence 311
3.1 Symmetries and conservation laws.......................................... 312
3.1.1 Euler and Navier-Stokes equations................................... 312
3.1.2 Symmetries........................................................ 315
3.1.3 Conservation laws................................................... 315
3.2 Anomalous scaling exponents............................................. 317
3.2.1 Multifractal models ................................................ 318
3.2.2 Random variables and correlation functions.......................... 321
3.2.3 Richardson-Kolmogorov concept of turbulence......................... 324
3.2.4 Scaling of the structure functions.................................. 326
3.2.5 Dissipative and dynamical scaling .................................. 327
3.2.6 Fusion rules in turbulence systems.................................. 334
3.3 Calculation of scaling exponents ......................................... 339
3.3.1 Basic formulas...................................................... 339
Contents ix
3.4 Bifurcations for the Kuramoto-Sivashinsky equation...................... 345
3.4.1 Symmetry: translations, reflections, and 0(2)-equivariance........ 347
3.4.2 Kuramoto-Sivashinsky equation .................................... 349
3.5 Strange attractors and turbulence ...................................... 356
3.5.1 The Taylor-Couette experiment .................................... 357
3.5.2 Dynamical systems with one observable............................. 358
3.5.3 Limit capacity and dimension...................................... 360
3.5.4 Dimension and entropy............................................. 362
3.6 Global attractor for Navier-Stokes equation ............................. 363
3.6.1 The ladder inequality............................................. 365
3.6.2 Estimates......................................................... 372
3.6.3 Length scales in the two-dimensional case......................... 374
3.6.4 Three-dimensional regularity...................................... 378
3.6.5 The attractor dimension........................................... 384
3.7 Hierarchical shell models ............................................... 390
3.7.1 Gledzer-Ohkitani-Yamada shell model............................... 390
3.7.2 (N,e)-sabra shell models ......................................... 392
3.7.3 Navier-Stokes equations in the common wavelets representation . . 399
3.8 Entropy principle maximum ............................................... 406
3.8.1 Entropy and probability........................................... 407
3.8.2 Derivation of the motion equations................................ 408
3.8.3 The hierarchical dynamical system................................. 411
3.8.4 Fokker-Planck equation............................................ 413
3.9 Appendix: inequalities................................................... 418
3.10 Exercises .............................................................. 419
Bibliography 421
4 Modeling of Flow over Blunted Bodies 427
4.1 Onsager’s theory......................................................... 429
4.1.1 General concept of a multi-component gas mixture.................. 429
4.1.2 Thermodynamic potentials, forces and flows........................ 431
4.1.3 Closing relations................................................ 432
4.2 Governing equations for hypersonic viscous gas flow ..................... 433
4.2.1 Conditions on the surface of discontinuity........................ 433
4.2.2 Governing parameters.............................................. 436
4.2.3 Transformation of initial equations............................... 438
4.3 Flow regimes for hypersonic viscous gas flow ............................ 440
4.3.1 Viscous shock layer............................................... 440
4.3.2 Vortex intersection, nonstrong and strong injection............... 440
4.3.3 Boundary layer, nonstrong and strong injection.................... 442
4.3.4 Boundary layer and strong struction............................... 443
4.4 Shock wave structure .................................................... 444
4.4.1 Outer sublayer.................................................... 445
4.4.2 Middle sublayer................................................... 446
4.4.3 Inner sublayer ................................................... 449
4.5 Viscous shock layer ..................................................... 450
4.5.1 Main equations.................................................... 450
4.5.2 Generalized Rankine-Hugoniot conditions at the shock wave .... 451
4.6 Models for shock sublayers .............................................. 453
X
Contents
4.6.1 Inviseid shock and boundary layers............................. 453
4.6.2 Injection gas layer............................................ 457
4.6.3 Viscous boundary and mixing gas layers......................... 459
4.6.4 Viscous boundary layer with strong suction .................... 462
4.6.5 Flow at viscous boundary layer................................. 465
4.7 Flow at injection gas layer ......................................... 469
4.7.1 General stagnation point ...................................... 470
4.7.2 Wings at incidence at slipping angles ......................... 472
4.7.3 Flow over swirling axisymmetric bodies......................... 473
4.8 Nonuniform flow at inviseid shock layer .............................. 474
4.8.1 Nonuniform flow of the far-wake type .......................... 475
4.8.2 Upstream swirling flow over axisymmetric bodies................ 480
4.9 Exercises ............................................................ 481
Bibliography 489
Index 493
Mathematics
Modeling in Fluid Mechanics: Instabilities and Turbulence is devoted to the-
oretical study of three key problems of modern fluid mechanics: hydrodynamic
instability, turbulence and hypersonic flow. Nonlinear phenomena arise in natural
sciences and applied mathematics and are responsible for various effects such
as jumps between modes, sudden onset or disappearance of periodic oscilla-
tions, loss or strengthening of stability and buckling of frames and shells. Math-
ematical models of hydrodynamic instabilities and turbulence provide qualita-
tive and quantitative analysis of nonlinear systems in fluid mechanics. The book,
consisting of four chapters accompanied by original exercises, is intended for
graduate and post-graduate students, engineers and researchers specializing in
the field of fluid mechanics and its applications.
Features
• Methods of asymptotic analysis, attractors, bifurcations and fractals used in
turbulence models are discussed. The Navier-Stokes equations are carefully
derived.
• A nonlinear model of the instability of hollow jets is developed to study
Rayleigh-Taylor instability of thin liquid films. Kelvin-Helmholtz instability
analysis is applied to supersonic and relativistic jets.
• The hierarchical shell models for turbulence are developed and their rela-
tionship to the entropy maximum principle is discussed. Conservation laws
of kinetic energy and enstrophy/helicity together with the entropy principle
maximum are used for building general shell models.
• Hypersonic motion over blunt bodies is analyzed and the complex structure
of boundary layers of a shock wave is found. Non-uniform flow at injection
gas layer and inviscid shock layer is studied.
Igor Gaissinski, D.Sc., Senior Scientist, Aerospace Engineering Faculty, Tech-
nion - Israel Institute of Technology, Haifa.
Vladimir Rovenski, D.Sc., Professor, Department of Mathematics, University of
Haifa.
®CRC Press
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|
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| author | Gaissinski, Igor Rovenski, Vladimir 1953- |
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| discipline | Physik |
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| id | DE-604.BV045147963 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:10:00Z |
| institution | BVB |
| isbn | 9781138506831 |
| language | English |
| lccn | 018000547 |
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| oclc_num | 1042087241 |
| open_access_boolean | |
| owner | DE-703 DE-634 |
| owner_facet | DE-703 DE-634 |
| physical | xiv, 495 Seiten Illustrationen, Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | CRC Press |
| record_format | marc |
| series2 | A Chapman & Hall book |
| spelling | Gaissinski, Igor Verfasser aut Modeling in fluid mechanics instabilities and turbulence Igor Gaissinski, Vladimir Rovenski Boca Raton ; London ; New York CRC Press [2018] xiv, 495 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Includes bibliographical references and index Fluid dynamics Mathematical models Überschallströmung (DE-588)4186626-5 gnd rswk-swf Turbulente Strömung (DE-588)4117265-6 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s Überschallströmung (DE-588)4186626-5 s Turbulente Strömung (DE-588)4117265-6 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Rovenski, Vladimir 1953- Verfasser (DE-588)12012985X aut Erscheint auch als Online-Ausgabe 978-1-351-02906-3 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030537670&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030537670&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Gaissinski, Igor Rovenski, Vladimir 1953- Modeling in fluid mechanics instabilities and turbulence Fluid dynamics Mathematical models Überschallströmung (DE-588)4186626-5 gnd Turbulente Strömung (DE-588)4117265-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4186626-5 (DE-588)4117265-6 (DE-588)4077970-1 (DE-588)4114528-8 |
| title | Modeling in fluid mechanics instabilities and turbulence |
| title_auth | Modeling in fluid mechanics instabilities and turbulence |
| title_exact_search | Modeling in fluid mechanics instabilities and turbulence |
| title_full | Modeling in fluid mechanics instabilities and turbulence Igor Gaissinski, Vladimir Rovenski |
| title_fullStr | Modeling in fluid mechanics instabilities and turbulence Igor Gaissinski, Vladimir Rovenski |
| title_full_unstemmed | Modeling in fluid mechanics instabilities and turbulence Igor Gaissinski, Vladimir Rovenski |
| title_short | Modeling in fluid mechanics |
| title_sort | modeling in fluid mechanics instabilities and turbulence |
| title_sub | instabilities and turbulence |
| topic | Fluid dynamics Mathematical models Überschallströmung (DE-588)4186626-5 gnd Turbulente Strömung (DE-588)4117265-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Fluid dynamics Mathematical models Überschallströmung Turbulente Strömung Strömungsmechanik Mathematisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030537670&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030537670&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gaissinskiigor modelinginfluidmechanicsinstabilitiesandturbulence AT rovenskivladimir modelinginfluidmechanicsinstabilitiesandturbulence |