Advances in Applied Mechanics (eBook)

Cover 1
Contents 6
Contributors 10
Preface 12
Chapter 1. A Unified Theory for Modeling Water Waves 14
I. Introduction 15
II. Fully Nonlinear Fully Dispersive (FNFD) Waves in Water of Variable Depth 20
III. Boundary Integral Closure 33
IV. Modeling FNFD Waves in Water of Uniform Depth 36
V. Weakly Nonlinear Fully Dispersive (WNFD) Water Wave Theory 39
VI. Weakly Nonlinear Weakly Dispersive (WNWD) Water Wave Models 43
VII. Fully Nonlinear Weakly Dispersive (FNWD) Water Wave Models 49
VIII. Higher-Order WNWD Long-Wave Models 53
IX. Nonlinear Wave–Wave Interactions 60
X. Soliton Generation by Resonant Forcing 75
XI. Channel Shape Effects on Wave Propagation and Generation 91
XII. Conclusion 93
Acknowledgments 95
References 95
Chapter 2. Coastal Hydrodynamics of Ocean Waves on Beach 102
I. Introduction 103
II. Linear Nondispersive Theory of Oblique Wave Run-Up on Uniform Beach 108
III. Lagrangian–Eulerian Hybrid Numerical Method for Run-up Computation 131
IV. Nonlinear Effects on Run-Up of Solitary Waves on Parabolic Beaches 140
V. Dispersive Effects on Run-Up of Waves on Beach 147
VI. Wave-Induced Longshore Current 166
VII. Conclusion 170
Appendix A. More Comparisons between the Present Results and other Theories 172
Acknowledgments 176
References 177
Chapter 3. Onset of Oscillatory Interfacial Instability and Wave Motions in Bénard Layers 180
I. Introduction 181
II. Summary of Results and Limitations of the Classical Theories 184
III. The Boussinesq Approximation and Surface Deformation 192
IV. Appropriate Generalizations of the Classical Theories 196
V. Some Recent Results on Patterned Convection 215
VI. Further Discussion of Oscillatory Motions: Surface and Internal Waves, and Boundary-Layer Effects 218
VII. Nonlinear Waves and Dissipative Solitons 225
VIII. Concluding Remarks 240
Acknowledgments 240
References 240
Chapter 4. Role of Cryogenic Helium in Classical Fluid Dynamics: Basic Research and Model Testing 252
I. Introduction 253
II. Brief Note on Helium 256
III. Some Examples of Flows at Very High Rayleigh and Reynolds Numbers 258
IV. Need for Studies at Conditions Approaching Ultra-High Parameter Values 260
V. Some Considerations about Large-Scale Helium Flows 268
VI. Superfluid Helium and the Hypothesis of Vortex-Coupled Superfluidity 273
VII. Summary of Instrumentation Development for Helium Turbulence 278
VIII. Limitations of Helium as a Hydrodynamic Test Fluid 283
IX. Concluding Remarks 284
Acknowledgments 285
References 285
Chapter 5. Recent Advances in Applications of Tensor Functions in Continuum Mechanics 290
I. Introduction 291
II. Nonlinear Constitutive Equations for Anisotropic Materials 293
III. Determination of Scalar Coefficients in Constitutive and Evolutional Equations 309
IV. Tensorial Generalization of Uniaxial Relations to Multiaxial States of Stress 312
V. Material Tensors of Rank Four 322
VI. Damage Tensors and Tensors of Continuity 344
VII. Stresses in a Damaged Continuum 353
VIII. Comparison with Own Experiments 359
References 372
Author Index 378
Subject Index 386