Theory and Computation in Hydrodynamic Stability

Description

The study of hydrodynamic stability is fundamental to many subjects, ranging from geophysics and meteorology through to engineering design. This treatise covers both classical and modern aspects of the subject, systematically developing it from the simplest physical problems, then progressing to the most complex, considering linear and nonlinear situations, and analyzing temporal and spatial stability. The authors examine each problem both analytically and numerically. Many relevant fluid flows are treated, including those where the fluid may be compressible, or those from geophysics, or those that require salient geometries for description. Details of initial-value problems are explored equally with those of stability. The text includes copious illustrations and an extensive bibliography, making it suitable for courses on hydrodynamic stability or as an authoritative reference for researchers. In this second edition the opportunity has been taken to update the text and, most importantly, provide solutions to the numerous extended exercises. Contents......Page 6 Preface to the Second Edition......Page 9 Preface......Page 11 1.1 History, Background and Rationale......Page 14 1.2 Initial-Value Concepts and Stability Bases......Page 24 1.3 Classical Treatment: Modal Expansions......Page 27 1.4 Transient Dynamics......Page 31 1.5 Asymptotic Behavior......Page 33 1.6 Role of Viscosity......Page 34 1.8 Spatial Stability Bases......Page 36 2.1 General Equations......Page 39 2.2 Kelvin–Helmholtz Theory......Page 54 2.3 Piecewise Linear Profile......Page 57 2.4 Inviscid Temporal Theory......Page 63 2.5 Critical Layer Concept......Page 70 2.6 Continuous Profiles......Page 74 2.7 Exercises......Page 82 3.1 Introduction......Page 89 3.2 Channel Flows......Page 90 3.3 Blasius Boundary Layer......Page 96 3.4 Falkner–Skan Flow Family......Page 99 3.5 Unbounded Flows......Page 101 3.6 Discrete and Continuous Spectra......Page 103 3.7 Exercises......Page 107 4.1 Introduction......Page 111 4.2 Gaster’s Transformation......Page 112 4.3 Incompressible Inviscid Flow......Page 114 4.4 Absolute and Convective Instabilities......Page 125 4.5 Incompressible Viscous Flow......Page 129 4.6 Discrete and Continuous Spectra......Page 133 4.7 Exercises......Page 139 5.1 Introduction......Page 141 5.2 Compressible Mixing Layer......Page 142 5.3 Compressible Boundary Layer......Page 164 5.4 Exercises......Page 178 6.1 Coordinate Systems......Page 181 6.2 Taylor Problem......Page 183 6.3 Gortler Vortices......Page 190 6.4 Pipe Flow......Page 193 6.5 Rotating Disk......Page 195 6.6 Trailing Vortex......Page 198 6.7 Round Jet......Page 200 6.8 Exercises......Page 203 7.1 General Properties......Page 204 7.2 Stratified Flow......Page 205 7.3 Effects of Rotation......Page 221 7.4 Baroclinic Flow......Page 226 7.5 The Ekman Layer......Page 229 7.6 Exercises......Page 235 8.1 The Initial-Value Problem......Page 238 8.2 Laplace Transforms......Page 242 8.3 Moving Coordinates and Exact Solutions......Page 245 8.4 Multiple Scale, Multiple Time Analysis......Page 253 8.5 Numerical Solution of Governing Partial Differential Equations......Page 257 8.6 Optimizing Initial Conditions......Page 261 8.7 Exercises......Page 270 9.1 Energy Equation......Page 272 9.2 Weakly Nonlinear Theory......Page 274 9.3 Secondary Instability Theory......Page 276 9.4 Resonant Wave Interactions......Page 285 9.5 PSE Theory......Page 291 9.6 Exercises......Page 298 10.1 Introduction......Page 300 10.2 Influence of Free Stream Turbulence and Receptivity......Page 301 10.3 Tollmien–Schlichting Breakdown......Page 304 10.4 Oblique Wave Breakdown......Page 305 10.5 Crossflow Vortex Breakdown......Page 307 10.6 Dean–Taylor–Gortler Vortex Breakdown......Page 311 10.7 Transition Prediction......Page 314 10.8 Exercises......Page 328 11.1 Introduction......Page 329 11.2 Governing Equations......Page 330 11.3 Temporal DNS Formulation......Page 333 11.4 Spatial DNS Formulation......Page 334 11.5 Large Eddy Simulation......Page 345 11.6 Applications......Page 346 11.7 Summary......Page 359 11.8 Exercises......Page 361 12.1 Introduction......Page 364 12.2 Effects of Flexible Boundaries......Page 365 12.3 Wave Induced Forcing......Page 380 12.4 Feed-Forward and Feedback Control......Page 381 12.5 Optimal Control Theory......Page 384 12.6 Exercises......Page 401 13.1 Experimental Facility......Page 402 13.2 Model Configuration......Page 404 13.3 Inducing Hydrodynamics Instabilities......Page 405 13.4 Measurement Instrumentation......Page 406 13.5 Signal Analysis......Page 409 13.6 Summary......Page 410 Appendix A Mathematical Formulas......Page 412 Appendix B Numerical Methods......Page 414 Appendix C Solutions to Exercises......Page 426 References......Page 530 Author Index......Page 557 Subject Index......Page 562