| About the Authors |
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ix | |
| Preface |
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xi | |
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1 Statistical Analysis and Spectral Method |
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3 | (54) |
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1.1 Statistical Analysis and Spectral Method |
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3 | (8) |
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3 | (2) |
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1.1.2 Probability Density and Statistical Moments |
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5 | (4) |
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1.1.3 Correlation Function |
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9 | (2) |
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1.2 Statistical Analysis of Turbulence |
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11 | (5) |
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1.2.1 Reynolds Stress and Turbulent Kinetic Energy |
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11 | (2) |
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1.2.2 Variable-Interval Time Average Method |
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13 | (3) |
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1.3 Fourier Transform and Spectrum |
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16 | (6) |
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16 | (2) |
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18 | (4) |
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22 | (1) |
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1.4 Spectral Series Expansion of Function |
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22 | (4) |
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22 | (1) |
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23 | (1) |
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1.4.3 Chebyshev Polynomials |
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24 | (2) |
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1.5 Fundamentals of Spectral Methods |
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26 | (12) |
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1.5.1 Fundamental Concepts |
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26 | (3) |
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1.5.2 Fourier--Galerkin Method |
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29 | (2) |
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1.5.3 Chebyshev--Tau Method |
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31 | (3) |
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34 | (4) |
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1.6 Spectral Method of Navier--Stokes Equations |
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38 | (16) |
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1.6.1 Time Integration Method |
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38 | (3) |
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1.6.2 Spectral Method based on Time Marching Algorithms (1) |
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41 | (9) |
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1.6.3 Spectral Method based on Time Marching Algorithms (2) |
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50 | (2) |
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1.6.4 Spectral Method based on Time-Split Method |
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52 | (2) |
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54 | (3) |
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55 | (2) |
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2 Wall Turbulence and Its Coherent Structure |
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57 | (58) |
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2.1 Boundary Layer Flow and Flow Stability |
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58 | (5) |
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2.1.1 Boundary Layer Flow |
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58 | (1) |
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59 | (2) |
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2.1.3 Linear Stability Theory of Flow |
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61 | (2) |
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2.2 Transition of Boundary Layer Flow |
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63 | (14) |
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63 | (1) |
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64 | (4) |
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2.2.3 Linear Instability and Transient Growth |
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68 | (3) |
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2.2.4 Nonlinear Instability and Turbulent Spot |
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71 | (4) |
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75 | (2) |
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2.3 Coherent Structure of Wall Turbulence |
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77 | (12) |
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2.3.1 Statistical Properties of Near-Wall Turbulence |
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78 | (4) |
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2.3.2 Structural Features and Identification of Streak |
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82 | (1) |
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2.3.3 Structural Features and Identification of Vortex |
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83 | (6) |
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2.4 Formation and Evolution of a Coherent Structure |
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89 | (13) |
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2.4.1 Formation and Instability of Streak |
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89 | (3) |
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2.4.2 Formation of a Vortex Structure |
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92 | |
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2.4.3 A Novel Coherent Motion: Soliton and Its Relevant Structures |
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91 | (11) |
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2.5 Bursting and Self-Sustaining of Wall Turbulence |
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102 | (5) |
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103 | (2) |
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2.5.2 Self-Sustaining of a Coherent Structure |
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105 | (2) |
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107 | (8) |
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109 | (6) |
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Part II CONTROL OF WALL TURBULENCE |
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3 Control of Turbulence with Active Wall Motion |
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115 | (80) |
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3.1 Stokes Second Problem |
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118 | (3) |
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3.2 Experiments of Wall Turbulence with Spanwise Wall Oscillation |
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121 | (15) |
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3.2.1 Incompressible Flow with Spanwise Wall Oscillation |
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121 | (6) |
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3.2.2 Compressible Flow with Spanwise Wall Oscillation |
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127 | (9) |
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3.3 Numerical Simulation of Wall Turbulence with Spanwise Wall Oscillation |
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136 | (17) |
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3.3.1 Wall Turblence with Spanwise Wall Oscillation |
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136 | (3) |
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3.3.2 Control Mechanism of Spanwise Wall Oscillation |
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139 | (8) |
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3.3.3 Wall Turbulence with Spanwise Traveling Wave on Wavy Wall |
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147 | (3) |
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3.3.4 Wall Turbulence with Streamwise Traveling Wave on Wavy Wall |
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150 | (3) |
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153 | (5) |
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155 | (1) |
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156 | (1) |
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157 | (1) |
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158 | (1) |
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3.5 Experiments of Wall Turbulence with Deformed Wall |
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158 | (6) |
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3.5.1 Incompressible Flow with Deformed Wall |
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158 | (2) |
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3.5.2 Compressible Flow with Deformed Wall |
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160 | (4) |
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3.6 Numerical Simulation of Wall Turbulence with Deformed Wall |
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164 | (28) |
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3.6.1 Wall Turbulence with Streamwise-Traveling Surface Deformation Wave |
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164 | (9) |
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3.6.2 Wall Turbulence with Sinusoidally Deformed Wall |
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173 | (4) |
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3.6.3 Wall Turbulence with Opposition Wall Deformation Control |
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177 | (11) |
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3.6.4 Control Mechanism of Deformed Wall |
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188 | (4) |
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192 | (3) |
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193 | (2) |
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4 Control of Turbulence by Lorentz Force |
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195 | (76) |
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197 | (3) |
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4.2 Experiments of Wall Turbulence with Spanwise Lorentz Force |
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200 | (14) |
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4.2.1 Control with Uniform Spanwise Oscillating Lorentz Force |
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200 | (6) |
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4.2.2 Control with Wavy Lorentz Force |
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206 | (8) |
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4.3 Numerical Simulation of Wall Turbulence with Spanwise Lorentz Force |
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214 | (46) |
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4.3.1 Spanwise Lorentz Force |
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214 | (2) |
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4.3.2 Generalized Stokes Layer Induced by Oscillating Lorentz Force |
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216 | (3) |
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4.3.3 Control with Spanwise Oscillating Lorentz Force |
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219 | (20) |
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4.3.4 Control with Wavy Lorentz Force |
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239 | (21) |
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4.4 Wall Turbulence with Wall-Normal Lorentz Force |
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260 | (5) |
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4.4.1 Three-Dimensional Lorentz Force Field |
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260 | (1) |
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4.4.2 Experiments on Wall Normal EM Actuator Tile |
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261 | (2) |
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4.4.3 Numerical Simulation of Wall Turbulence with Normal Lorentz Force |
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263 | (2) |
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265 | (6) |
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267 | (4) |
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Part III OPTIMAL FLOW CONTROL |
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5 Linear Optimal Flow Control |
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271 | |
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273 | (7) |
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273 | (4) |
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5.1.2 Optimal Control for Ordinary Differential Equations |
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277 | (3) |
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5.2 Optimal Control of Linear Quadratic Systems |
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280 | (10) |
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5.2.1 Linear Quadratic Optimal Control |
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280 | (7) |
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5.2.2 Discrete Linear Quadratic Systems |
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287 | (1) |
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5.2.3 Linear Quadratic Gaussian (LQG) Control in the Presence of Noise |
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288 | (2) |
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5.3 Linear Process in Near-Wall Turbulent Flow |
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290 | (4) |
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5.4 Linear Optimal Control of Two-Dimensional Flow |
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294 | (11) |
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5.4.1 Linearization of Navier--Stokes Equations |
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294 | (2) |
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5.4.2 Spectral Decomposition of Linearized Flow |
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296 | (3) |
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5.4.3 Standard State-Space Representations of Linearized Flow |
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299 | (3) |
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5.4.4 Linear Optimal Control of Channel Flow |
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302 | (3) |
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5.5 Linear Optimal Control of Three-Dimensional Flow |
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305 | (4) |
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309 | |
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310 | |