About the Authors ix
Preface xi
Part I WALL TURBULENCE
1 Statistical Analysis and Spectral Method 3
1.1 Statistical Analysis and Spectral Method 3
1.1.1 Average Value 3
1.1.2 Probability Density and Statistical Moments 5
1.1.3 Correlation Function 9
1.2 Statistical Analysis of Turbulence 11
1.2.1 Reynolds Stress and Turbulent Kinetic Energy 11
1.2.2 Variable-Interval Time Average Method 13
1.3 Fourier Transform and Spectrum 16
1.3.1 Harmonic Wave 16
1.3.2 Fourier Transform 18
1.3.3 Energy Spectrum 22
1.4 Spectral Series Expansion of Function 22
1.4.1 Orthogonal Basis 22
1.4.2 Fourier Series 23
1.4.3 Chebyshev Polynomials 24
1.5 Fundamentals of Spectral Methods 26
1.5.1 Fundamental Concepts 26
1.5.2 Fourier-Galerkin Method 29
1.5.3 Chebyshev-Tau Method 31
1.5.4 Helmholtz Equation 34
1.6 Spectral Method of Navier-Stokes Equations 38
1.6.1 Time Integration Method 38
1.6.2 Spectral Method based on Time Marching Algorithms (1) 41
1.6.3 Spectral Method based on Time Marching Algorithms (2) 50
1.6.4 Spectral Method based on Time-Split Method 52
1.7 Closed Remarks 54
References 55
2 Wall Turbulence and Its Coherent Structure 57
2.1 Boundary Layer Flow and Flow Stability 58
2.1.1 Boundary Layer Flow 58
2.1.2 Flow Stability 59
2.1.3 Linear Stability Theory of Flow 61
2.2 Transition of Boundary Layer Flow 63
2.2.1 Basic Process 63
2.2.2 Receptivity Stage 64
2.2.3 Linear Instability and Transient Growth 68
2.2.4 Nonlinear Instability and Turbulent Spot 71
2.2.5 Bypass Transition 75
2.3 Coherent Structure of Wall Turbulence 77
2.3.1 Statistical Properties of Near-Wall Turbulence 78
2.3.2 Structural Features and Identification of Streak 82
2.3.3 Structural Features and Identification of Vortex 83
2.4 Formation and Evolution of a Coherent Structure 89
2.4.1 Formation and Instability of Streak 89
2.4.2 Formation of a Vortex Structure 92
2.4.3 A Novel Coherent Motion: Soliton and Its Relevant Structures 97
2.5 Bursting and Self-Sustaining of Wall Turbulence 102
2.5.1 Bursting Event 103
2.5.2 Self-Sustaining of a Coherent Structure 105
2.6 Closed Remarks 107
References 109
Part II CONTROL OF WALL TURBULENCE
3 Control of Turbulence with Active Wall Motion 115
3.1 Stokes Second Problem 118
3.2 Experiments of Wall Turbulence with Spanwise Wall Oscillation 121
3.2.1 Incompressible Flow with Spanwise Wall Oscillation 121
3.2.2 Compressible Flow with Spanwise Wall Oscillation 127
3.3 Numerical Simulation of Wall Turbulence with Spanwise Wall Oscillation 136
3.3.1 Wall Turblence with Spanwise Wall Oscillation 136
3.3.2 Control Mechanism of Spanwise Wall Oscillation 139
3.3.3 Wall Turbulence with Spanwise Traveling Wave on Wavy Wall 147
3.3.4 Wall Turbulence with Streamwise Traveling Wave on Wavy Wall 150
3.4 Deformed Wall 153
3.4.1 Shape Memory Alloy 155
3.4.2 Piezoceramics 156
3.4.3 Magnet 157
3.4.4 Cam Mechanism 158
3.5 Experiments of Wall Turbulence with Deformed Wall 158
3.5.1 Incompressible Flow with Deformed Wall 158
3.5.2 Compressible Flow with Deformed Wall 160
3.6 Numerical Simulation of Wall Turbulence with Deformed Wall 164
3.6.1 Wall Turbulence with Streamwise-Traveling Surface Deformation Wave 164
3.6.2 Wall Turbulence with Sinusoidally Deformed Wall 173
3.6.3 Wall Turbulence with Opposition Wall Deformation Control 177
3.6.4 Control Mechanism of Deformed Wall 188
3.7 Closed Remarks 192
References 193
4 Control of Turbulence by Lorentz Force
