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Wall Turbulence Control

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Table of Contents

Preface vii Notations ix Chapter 1. General Points 1 1.1. Introduction 1 1.2. Tools to analyze and develop control strategies 2 1.2.1. Numerical simulations 2 1.2.2. Sensors 3 1.2.3. Actuators 20 Chapter 2. Summary of the Main Characteristics of Wall Turbulence 23 2.1. Introduction 23 2.2. General equations 23 2.2.1. Eulerian relations 24 2.3. Notations 25 2.4. Reynolds equations 26 2.5. Exact relations and FIK identity 27 2.6. Equations for a turbulent boundary layer 32 2.7. Scales in a turbulent wall flow 34 2.8. Turbulent viscosity closures 35 2.9. Turbulent intensities of the velocity components 47 2.10. Vorticity and near wall coherent structures 51 Chapter 3. Passive Control 65 3.1. Introduction 65 3.2. Large eddy (outer layer) breakup devices, LEBUs (OLDs) 66 3.2.1. General 66 3.2.2. Alteration of the inner structure by outer layer devices 67 3.3. Riblets 72 3.3.1. General 72 3.3.2. Effect of the riblets on the fine structure of wall turbulence 76 3.3.3. Effect of the protrusion height 84 3.4. Superhydrophobic surfaces 93 Chapter 4. Active Control 99 4.1. Introduction 99 4.2. Local blowing 100 4.3. Ad-hoc control 107 4.4. Transverse wall oscillations 115 4.5. Alternated spanwise Lorenz forcing and electromagnetic (EM) control 123 4.6. Extensions of spanwise forcing 131 4.7. Reynolds number dependence 132 4.8. Suboptimal active control 134 4.9. Optimal active control 143 4.10. Optimal linear control 147 4.11. Neural networks 156 4.12. Stochastic synchronization of the wall turbulence and dual control 157 Bibliography 167 Index 185

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