Transport and Coherent Structures in Wall Turbulence

Sedat TARDU is Associate Professor at Grenoble University in France where he teaches turbulent shear flows, heat transfer, fluid dynamics and chaos. His research area includes canonical and non-canonical wall turbulence, active and passive control of near-wall turbulence, unsteady wall layers, mixing and micro mixing and microfluidics. He has been a visiting researcher in several universities (Ecole Polytechnique Fédérale de Lausanne, Imperial College London, Beihang Un. Beijing). He is the author of more than 250 papers in peer-reviewed journals, and international conferences as well as several chapters in books.

• Introduction xiMain Notations xvChapter 1 General Points 11.1 Introduction 11.2 General equations 21.2.1 Eulerian relations 21.3 Notations 51.4 Reynolds equations 51.5 Exact relations in a fully developed turbulent channel flow 71.6 Equations for a turbulent boundary layer 121.7 Scales in a wall-bounded turbulent flow 141.8 Eddy viscosity closures 151.9 Turbulent intensities of the velocity components 321.10 Fine structure 381.11 Vorticity 421.11.1 Characteristics of vorticity field near to the wall 451.11.2 Turbulent intensities of the fluctuating vorticity components 52Chapter 2. Transport Phenomena in Wall Turbulence 552.1 Introduction 552.2 Transport equations 562.3 Models of return to isotropy 632.4 Transport of turbulent kinetic energy 662.5 Transport of the velocity gradient 732.6 Transport of the Reynolds stress -uv 752.7 Effects of the Reynolds number on transport 772.8 Dissipation 822.8.1 Dissipation of kinetic energy 822.8.2 Dissipation linked to the transport equations for the Reynolds stresses 872.9 Pressure 922.9.1 Wall pressure 932.9.2 Spectral density 952.9.3 Decomposition into slow and rapid components 1012.10 Anisotropy 1132.11 Rapid distortion 121Chapter 3 Near-wall Coherent Structures: History, Identification and Detection 1293.1 Introduction 1293.2 History 1303.3 Single-point Eulerian detection 1363.3.1 Detection in quadrant II 1393.3.2 Detection by the u-level (u-l) 1433.3.3 Detection by VITA and VISA 1443.4 Stochastic estimation 1483.5 Wavelets and wall turbulence 1533.6 Critical points and topology 1543.6.1 Critical points 1543.6.2 Application of the concept of critical points to the topology of turbulence 1573.6.3 Extension of the detection Q - Δ 1653.6.4 A few significant results relating to the topology of wall turbulence 1693.7 Pressure field and vortices 1763.8 Vorticity and vortices 1793.9 Transport of invariants 1823.10 “Lambda-2” criterion 1863.11. Relations between the topological invariants and the λ 2 technique 1883.12 Summary 1923.13 Lagrangian detection 194Chapter 4. Coherent Wall Structures: Dynamics and Contribution to Turbulent Activity 1994.1 Introduction 1994.2 Structural morphology of wall turbulence Quasi-streamwise vortices or hairpin vortices? 2004.3 Frequency distribution of energetic events in the inner sublayer 2054.4 Quadrant-based structure of the Reynolds shear stress 2124.5 Streaks 2154.6 Wavelet analysis, at low Reynolds numbers, of the vorticity layers surrounding the streaks 2214.7 Effect of coherent structures on local wall friction 2264.8 Effect of coherent structures on wall pressure 2344.9 Active and passive structures 2354.10 Particle trajectories: Lagrangian approach 2454.10.1 Lagrangian description and transport by turbulent diffusion 2454.10.2 Lagrangian description of transport by energetic events 2484.11 Dynamical systems approach 2574.11.1 Karhunen–Loève series 2584.11.2 POD and wall turbulence 2594.11.3 Chaotic synchronization 264Chapter 5. Regeneration and Self-maintaining of Coherent Structures 2735.1 Introduction 2735.2 Consensual structural elements 2745.3 Conceptual models 2755.3.1 Oseen vortex in a 2D mean shear 2755.3.2 Synthetic wall turbulence 2845.3.3 Viscous response of the flow to the convection of a vortex structure near to the wall 2895.4 Generation of streaks and inner shear layers: simplified theoretical models 2975.5 Elongated structures and streak formation 3035.6 Regeneration of vortex structures Observations deduced from direct numerical simulations 3055.7 Stability of streaks 3175.7.1 Linear stability 3175.7.2 Statistics in the inner layer 3255.7.3 Transient growth and algebraic growth 3265.7.4 Bypass transition 3355.7.5 Transient growth and bypass transition of the streaks 3425.7.6 Nonlinear transient growth 3485.8 Instability of streaks, their repercussions and self-maintaining of structures 3515.9 Triggering of the mechanism 3585.10 Formation of arch vortices Generation of new streamwise structures 3595.11 Discussion 3605.12 A heuristic model 363Chapter 6. Large- and Very Large-scale Structures 3736.1 Introduction 3736.2 Clusters of coherent structures 3746.2.1 History 3746.3 Characteristics of packets of structures at moderate Reynolds numbers 3796.4 Kinematic consequences of coherent clustering of structures 3816.5 Regeneration of the packets 3896.6 Clustering of packets Very large-scale motions 3946.7 Amplitude modulation by very large-scale motions 3986.8 Dynamic role of very large-scale motions 410Bibliography 423Index 455