ISBDN: 3540421815
TITLE: The Origin of Turbulence in Near-Wall Flows
AUTHOR: Boiko, Grek, Dovgal, Kozlov
TOC:

1 Fundamentals of stability theory 1
1.1 Concept of hydrodynamic stability 1
1.2 Stability of fluid motion in time 3
1.2.1 Critical parameters for onset of instability 4
1.2.2 Growth of disturbance energy 6
1.2.3 Formulation of linear hydrodynamic stability problems 7
1.2.4 Inviscid linear stability problem 15
1.3 Instability in space 19
1.4 Completeness of solutions for the Orr-Sommerfeld and Squire equations 22
1.5 Lift-upeffect 27
1.5.1 Inviscid algebraic instability 28
1.5.2 Transient disturbance growth 31
1.5.3 Pseudospectra of the linearized Navier-Stokes operator 32
1.5.4 Optimal disturbances 34
1.5.5 Numerical range 37
2 Development of linear disturbances in near-wall flows 39
2.1 The flat plate boundary layer 39
2.1.1 Historical issues 39
2.1.2 Non-parallel effects 44
2.1.3 Wave packets 50
2.2 Plane Poiseuille flow 57
2.2.1 Theoretical approach 57
2.2.2 Experimental linear stability investigations 58
2.2.3 Transient growth 60
2.3 Three-dimensional boundary layers 62
2.3.1 Swept-wing flow 62
2.3.2 Flow instability at a concave wall 66
3 Receptivity of laminar near-wall flows 69
3.1 Formulation of receptivity problem 69
3.2 Localized and distributed generation 69
3.3 Outline of theoretical approaches to receptivity 71
3.3.1 Perturbation analysis 72
3.3.2 Adjoint functions and the 'efficiency' of generation 73
3.3.3 Numerical simulation 75
3.4 Experimental approaches to the receptivity investigation 75
3.5 Receptivity of twodimensional boundary layers 79
3.5.1 Leading-edge receptivity 80
3.5.2 Receptivity caused by surface geometry variations 82
3.5.3 Excitation of instability waves by spatially localized disturbances 85
3.6 Receptivity of a three-dimensional boundary layer 88
3.6.1 Swept-wing receptivity 88
3.6.2 Excitation of Grtler vortices 91
4 Late stages of transition 93
4.1 Onset of non-linearity 93
4.1.1 Amplitude criteria for appearance of non-linearity stimulated by Tollmien-Schlichting wave growth 94
4.1.2 Conditional stability and weakly non-linear theories 95
4.2 Basic transition scenarios in quasi-twodimensional flows 98
4.2.1 K-regime of transition 100
4.2.2 Subharmonic transition 102
4.3 Theoretical approaches for the onset of three dimensionality and breakdown 104
4.3.1 Resonance model of the subharmonic growth 104
4.3.2 Theory of linear secondary linear instability 104
4.3.3 Local high-frequency secondary instability 107
4.3.4 Direct numerical simulations 110
4.4 Appearance and development of turbulence 110
4.4.1 Wave combinations and intermittency 111
4.4.2 Turbulent spots 115
4.5 Transition to turbulence in flows modulated by streamwise vortices 119
4.5.1 Instability of crossflow vortices 121
4.5.2 Instability of Grtler vortices 124
4.5.3 Experimental modelling of streamwise vortex instabilities 125
5 Laminar-turbulent transition at high free-stream turbulence level 131
5.1 Streaks in the Blasius boundary layer 132
5.2 Experimental and theoretical modelling of the streak development 134
5.2.1 Streak generation at the leading edge 139
5.2.2 Local generation of streaks from the wall 142
5.2.3 Distributed receptivity 147
5.3 Transition mechanisms at high free-stream turbulence 154
5.3.1 Tollmien-Schlichting waves in the presence of streaks 155
5.3.2 Interaction of the streaks with Tollmien-Schlichting waves 160
5.3.3 Turbulent spots 162
5.3.4 Transition scenario at a high free stream turbulence 164
6 Transition to turbulence in separation bubbles 167
6.1 Problem formulation, substantiation and approaches 167
6.2 Instability of separated flows to small-amplitude disturbances 170
6.2.1 Waveform 171
6.2.2 Growth rates 173
6.2.3 Propagation velocities 177
6.2.4 Instability of an axisymmetric flow 178
6.2.5 Flow instability at separation of a three-dimensional boundary layer 179
6.3 Excitation of instability waves in separation bubbles 182
6.4 Wave interactions 184
6.4.1 Subharmonic excitation 184
6.4.2 Some other non-linear mechanisms 187
6.4.3 Effects of the initial spectrum on the transition 188
6.5 Backward effects of the disturbed flow in separation regions 189
6.6 Laminar-turbulent transition and the origin of coherent vortices 192
6.7 Implication of instability to separation control 194
7 Transition prediction and control 197
7.1 Transition prediction on the basis of linear stability theory 198
7.2 Basic flow control techniques 202
7.2.1 Mean flow adjustment 203
7.2.2 Riblets 209
7.2.3 Wave cancellation 213
7.2.4 Engineering application of the wave cancellation technique 215
References 219
Index 265
END
