Preface ....................................................... vii
Nomenclature .................................................. xii
1 Introduction ................................................. 1
1.1 The fact of turbulent flow .............................. 1
1.2 Broad options in modelling .............................. 2
1.3 A preview of the mean-strain generation processes in
the stress-transport equation ........................... 5
1.4 Some consequences of the no-slip boundary condition
at a wall ............................................... 9
1.5 Sequencing of the material ............................. 11
2 The exact equations ......................................... 13
2.1 The underpinning conservation equations ................ 13
2.2 The Reynolds equations ................................. 15
2.3 The second-moment equations ............................ 23
3 Characterization of stress and flux dynamics: elements
required for modelling ...................................... 33
3.1 Introduction ........................................... 33
3.2 Energy flow processes in turbulence .................... 33
3.3 The spectral character of turbulence ................... 38
3.4 The ε-equation ......................................... 43
3.5 Transport equation for the mean-square scalar
variance,  ........................................... 46
3.6 Transport equation for dissipation of scalar variance,
εθθ .................................................... 49
3.7 Turbulence anisotropy, invariants and realizability .... 50
4 Approaches to closure ....................................... 60
4.1 General remarks and basic guidelines ................... 60
4.2 Pressure interactions, and Φij and Φθj the Poisson
equation ............................................... 63
4.3 The basic second-moment closure for high-Ret flow
regions ................................................ 67
4.4 Pressure-strain models from tensor expansion ........... 86
4.5 Turbulence affected by force fields ................... 113
4.6 Modelling the triple moments .......................... 134
5 Modelling the scale-determining equations .................. 143
5.1 The energy dissipation rate, ε ........................ 143
5.2 Other scale-determining equations ..................... 156
5.3 Multi-scale approaches ................................ 160
5.4 Determining евв, the dissipation rate of ........... 167
6 Modelling in the immediate wall vicinity and at low Ret .... 170
6.1 The nature of viscous and wall effects: options for
modelling ............................................. 170
6.2 The structure of the near-wall sublayer ............... 173
6.3 Wall integration (WIN) schemes ........................ 188
6.4 Illustration of the performance of two near-wall
models ................................................ 214
6.5 Elliptic relaxation concept ........................... 229
7 Simplified schemes ......................................... 240
7.1 Rationale and organization ............................ 240
7.2 Reduced transport-equation models ..................... 241
7.3 Algebraic truncations of the second-moment
equations ............................................. 247
7.4 Linear eddy-viscosity models .......................... 270
7.5 The use of ASMs and linear EVMs within an unsteady
RANS framework ........................................ 301
8 Wall functions ............................................. 313
8.1 Early proposals ....................................... 313
8.2 Towards a generalization of the wall-function
concept: preliminaries ................................ 319
8.3 Analytical wall functions (AWF): the Manchester
scheme ................................................ 322
8.4 A Simplified AWF (SAWF): the Delft scheme ............. 331
8.5 Blended wall treatment (BWT) .......................... 335
8.6 Numerical wall functions (NWF) ........................ 341
References .................................................... 348
Index ......................................................... 373
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