Front Cover -- Advanced Approaches in Turbulence -- Copyright -- Contents -- Contributors -- Preface -- 1 Basics of turbulence -- 1.1 Introduction -- 1.2 Eddy diffusion -- 1.3 Scales of turbulence -- 1.3.1 Isotropic decay -- 1.3.2 Stretching and diffusion of vorticity -- 1.4 Spectral equations -- 1.4.1 Isotropic turbulence -- 1.4.2 Shear and streaks -- 1.5 Averaged equations -- 1.5.1 Jets -- 1.5.2 Boundary layer -- 1.6 The form of turbulence models -- 1.6.1 Two equation models -- 1.6.2 Reynolds stress transport -- 1.7 Conclusion -- References -- 2 Direct numerical and large-eddy simulation of complex turbulent flows -- 2.1 Introduction -- 2.2 Error as a function of scale -- 2.2.1 Modified wavenumber -- 2.2.2 Nonlinear sources of error -- 2.2.3 Time advancement error as a function of scale -- 2.3 Analysis of numerical errors in large-eddy simulation using statistical closure theory -- 2.3.1 EDQNM closure -- 2.3.2 EDQNM-LES and the inclusion of numerical error -- 2.3.3 EDQNM model -- 2.3.4 Relative magnitudes of error -- 2.4 Simulations in complex geometries -- 2.4.1 Decay of isotropic turbulence -- 2.4.2 Gas turbine combustor -- 2.5 Simulating the flow around moving bodies -- 2.5.1 Fluid phase -- 2.5.2 Solid phase -- 2.5.3 The effects of interpolation -- 2.5.4 Particles in a turbulent channel -- 2.6 What is a 'canonical' flow? -- 2.6.1 Jets in crossflow -- 2.6.2 DNS of turbulent channel flow over random rough surfaces -- 2.7 The analysis of 'big data' -- 2.7.1 DMD of large datasets and numerical error -- 2.7.2 Analysis of wall-pressure fluctuation sources in turbulent channel flow -- 2.8 Bridging the Reynolds number divide -- 2.9 Concluding remarks -- Acknowledgments -- References -- 3 Large-eddy simulations -- 3.1 Introduction -- 3.1.1 Motivation -- 3.2 Governing equations -- 3.2.1 Filtering.