Vorwort; Abstract; Zusammenfassung; Contents; 1 Introduction; 2 Direct Numerical Simulation of Turbulent Flows; 3 Statistical Properties of Turbulence Obtained by DNS; 4 Dynamics of Turbulent Mixing; 5 Decomposition of Turbulent Fields by the Method of "Turbulent Line Segments"; 6 Regular and Anomalous Scaling of Two-PointStatistics and Gradients; 7 Summary and Conclusion; A Normalization of the Scalar Gradient PDF; B Skewness of the Longitudinal Velocity Gradients; C Normalized Moments of the Energy Dissipation; D Reynolds Number Dependence of the Scalar Flux Spectrum; References