A New Hypothesis on the Anisotropic Reynolds Stress Tensor for Turbulent Flows

1 Introduction.- 1.1 Historical Background and Literature Review.- 1.2 Governing Equations of Incompressible Turbulent Flows.- 1.3 Summary.- References.- 2 Theoretical Principles and Galilean Invariance.- 2.1 Introduction.- 2.2 Basic Principles of Advanced Turbulence Modelling.- 2.3 Summary.- References.- 3 The k-w Shear-Stress Transport (SST) Turbulence Model.- 3.1 Introduction.- 3.2 Mathematical Derivations.- 3.3 Governing Equations of the k-w SST Turbulence Model.- 3.4 Summary.- References.- 4 Three-Dimensional Anisotropic Similarity Theory of Turbulent Velocity Fluctuations.- 4.1 Introduction.- 4.2 Similarity Theory of Turbulent Oscillatory Motions.- 4.3 Summary.- References.- 5 A New Hypothesis on the Anisotropic Reynolds Stress Tensor.- 5.1 Introduction.- 5.2 The Anisotropic Reynolds Stress Tensor.- 5.3 An Anisotropic Hybrid k-w SST/STM Closure Model for Incompressible Flows.- 5.4 Governing Equations of the Anisotropic Hybrid k-w SST/STM Closure Model.- 5.5 On the Implementationof the Anisotropic Hybrid k-w SST/STM Turbulence Model.- 5.6 Summary.- References.- Appendices: Additional Mathematical Derivations.- A.1 The Unit Base Vectors of the Fluctuating OrthogonalCoordinate System.- A.2 Galilean Invariance of the Unsteady Fluctuating VorticityTransport Equation.- A.3 The Deviatoric Part of the Similarity Tensor.