Introduction: Physical description and significance of turbulent flows. Transition and onset of turbulence; Turbulent free shear and wall-bounded flows; Challenges and complexities. Direct Numerical Simulation (DNS): Introduction; Governing Equations; Computational cost; Examples of DNS of channel and free-shear flows. Large Eddy Simulation (LES): Introduction; Filtering; Filtered conservation equations; Smagorinsky’s model; Appraisal and perspective. Reynolds Averaged Equations: Reynolds averaging; Reynolds averaged equations; Closure problem. Turbulent Viscosity Models: Turbulent viscosity hypothesis; Algebraic models; Turbulent-kinetic-energy models; Exact and modelled equations for turbulent-kinetic-energy and its dissipation; Modifications for wall effects and buoyancy- driven flows. Reynolds-Stress Models: Introduction; Closure relations; Examples; Limitations
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