Advanced Modelling of Turbulent Flows and Transport

1. introductory lecture on the course

2. statistical description of turbulence (mean flow, higher statistical moments, (auto)correlations, Taylors hypothesis)

3. experimental techniques (single point vs. field measurements, flow visualisation, measurement techniques)

4. balance equations I (continuity equation, Navier-Stokes equations, turbulent kinetic energy)

5. Reynolds decomposition (ensemble averaging, Reynolds equations, closure problem, energy transfer, Kolmorogov scales, energy spectrum, Kolmogorovs 5/3 law)

6. balance equations II (2DH/3D shallow water equations for free surface flows, scaling, hydrostatic pressure, wind stress, bottom friction, horizontal mixing, vertical mixing, constituent transport)

7. numerical techniques for 2DH shallow water equations (recap computational modelling, staggered schemes, time marching, momentum conservation, rapidly varied flows, flooding and drying)

8. turbulence modelling (mixing layer hypothesis, eddy viscosity concept, k-epsilon, LES)

9. numerical aspects of 3D turbulence modelling (regular vs. flexible meshes, sigma layers vs. z-layers for free surface flows, artificial vertical mixing, finite volume method, higher order upwind schemes+flux limiting)

10. turbulent flows in practice (boundary layers, law-of-the-wall, wall roughness, free surface flows in complex geometries, separation and recirculation)

11. turbulence diffusion (Reynolds analogy, dispersion, spreading)

12. non-hydrostatic flow modelling (vertical acceleration, subgrid, lock exchange, high performance computing)