Applied Turbulence Modelling in Marine WatersThe simulation of turbulent mixing processes in marine waters is one of the most pressing tasks in oceanography. It is rendered difficult by the various complex phenomena occurring in these waters like strong stratification, ex ternal and internal waves, wind generated turbulence, Langmuir circulation etc. The need for simulation methods is especially great in this area because the physical processes cannot be investigated in the laboratory. Tradition ally, empirical bulk type models were used in oceanography, which, however, cannot account for many of the complex physical phenomena occurring. In engineering, statistical turbulence models describing locally the turbulence mixing processes were introduced in the early seventies, such as the k E model which is still one of the most widely used models in Computational Fluid Dy namics. Soon after, turbulence models were applied more and more also in the atmospheric sciences, and here the k kL model of Mellor and Yamada became particularly popular. In oceanography, statistical turbulence mod els were introduced rather late, i. e. in the eighties, and mainly models were taken over from the fields mentioned above, with some adjustments to the problems occurring in marine waters. In the literature on turbulence model applications to oceanography problems controversial findings and claims are reported about the various models, creating also an uncertainty on how well the models work in marine water problems. |
Contents
2 Basic model assumptions | 6 |
3 Boundary layer models | 29 |
4 Numerics | 97 |
5 The GOTM model | 111 |
6 Idealised test cases | 116 |
7 Oceanic and limnic applications | 135 |
8 Future Perspectives | 179 |
9 Appendix | 184 |
193 | |
213 | |
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Common terms and phrases
advection algebraic analytical solution assumption average Baumert and Peters bottom boundary conditions boundary layer buoyancy buoyancy production Burchard and Baumert calculated Canuto convective derived discretisation discussed eddy viscosity entrainment equilibrium Galperin GOTM gradient Richardson number grid horizontal Hossain idealised internal wave Julian Day Julian Day 1999 k-8 model k-k-L model Kantha and Clayson Lago Maggiore Langmuir circulation Large Eddy Simulation Liverpool Bay Luyten macro length scale measurements Mellor and Yamada mixed layer mixed layer depth model results normalised Northern North Sea one-dimensional panel parameterisation problem pycnocline quasi-equilibrium reproduced Reynolds stress Rodi roughness length second moments second-moment closure sets of stability shear probe shear production stability functions stable stratification steady-state Richardson number surface waves three-dimensional models tion transport equation turbulence closure models turbulence models turbulent dissipation rate turbulent kinetic energy two-equation models Umlauf and Burchard values vertical vertical advection wave breaking wave-enhanced layer