The 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.

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This book gives an overview of statistical turbulence modelling with applications to oceanography and limnology. It discusses how these models can be derived from the Naiver-Stokes equations and how step by step simplications result in models applicable to numerical simulations for realistic solutions. Possibilities for considering additional effects such as breaking surface waves and Langmuir circulation are discussed. Relevant methods for the numerical discretisation of the turbulence models are presented. Results from one -dimensional simulations are shown for various oceanic and limnic water column studies. The integration of these turbulence models in three-dimensional models are some selected results are also given.

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