Ein Algebrisches Turbulenzmodel für Ästuare

The density distribution within a fluid is of great importance for flow and transport phenomena in geophysical computational fluid dynamics. All turbulent exchange processes are influenced by buoyancy effects and must be adequately considered in numerical models. Parameterizations of the vertical eddy viscosity and eddy diffusivity are presented for application in estuarine simulations. This model is implemented in a 2D vertically structured finite difference scheme. The algebraic turbulence model is based on the mixing length assumption and damping functions. Schematic test cases and a long term simulation of three months for a salt wedge estuary show that this is an adequate parameterization of the turbulent exchange processes. Without any change of coefficients the model is applied to a well mixed estuary giving equally satisfactory results. A comparison of commonly used mixing length approaches for homogeneous and stratified flows shows differences near the surface which modify the flow field considerably and consequently effect the advective transport of scalar quantities. Simulations of laboratory experiments corroborate a mixing length formulation for the eddy viscosity which can be derived from free surface flow conditions assuming the logarithmic velocity profile and a linear shear stress distribution. The applied damping functions depend on the gradient Richardson number and comply with limiting conditions which are derived from energy redistribution considerations. The coefficients of these functions are determined from data of the atmospheric layer which is an environment quite different from the intended area of application, so as to avoid any system specific calibration. A comparison of model runs in a case-study of the Trave estuary demonstrates that constant eddy coefficients lead to systematic errors even within short simulation periods. With the algebraic turbulence model presented in this study simulations of estuaries which are primarily characterized by an equilibrium of horizontal advection and vertical diffusion reproduce even complex transport processes with sufficient accuracy