In search of improving the numerical accuracy of the k−ɛ model by a transformation to the k−τ model

This study presents a detailed comparison between the k−ɛ and k−τ turbulence models. It is demonstrated that the numerical accuracy of the k−ɛ turbulence model can be improved in geophysical and environmental high Reynolds number boundary layer flows. This is achieved by transforming the k−ɛ model to the k−τ model, so that both models use the same physical parametrisation. The models therefore only differ in numerical aspects. A comparison between the two models is carried out using four idealised one-dimensional vertical (1DV) test cases. The advantage of a 1DV model is that it is feasible to carry out convergence tests with grids containing 5 to several thousands of vertical layers. It is shown hat the k−τ model is more accurate than the k−ɛ model in stratified and non-stratified boundary layer flows for grid resolutions between 10 and 100 layers. The k−τ model also shows a more monotonous convergence behaviour than the k−ɛ model. The price for the improved accuracy is about 20% more computational time for the k−τ model, which is due to additional terms in the model equations. The improved performance of the k−τ model is explained by the linearity of τ in the boundary layer and the better defined boundary condition.