The influence of turbulence closure strategy on numerical models of shallow water systems

The selection of appropriate turbulence closure strategies is fundamental to any modeling effort. While a number of closure models are presently available, little emphasis has been placed on examining differences between methods or on developing reliable parameter estimates. Through a series of individual papers, this work examines closure strategies using model comparisons and investigations under different flow conditions.;The first paper compares the nonlinear frictional behavior of two-dimensional and three-dimensional models in a shallow, friction-dominated embayment. Closure in the two dimensional model is achieved using a quadratic friction relation, while the three-dimensional model employs three different flow-dependent eddy viscosity expressions. The results indicate that all of the models may be calibrated to produce nearly identical elevation amplitudes at the dominant frequency. However, systematic differences arise at overtide frequencies and are shown to be related to the influence of the nonlinear velocity and finite amplitude terms relative to the linear terms in the governing equations.;An advanced turbulence strategy is explored in the second paper using a one-dimensional model which incorporates the Mellor-Yamada level 2.5 closure. The model equations and their solution by the finite element method are presented, and a collection of point model test cases is considered in the third paper in order to verify the model and to understand its behavior under a variety of flow situations. The test cases are organized in the form of an archive to be used as a resource for future model development.;Different closure schemes are compared in the final two papers. Convergence calculations suggest that the increase in efficiency of a stress-based approach to the vertical momentum equations does not extend to the solution of the turbulence energy and length scale equations. Significant benefit is realized only when a specified eddy viscosity closure is adopted. Comparisons between advanced and simplified methods are also used to determine optimum parameters for the simplified models over a range of flow conditions. The results illustrate that accurate solutions may be achieved using simplified closures when a judicious choice of parameters is made.