Turbulence Closures for Estuarine Mixing: Implementation and Applications of a Generic Length Scale Method in the 3D Oceanographic Model ROMS

Numerical oceanographic models require parameterization of subgrid scale turbulence mixing - referred to as turbulence closures. Recently, Umlauf and Burchard (submitted 2002) introduced a Generic Length Scale (GLS) method that provides a canonical form to represent several popular two-equation closures such as Mellor and Yamada Level 2.5 (KKL), k-epsilon (KE), k-omega (KW88), and a new generic closure (GC) proposed by Umlauf and Burchard (2002). This GLS method and stability functions of Galperin, Kantha and Clayson, and Canuto have been implemented in the Regional Ocean Modeling System, a full-featured community three-dimensional primitive equation oceanographic model (ROMS v2.0, http://marine.rutgers.edu/po/index.php). ROMS also contains turbulence closures based on the original Mellor Yamada Level 2.5 method (MY25), the KPP scheme, or a user-defined analytical expression. Oceanographic modelers now have the flexibility to test and compare several types of turbulence closures in one 3D numerical model. We performed numerical experiments with the original MY25 method and the GLS method implemented as KKL, KE, KW88, and the new proposed closure GC. Three idealized cases were simulated: steady uniform open channel flow, surface-stress induced mixed-layer deepening, and estuarine circulation. Results highlight differences and similarities among the closure methods. Significant differences arise because of the pragmatic requirement to place minimum and/or maximum bounds on turbulent length scales and turbulent kinetic energy. For the first test case the KE, KW88, and GC methods produce similar results, with the KW88 closure agreeing most closely with the analytical solution. The KKL (and MY25) results agree least with the analytical solution, largely because they require an additional parameterization of a "wall proximity function". Larger differences were found in the mixed-layer deepening and the estuary test cases because of the limitation imposed on the turbulent length scale and the selection of the buoyancy parameter. For the GLS method the length scale limitation is imposed on all aspects of the solution for turbulent kinetic energy and for the prognostic variable of the second equation. However, for the MY25 method, the length scale is only limited in the stability function and eddy viscosity calculations, not in the wall proximity or dissipation. Thus, results from GLS set to KKL will differ from results using the original formulation of the MY25 closure. Comparison of results from the MY25 method to results from GLS as KKL demonstrate enhanced entrainment rates (up to 30 %) for the mixed-layer deepening case and an estuarine turbidity maximum displaced by up to 20 km. Additional differences will be presented from results with the KE, KW88, and GC closures.