Reducing spurious diapycnal mixing in ocean circulation models

Abstract

Spurious diapycnal mixing of water masses occurs in ocean circulation models as an artifact of numerical algorithms used to advect temperature and salinity. Most of the ocean models used in climate research are based on geopotential vertical coordinates, which intersect isopycnal surfaces. The non-alignment of coordinate surfaces with isopycnals causes spurious diapycnal mixing during horizontal advection of a water-parcel by high-order upwind transport schemes. The growth in the potential energy of the system appears without any sources. This behavior is physically incorrect and leads to an energetic inconsistency and incorrect water mass transformation. Therefore, spurious diapycnal mixing in ocean models is one of the reasons that lead to the incorrect hydrological state of the ocean basins after some integration time. Improvements are required which would reduce spurious mixing in ocean models. Three ways that can potentially reduce spurious diapycnal mixing are considered in the current work. First, it is the design of more accurate advection schemes with reduced truncation error which leads to a decrease in numerical mixing in a system. The second way is the stabilization of central high-order advection schemes by isoneutral diffusion. And the last option is a choice of the right mesh. The current work analyses the stability of numerical implementation of isoneutral diffusivity on triangular meshes of Finite volumE Sea-ice Ocean Model, version 2 (FESOM2). It proposes a new compact advection scheme characterized by a reduced truncation error compared to other finite volume schemes in FESOM2. It shows that the application of isoneutral diffusion to stabilize central schemes can reduce spurious diapycnal mixing in models, however, it requires special tuning for every initial state of a model. It is also found out that mesh irregularity does not necessarily imply an enhanced numerical mixing in a system, however, it might depend on the type of triangles.