Comparison of physical to numerical mixing with different tracer advection schemes in estuarine environments

The numerical simulation of estuarine dynamics requires accurate prediction for the transport of tracers, such as temperature and salinity. During the simulation of these processes, all the numerical models introduce two kinds of tracer mixing: (1) by parameterizing the tracer eddy diffusivity through turbulence models leading to a source of physical mixing and (2) discretization of the tracer advection term that leads to numerical mixing. Physical and numerical mixing both vary with the choice of horizontal advection schemes, grid resolution, and time step. By simulating four idealized cases, this study compares the physical and numerical mixing for three different tracer advection schemes. Idealized domains only involving physical and numerical mixing are used to verify the implementation of mixing terms by equating them to total tracer variance. Among the three horizontal advection schemes, the scheme that causes the least numerical mixing while maintaining a sharp front also results in larger physical mixing. Instantaneous spatial comparison of mixing components shows that physical mixing is dominant in regions of large vertical gradients, while numerical mixing dominates at sharp fronts that contain large horizontal tracer gradients. In the case of estuaries, numerical mixing might locally dominate over physical mixing; however, the amount of volume integrated numerical mixing through the domain compared to integrated physical mixing remains relatively small for this particular modeling system.