The Effect of Mixing Locality on Overturning Circulation

Diapycnal mixing is an important process for maintaining the meridional overturning circulation in the ocean. One contribution to diapycnal mixing in models is spurious, resulting from numerical operators such as horizontal advection. The spurious mixing present in models leads to a lower bound on effective diffusivity, so that low diffusivity regimes can't be simulated. Commonly-used methods for quantifying the spurious mixing in models require closed basins without buoyancy forcing, and are at best able to provide a single vertical profile for the entire domain. An estimate of the amount of spurious mixing and its spatial location can however be diagnosed from tracer variance statistics (e.g. Burchard and Rennau, 2007).

We investigate the sensitivity of an overturning circulation to variations in mixing by specifying the spatial location of diffusivity in an idealised numerical model. To minimise spurious mixing in the interior, a hybrid vertical coordinate is used, combining a $z^*$ mixed layer with an isopycnal interior, with a transition layer in between. The spurious diffusion is diagnosed using the variance decay method. By reducing the lower bound on spurious diffusivity, we are able to directly test a wide range of diffusivity profiles, including profiles that are uniform with depth, surface-enhanced, and boundary-enhanced.