Shear Dispersion and Error Decay in Idealized Twin Experiments

Abstract

In understanding how errors decay in twin experiments, previous studies have shown that it can be due to bottom friction or geostrophic adjustment. However, there are quantities, such as passive tracers, that may not be recovered by either of these mechanisms. This study seeks a mechanism that can cause errors to decay in the absence of bottom friction or geostrophic adjustment. Consider the particular case of an isopycnic layer where the velocity is perfectly known but the layer thickness is not. It will be argued that the errors in layer thickness decay by processes similar to that of tracer homogenization. Based on the fact that the homogenization is achieved by an initial rapid shear dispersion, it is hypothesized that the error decay is initially by shear dispersion. This hypothesis is tested using idealized twin experiments based on an eddy-resolving isopycnic channel model. A series of experiments with different diffusivities supports the idea that the initial decay timescale approximates to the shear dispersion timescale.