Tracer-based estimates of eddy-induced diffusivities. (June 2020) - Haigh, Michael; Sun, Luolin; Shevchenko, Igor; Berloff, Pavel
Abstract: This study provides estimates of the mean eddy-induced diffusivities of passive tracers in a three-layer, double-gyre quasigeostrophic (QG) simulation. A key aspect of this study is the use of a spatial filter to separate the flow and tracer fields into small-scale and large-scale components, and we compare results with those obtained using Reynolds temporal averaging. The eddy tracer flux is related to a rank-2 diffusivity tensor via the flux-gradient relation, which is solved for a pair of tracers with misaligned large-scale gradients. We concentrate on the symmetric part of the resulting diffusivity tensor which represents irreversible mixing processes. The eigenvalues of the symmetric tensor exhibit complicated behaviour, but a particularly dominant and robust feature is the positive/negative eigenvalue pairs, which physically represent filamentation of the tracer concentration. The large off-diagonal diffusivity tensor component is the primary contributor to the eigenvalue polarity, and since this is such a prevalent feature we argue that the (horizontal) eddy-induced diffusivity should always be treated as a full 2 × 2 tensor. Diffusivity magnitudes are largest in the upper layer and in the eastward jet region, where the eddying flow is strongest. After removing the rotational part of the eddy tracer flux, typical mean diffusivities (eigenvalues) in the upper-layer are on the order of 10 3 m 2 s −1 in the jet region and 10 2 m 2 s −1 elsewhere. We also confirm that the time-mean of the diffusivity calculated from instantaneous fluxes is not the same as the diffusivity associated with the time-mean fluxes. Highlights: We use novel filtering methods to derive eddy-induced tracer diffusivities. Scales are separated using a spatial filter. Horizontal passive tracer diffusivities span many orders of magnitude. Diffusivity eigenvalue pairs are robustly of opposite sign. The diffusivity ought to be treated as a full rank-2 tensor.