The Interplay of Model Resolution, Eddy Geometry and Eddy-Mean Flow Feedbacks

A geometric decomposition of eddy-mean flow feedbacks (Waterman and Lilly 2015) is a description of eddy-mean flow interactions in terms of the patterns of eddy variance ellipse geometry. It has the potential to offer new insights into eddy-mean flow interactions by identifying the ingredients of the eddy motion that have a mean flow forcing effect, describing the eddy forcing in terms of a lower order (less-differentiated) description of the flow, and linking eddy feedbacks to spatial patterns of variance ellipse geometry that can suggest physical mechanisms underpinning these effects.

In this study we employ the geometric decomposition framework to gain insight into the breakdown of eddy-mean flow feedbacks with the degradation of model resolution. To do so, we perform a series of experiments with an idealized model and examine the impact of spatial resolution on eddy shape, propagation and feedback characteristics. We find a rapid breakdown in the eddy feedback as the spatial resolution is degraded, despite the fact that eddy energy remains well-resolved. Investigation into eddy geometry reveals that although the average eddy size is unchanged as the model resolution is degraded, eddy shape is not. This is significant, as eddy anisotropy plays a critical role in allowing eddies to propagate against the mean flow and feedback onto mean dynamics. These results thus suggest that the failure to adequately resolve eddy shape properties, in particular the small length scales in one direction to resolve eddies with large anisotropy, can result in a critically reduced eddy effect at a model spatial resolution that nevertheless well resolves the eddy size.

The relevance of lessons learned using the idealized model is then tested in a realistic ocean general circulation model, specifically by comparing eddy shape and feedback characteristics in a configuration of the MOM5 at 1/4 and 1/10 degree horizontal resolution and 50 and 75 level vertical resolution. The exercise highlights the importance of both horizontal and vertical resolution in setting eddy anisotropy, and thus eddy-mean flow feedbacks.

REFERENCE: Waterman S. and J. M. Lillly (2015). Geometric decomposition of eddy feedbacks in barotropic systems. J. Phys. Oceanogr., 45 (4), 1009-1024 (doi: 10.1175/JPO-D_14-0177.1).