Rachel Robey, Department of Applied Mathematics, University of Colorado Boulder

Towards a new vertical coordinate to optimally resolve ocean mesoscale eddy dynamics in high-resolution models

Quasigeostrophic (QG) dynamics are a canonical model for ocean mesoscale turbulence (balanced turbulence at scales of 10-100 km). Many investigations of QG turbulence use two layers and focus on the inverse energy cascade that occurs at the larger end of the range of scales. At the smaller scales, the flow is characterized by a forward cascade of QG potential enstrophy to dissipative scales and a complex exchange of energy among vertical modes and across horizontal scales. Accurate representation of these dynamics is important for eddying ocean models to describe the energetics of mesoscale eddies and their associated tracer transports and air-sea interactions. Literature suggests insufficient vertical resolution can fail to support the full range of horizontal scales at high resolutions. Limitations of vertical layers can also result in notable sensitivities to the choice of vertical grid; preliminary investigations with the MOM6 ocean model displayed particular sensitivity in the kinetic energy profiles.

We present a new vertical coordinate, between geopotential and isopycnal, that enables the vertically-discrete model to optimally represent vertical modes and their nonlinear interactions by concentrating vertical resolution in areas of strong stratification. We motivate the new coordinate by an analytical argument based on the structure of Sturm-Liouville eigenfunctions, demonstrate its superior ability to resolve wave speeds, vertical modes and their nonlinear interactions, and show preliminary comparisons of QG turbulence simulations using the novel grid against results with using existing state–of-the-art vertical ocean grids.