The Energy Exascale Earth System Model (E3SM) is a new coupled Earth system model sponsored by the U.S Department of Energy. Here we present E3SM global simulations using active ocean and sea ice that are driven by the Coordinated Ocean‐ice Reference Experiments II (CORE‐II) interannual atmospheric forcing data set. The E3SM ocean and sea ice components are MPAS‐Ocean and MPAS‐Seaice, which use the Model for Prediction Across Scales (MPAS) framework and run on unstructured horizontal meshes. For this study, grid cells vary from 30 to 60 km for the low‐resolution mesh and 6 to 18 km at high resolution. The vertical grid is a structured z‐star coordinate and uses 60 and 80 layers for low and high resolution, respectively. The lower‐resolution simulation was run for five CORE cycles (310 years) with little drift in sea surface temperature (SST) or heat content. The meridional heat transport (MHT) is within observational range, while the meridional overturning circulation at 26.5°N is low compared to observations. The largest temperature biases occur in the Labrador Sea and western boundary currents (WBCs), and the mixed layer is deeper than observations at northern high latitudes in the winter months. In the Antarctic, maximum mixed layer depths (MLD) compare well with observations, but the spatial MLD pattern is shifted relative to observations. Sea ice extent, volume, and concentration agree well with observations. At high resolution, the sea surface height compares well with satellite observations in mean and variability.

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The use of spatially varying eddy diffusivities is explored with the extended Gent-McWilliams (eGM) closure for both passive tracers and potential vorticity (PV). Numerical experiments are conducted with a wind-forced isopycnal channel model. It is shown that, the eGM closure with eddy diffusivities derived from a high-resolution reference solution produces the best results compared to the reference solution in terms of the thickness, PV profiles and volume fluxes. The use of spatially varying eddy diffusivities also removes the unphysical reverse jets near the channel walls shown by the eGM with constant eddy diffusivities.

In this article we propose finite‐volume schemes for solving the inviscid and viscous quasi‐geostrophic equations on coastal‐conforming unstructured primal–dual meshes. Several approaches for enforcing the boundary conditions are also explored along with these schemes. The pure transport parts in these schemes are shown to conserve the potential vorticity along fluid paths in an averaged sense, and conserve the potential enstrophy up to the time truncation errors. Numerical tests based on the centroidal Voronoi–Delaunay meshes are performed to confirm these properties, and to distinguish the dynamical behaviours of these schemes. Finally some potential applications of these schemes in different situations are discussed.