Impact of the “Symmetric Instability of the Computational Kind” at mesoscale- and submesoscale-permitting resolutions

The energy- and enstrophy-conserving momentum advection scheme (EEN) used over the last 10 years in NEMO is subject to a spurious numerical instability. This instability, referred to as the Symmetric Instability of the Computational Kind (SICK), arises from a discrete imbalance between the two components of the vector-invariant form of momentum advection. The properties and the method for removing this instability have been documented by Hollingsworth et al. (1983), but the extent to which the SICK may interfere with processes of interest at mesoscale- and submesoscale-permitting resolutions is still unkown. In this paper, the impact of the SICK in realistic ocean model simulations is assessed by comparing model integrations with different versions of the EEN momentum advection scheme. Investigations are undertaken with a global mesoscale-permitting resolution (1/4 °) configuration and with a regional North Atlantic Ocean submesoscale-permitting resolution (1/60 °) configuration. At both resolutions, the instability is found to alter primarily the most energetic current systems, such as equatorial jets, western boundary currents and coherent vortices. The impact of the SICK is found to increase with model resolution with a noticeable impact at mesoscale-permitting resolution and a dramatic impact at submesoscale-permitting resolution. The SICK is shown to distort the normal functioning of current systems, by redirecting the slow energy transfer between balanced motions to a spurious energy transfer to internal inertia-gravity waves and to dissipation. Our results indicate that the SICK is likely to have significantly corrupted NEMO solutions (when run with the EEN scheme) at mesocale-permitting and finer resolutions over the last 10 years.