Treffer: Exploring Baroclinic Instability of the Computational Kind (BICK) in Numerical Simulations of the Ocean.

Primitive‐equation models are essential tools for studying ocean dynamics and their ever‐increasing resolution uncovers ever finer scales. At mesoscales and submesoscales, baroclinic instability is one of the main drivers of turbulence, but spurious numerical instabilities can also arise, leading to nonphysical dynamics. This study investigates a spurious instability termed Baroclinic Instability of Computational Kind (BICK), discovered in Arakawa and Moorthi (1988, https://doi.org/10.1175/1520‐0469(1988)045<1688:BIIVDS>2.0.CO;2) and Bell and White (2017, https://doi.org/10.1016/j.ocemod.2017.08.001), through idealized configurations using a vertical (Modified) Lorenz grid. Here, we explore the growth of BICK within quasi‐geostrophic (QG) and hydrostatic primitive‐equation (HPE) frameworks for different setups: the canonical Eady configuration, stratification‐modified Eady configurations, and a surface‐intensified jet configuration. Our results confirm that the emergence of BICK is specific to the vertical staggering of the (Modified) Lorenz grids. Its growth is consistent with linear QG theory, and BICK is confined near the surface and bottom boundaries. In HPE simulations, the nonlinear evolution of BICK generates small‐scale spurious eddies and reduces frontal sharpness. Increasing the number of levels reduces BICK's horizontal scale down to below the model's effective resolution. We illustrate this property using regional HPE simulations with a varying number of levels. BICK is found to significantly affect the vertically under‐resolved simulations by introducing small‐scale noise from both the bottom and surface boundaries. Our recommendation is to keep the ratio between the model horizontal (δx) $(\delta x)$ and vertical (δz) $(\delta z)$ resolution greater than 2N/f $2N/f$, where N $N$ is the Brunt‐Väisälä frequency and f $f$ the Coriolis parameter, to minimize the impact of BICK on the dynamics. Plain Language Summary: Numerical simulations of the ocean circulation are routinely used to investigate regional dynamics. In recent years, increases in their resolution have allowed the community to explore new ranges of fine‐scale dynamics. However, these new regimes of dynamics come with new numerical challenges inherent to the increase in resolution. In addition to physical instabilities, numerical instabilities artificially introduce spurious fine‐scale dynamics. Here, we investigate such an instability called Baroclinic Instability of the Computational Kind (BICK), identified in previous studies. We study BICK in different configurations, from idealized to realistic setups. We show that BICK is initially excited close to the bottom or surface boundaries, especially where the density changes rapidly over small scales along the boundaries. We illustrate the effects of this instability on a regional simulation of the Mozambique Channel circulation. Specifically, we show that, contrary to common practices, the vertical resolution of the grid has to be refined hand‐in‐hand with the horizontal resolution in order to tone down BICK. By identifying the conditions that trigger BICK, we aim to unravel the physical dynamics and numerical artifacts of small‐scale ocean simulations. Key Points: Ocean models that generally use the Lorenz vertical grid staggering can suffer from the spurious numerical instability called Baroclinic Instability of the Computational Kind (BICK)The nonlinear evolution of BICK produces spurious small scale eddies and reduces frontal sharpnessIn order to avoid the development of BICK, we recommend to design the grid such that δx/δz >2N/f [ABSTRACT FROM AUTHOR]

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