A New Numerical Scheme for Nonlinear Ocean Dynamics

Simone Silvestri and Greg Wagner have made substantial progress in improving the numerical accuracy of the ocean component of the CliMA model, Clima-Ocean. Typical finite-volume ocean models for climate prediction use “second-order” schemes to discretize terms in the ocean’s momentum balance. But second-order momentum advection schemes are noisy, and therefore must be paired with artificial viscous terms to suppress spurious oscillations and prevent numerical instability. Artificial viscosity has the unfortunate side effect of artificially suppressing ocean mesoscale turbulence, which plays a fundamental role in Earth’s climate system by transporting heat poleward and determining the ocean’s density stratification.

surface vorticity at different resolutions

Improving the representation of mesoscale ocean eddies has the potential to mitigate important biases in ocean and climate predictions. To this end, Simone Silvestri and and Greg Wagner have developed a new, accurate and non-noisy momentum advection scheme for global ocean models. Remarkably, the new momentum advection scheme requires no explicit artificial viscosity for numerical stability—the first of its kind for global ocean models on the sphere. Ocean simulations with the new momentum advection scheme express more energetic mesoscale motions, especially at the awkward “eddy permitting” resolutions where mesoscale turbulence is partially, but not fully resolved. Simone presented their work at the 2022 American Geophysical Conference Fall Meeting 2022 in Chicago  and the 2023 SIAM Conference in Computational Science and Engineering in Amsterdam, receiving high praises from the ocean modeling community.

Because the new scheme requires no artificial viscosity, it adapts to increasing spatial resolution without the need to adjust viscosities and is thus useful not only for global simulations but also for regional high-resolution ocean modeling. The improved numerical scheme means that Clima-Ocean can focus on missing physics, rather than numerics, in parameterizing fluxes associated with the remaining, truly subgrid-scale component of the mesoscale turbulence spectrum.