Evaluation of Analytical Turbulence Closures for Quasi-Geostrophic Ocean Flows with Coastal Boundaries

TL;DR

This work addresses the challenge of simulating quasi-geostrophic ocean flows with coastal boundaries by extending a pseudo-spectral QG solver to incorporate Brinkman volume penalization, sponging, and inflow handling. It benchmarks four analytical SGS closures—Smagorinsky, Dynamic Smagorinsky, Leith, and Dynamic Leith—on idealized island and cape geometries under a beta-plane and assesses them with both a priori and a posteriori analyses. The results show moderate to weak a priori correlations, with a posteriori assessments revealing weak overall SGS performance and substantial phase errors, indicating closures struggle to accurately reconstruct coast-influenced eddy dynamics. These findings highlight limitations of purely eddy-diffusivity closures in coastal QG flows and motivate exploration of structural, data-driven, or stochastic closure approaches to improve LES realism near boundaries.

Abstract

Numerical turbulence simulations typically involve parameterizations such as Large Eddy Simulations (LES). Applications to geophysical flows, especially ocean flows, are further complicated by the presence of complex topography and interior landforms such as coastlines, islands, and capes. In this work, we extend pseudo-spectral quasi-geostrophic (QG) numerical schemes and GPU-based solvers to simulate flows with coastal boundaries using the Brinkman volume penalization approach. We incorporate sponging and a splitting scheme to handle inflow and aperiodic boundary conditions. We evaluate four analytical sub-grid-scale (SGS) closures based on the eddy viscosity hypothesis: the standard Smagorinsky and Leith closures, and their dynamic variants. We show applications to QG flows past circular islands and capes with the beta-plane approximation. We perform both a priori analysis of the SGS closure terms as well as a posteriori assessment of the SGS terms and simulated vorticity fields. Our results showcase differences between the various closures, especially their approach to phase and feature reconstruction errors in the presence of coastal boundaries.

Figures (9)

• Figure 1: Set-up of domain for flow past a cylinder or idealized island. The computational domain consists of land (grey) and a sponge layer (yellow). Dotted black lines show the region of interest.
• Figure 2: Evolution of parameters and metrics over time for flow past circular islands with $\beta=0$
• Figure 3: Vorticity plot of the filtered field (a), and vorticity fields of LES most similar (minimum phase shift error) to the filtered field (b-f) for flows past the circular island with $\beta=0$
• Figure 4: Set-up of domain for flow past an idealized cape. The computational domain consists of land (grey) and a sponge layer (yellow). Dotted black lines show the region of interest.
• Figure 5: Fully-resolved vorticity fields for flows past an idealized cape with various $\beta$, all at the same time instant.