MQGeometry-1.0: a multi-layer quasi-geostrophic solver on non-rectangular geometries

Abstract. This paper presents MQGeometry, a multi-layer quasi-geostrophic (QG) equations solver for non-rectangul ar geometries. We advect the potential voriticity (PV) with finite volumes to ensure global PV conservation thanks to a staggered discretization of the PV and stream-function (SF). Thanks to this staggering, the PV is defined inside the domain, removing the need for defining the PV on the domain's boundary. We compute PV fluxes with upwind-biased interpolations whose implicit dissipation replaces the usual explicit (hyper-)viscous dissipation. The presented discretization does not require the tuning of any additional parameter, e.g. additional eddy viscosity. We solve the QG elliptic equation with a fast discrete sine transform spectral solver on rectangular geometry. We extend this fast solver to non-rectangular geometries using the capacitance matrix method. We validate our solver on a vortex-shear instability test case in a circular domain, a vortex-wall interaction test-case, and on an idealized wind-driven double-gyre configuration in a octogonal domain at a eddy-permitting resolution. We release a concise, efficient, and auto-differentiable PyTorch implementation of our method to facilitate future developments upon this new discretization, e.g. machine learning parameterization or data-assimilation techniques.