Comparison of numerical advection schemes in two-dimensional turbulence simulation

Abstract

Abstract The influence of numerical approximations on statistical characteristics of modelled two-dimensional turbulence sustained by a stochastic external forcing is studied. The ability of various finite-difference and semi-Lagrangian schemes to reproduce reliably the dual energy and enstrophy cascades for coarse spatial resolution is tested. It is also studied how the requirement of preserving invariants inherent to a two-dimensional ideal fluid is important relative to numerical schemes. The results of calculations with high spatial resolution were taken as a reference solution. The choice of studied schemes was motivated by their use in atmosphere and ocean numerical models, in particular, in the Institute of Numerical Mathematics climate model (INMCM) and semi-Lagrangian absolute vorticity (SLAV) model of medium-range weather forecast. The importance of conservation laws for integral vorticity and enstrophy is revealed in the numerical experiments with a small-scale external forcing.