The impact of advection schemes on lateral shear and baroclinic instability

Abstract

This research quantifies spurious dissipation and mixing of several different advection schemes in some idealised experiments including lateral shear and baroclinic instabilities in the framework of one ocean model. The advection schemes are categorised based on their dissipative behaviour using several different methods such as background potential energy and numerical dissipation analysis. Such analyses help to choose between highly accurate but complex schemes and lower order less complex schemes balancing accuracy and computational costs. The Weighted Essentially Non-Oscillatory (WENO), the 5-point-stencil Monotonicity Preserving (MP5) advection schemes are used as highly accurate complex schemes. The Total Variation Diminishing (TVD) schemes and the simple upwind schemes as less complex advection schemes are also compared. The analyses show that the MP5 scheme and the SPL-max-1/3 (Symmetric Piecewise-Linear) as a TVD advection scheme provide the best results although the MP5 scheme is approximately 2.3 times more expensive than the SPL-max- 1/3 scheme in this implementation. In contrast to the configuration of baroclinic instability test case with a small Rossby number, when significant differences between schemes become apparent, the different advection schemes behave similarly for a larger Rossby number. Another major outcome of the present study is that positive global numerical dissipation and positive background potential energy evolution delay the restratification process.