Assessment of spurious mixing in adaptive mesh simulations of the two-dimensional lock-exchange

Numerical simulations are used to evaluate the impact of adaptive meshes on the two-dimensional lock-exchange flow. In particular, the diapycnal mixing is quantified through calculation of the background potential energy. The choice of metric, which guides the mesh adapt, is fundamental to the success of an adaptive mesh simulation. The performance of different Hessian-based metrics is assessed and cases that both outperform and underperform, compared to fixed mesh simulations, are evaluated. The differences in performance result from the different forms of the metric and the extent to which smaller-scale fluctuations can influence the adapted mesh. The best performing metric produces levels of diapycnal mixing that are comparable to high resolution fixed mesh simulations that use one to two orders of magnitude more mesh vertices. Comparison of the mixing with the numerical simulations of ضzgِkmen et al. (2007) also demonstrates the validity of the adaptive mesh simulations.