Abstract
Atmospheric motions are generally characterized by a wide range of multiple length and time scales, and a numerical method must use a fine grid to resolve such a wide range of scales. Furthermore, a very fine grid requires an extremely small time step in order to keep explicit time integration schemes stable. Therefore, high-resolution meteorological simulations are very expensive.
A novel multiscale modeling approach is, therefore, presented for simulating atmospheric flows. In this approach, a prognostic variable representing a highly intermittent multiscale feature is decomposed into a significant and a nonsignificant part using wavelets, where the significant part is represented by a small fraction of the wavelet modes. The proposed multiscale methodology has been verified for simulating three cases: Smolarkiewicz’s deformational flow model, warm thermals in a dry atmosphere, and the dynamics of a vortex pair with ambient stable stratification. Comparisons with benchmark simulations and with a reference model are evidence for the convergence and stability of the proposed model. The comparison with the reference model has revealed that about 93% of the grid points are not necessary to resolve the significant motion in a warm thermal simulation, saving about 96% of the CPU time. Moreover, the CPU time varies linearly with the number of significant wavelet modes, showing that the present fully implicit adaptive model is asymptotically optimal for this simulation. These primary results point toward the benefit of constructing multiscale atmospheric models using the adaptive wavelet methodology.
