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On the representation of gravity waves in numerical models of the shallow water equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mohebalhojeh, Ali R. Dritschel, David G. |
| Copyright Year | 2000 |
| Abstract | Summary We examine in detail the gravity waves, or imbalanced motions, that develop during the evolution of vortical o ws in numerical models of the shallow water (SW) equations. The focus here is on nearlybalanced o ws, with small but non-zero gravity wave (GW) activity. For properly initialised o ws, it is reasonable to expect small GW activity when Froude numbers F r < 1 and Rossby numbers Ro < 1. The guiding principle in the present study is that an accurate representation of potential vorticity (PV) is the prerequisite to a fair assessment of the generation of gravity waves. The Contour-Advective Semi-Lagrangian (CASL) algorithm for the shallow water equations (Dritschel et al. 1999) is applied, as it shows a remarkable improvement in the simulation of PV. However, it is shown that the standard CASL algorithm for SW leads to a noticeable numerical generation of gravity waves. The false generation of GWs can equivalently be thought of as the false, or numerical, breakdown of balance. In order to understand the maintenance of balance in the SW equations, a hierarchy of CASL algorithms is introduced. The main idea behind the new hierarchy is to partially implement PV-inversion, balancing algorithms directly within the SW algorithm, while still permitting imbalanced motions. The results of the rst three members of the hierarchy, CA0 (standard CASL), CA1, and CA2 are described and are compared with the results of two other SW algorithms, a pseudo-spectral and a semi-Lagrangian one. The main body of results is obtained for a highly ageostrophic regime of o w, with jRojmax 1 and F rmax 0:5, where sub-index 'max' denotes maximum over the domain. We also explore other o w regimes in the relevant parts of the Ro-F r parameter space. We nd that, for a given resolution and Froude number, there is an optimal CASL algorithm, i.e. one which gives rise to the least numerical generation of gravity waves. |
| Starting Page | 669 |
| Ending Page | 688 |
| Page Count | 20 |
| File Format | PDF HTM / HTML |
| DOI | 10.1002/qj.49712656314 |
| Volume Number | 126 |
| Alternate Webpage(s) | http://www-vortex.mcs.st-and.ac.uk/~arm/pubs/f-casl.pdf |
| Alternate Webpage(s) | https://doi.org/10.1002/qj.49712656314 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
