Wave analysis for different splittings of the shallow water equations on the \(\beta \)-plane. (English) Zbl 1142.76340
Summary: The effects of operator splitting on the wave solutions of the linearized shallow water equations have been investigated by Á. Havasi [in: Large-Scale Scientific Computing: 5th International Conference, LSSC 2005, Sozopol, Bulgaria, June 6–10, 2005, Lect. Notes Computer Science 3743, Springer (2006; Zbl 1142.76438)] by directional decomposition of the sub-operators and by the constant Coriolis parameter \(f\). This-so-called \(f\)-plane-approximation does not allow the formation of Rossby waves, which play a major role in the evolution of midlatitude weather systems. In this paper we apply \(\beta \)-plane approximation in the shallow water equations and examine how the resulting Rossby-gravity waves are influenced by the separation of different physical effects in some concrete splitting schemes.
MSC:
| 76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |
Keywords:
operator splitting; shallow water model; rossby waves; gravity waves; spectrum approximationCitations:
Zbl 1142.76438References:
| [1] | Havasi, Á., Dispersion analysis of operator splittings in the linearized shallow water equations, (Lirkov, I.; Margenov, S.; Wasniewski, J., Large-Scale Scientific Computing: 5th International Conference, LSSC 2005, Sozopol, Bulgaria, June 6-10, 2005. Large-Scale Scientific Computing: 5th International Conference, LSSC 2005, Sozopol, Bulgaria, June 6-10, 2005, Lecture Notes in Computer Science, vol. 3743 (2006), Springer) · Zbl 1142.76438 |
| [2] | Zlatev, Z., Computer Treatment of Large Air Pollution Models (1995), Kluwer Academic Publisher · Zbl 0852.65058 |
| [3] | Botchev, M.; Faragó, I.; Havasi, Á., Testing weighted splitting schemes on a one-column transport-chemistry model, Int. J. Env. Pol., 22, 1/2, 3-16 (2004) |
| [4] | Dimov, I.; Faragó, I.; Havasi, Á.; Zlatev, Z., Operator splitting and commutativity analysis in the Danish Eulerian Model, Math. Comp. Sim., 67, 217-233 (2004) · Zbl 1063.92051 |
| [5] | D. Lanser, A comparison of operator splitting and approximate matrix factorization for the shallow water equations in spherical geometry. Technical Report MAS-R0115, CWI, Amsterdam, 2001; D. Lanser, A comparison of operator splitting and approximate matrix factorization for the shallow water equations in spherical geometry. Technical Report MAS-R0115, CWI, Amsterdam, 2001 |
| [6] | Pedlosky, J., Geophysical Fluid Dynamics (1998), Springer |
| [7] | T. Práger, Numerical prognostics I. Tankönyvkiadó, Budapest (1992) (in Hungarian); T. Práger, Numerical prognostics I. Tankönyvkiadó, Budapest (1992) (in Hungarian) |
| [8] | Strang, G., On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5, 3 (1968) · Zbl 0184.38503 |
| [9] | Strang, G., Accurate partial difference methods I: Linear Cauchy problems, Archive for Rational Mechanics and Analysis, 12, 392-402 (1963) · Zbl 0113.32303 |
| [10] | Csomós, P.; Faragó, I.; Havasi, Á., Weighted sequential splitting and their analysis, Comput. Math. Appl., 50, 1017-1031 (2005) · Zbl 1086.65053 |
| [11] | Gnandt, B., A new operator splitting method and its numerical investigation, (Faragó, I.; Georgiev, K.; Havasi, Á., Proceedings of the NATO Advanced Research Workshop, Borovetz, Bulgaria, 8-12 May, 2004. Proceedings of the NATO Advanced Research Workshop, Borovetz, Bulgaria, 8-12 May, 2004, Series: Nato Science Series: IV: Earth and Environmental Sciences, vol. 54 (2005)), 229-241 |
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