Two problems in computational wave dynamics are considered: (i) the use
of Klemp-Wilhelmson time splitting at large scales and (ii) analysis of wave-wave
instabilities in nonhydrostatic and rotating mountain waves.
The use of Klemp-Wilhelmson (KW) time splitting for large-scale and global
modeling is assessed through a series of von Neumann accuracy and stability analyses.
Two variations of the KW splitting are evaluated in particular: the original acousticmode
splitting of Klemp and Wilhelmson (KW78) and a modified splitting due to
Skamarock and Klemp (SK92) in which the buoyancy and vertical stratification terms
are treated as fast-mode terms. The large-scale cases of interest are the problem of
Rossby wave propagation on a resting background state and the classic baroclinic
Eady problem. The results show that the original KW78 splitting is surprisingly
inaccurate when applied to large-scale wave modes. The source of this inaccuracy is
traced to the splitting of the hydrostatic balance terms between the small and large
time steps. The errors in the KW78 splitting are shown to be largely absent from the
SK92 scheme.
Resonant wave-wave instability in rotating mountain waves is examined using
a linear stability analysis based on steady-state solutions for flow over an isolated
ridge. The analysis is performed over a parameter space spanned by the mountain height (Nh/U) and the Rossby number (U/fL). Steady solutions are found using a
newly developed solver based on a nonlinear Newton iteration. Results from the
steady solver show that the critical heights for wave overturning are smallest for
the hydrostatic case and generally increase in the rotating wave regime. Results of
the stability analyses show that the wave-wave instability exists at mountain heights
even below the critical overturning values. The most unstable cases are found in
the nonrotating regime while the range of unstable mountain heights between initial
onset and critical overturning is largest for intermediate Rossby number.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-12-7400 |
| Date | 2009 December 1900 |
| Creators | Viner, Kevin Carl |
| Contributors | Epifanio, Craig C. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | application/pdf |
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