As pointed out by Farrell, a normalmode analysis alone may be not enough for a convicing investigation of baroclinic stability. In some models growth rates can be achieved large enough to enable nonlinear growth also in parameter ranges of neutral normalmodes. According to
Farrell one has also to consider that structures, which achieve optimal growth for a given, fixed time interval (i.e. the singular vectors). Fischer (1998) investigated this problem for the classical Eady-model with q' = 0
- a case which can be treated analytically. In this paper we want to give a short overview of an investigation of singular vectors in Eady-models with β ≠ 0 and q' = 0. Our aim was to understand the influence of β ≠ 0 on optimal growth. Qualitative differences to Fischer’s results are only found at small wavenumbers below the longwave cutoff. The most remarkable difference beyond the longwave cutoff is the fact, that the singular vectors of the model with β ≠ 0 grow faster in the upper half of the fluid than in the lower half for the considered basic flows. The growth rates for parameter ranges of neutral normalmodes are too small to enable nonlinear growth effects in meteorologically relevant times. For long timescales we find, that the cutoffs must be understood more as a smooth transition to instability.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-216919 |
| Date | 03 January 2017 |
| Creators | Faulwetter, Robin, Metz, Werner |
| Contributors | Universität Leipzig, Fakultät für Physik und Geowissenschaften, Universität Leipzig, Fakultät für Physik und Geowissenschaften |
| Publisher | Universitätsbibliothek Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:article |
| Format | application/pdf |
| Source | Wissenschaftliche Mitteilungen des Leipziger Instituts für Meteorologie ; 22 = Meteorologische Arbeiten aus Leipzig ; 6 (2001), S. 137-156 |
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