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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Singular vectors of Eady-models with β ≠ 0 and q' = 0

Faulwetter, Robin, Metz, Werner 03 January 2017 (has links) (PDF)
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.
2

Singular vectors of Eady-models with β ≠ 0 and q' = 0

Faulwetter, Robin, Metz, Werner 03 January 2017 (has links)
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.

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