Editorial Type:
Article
Article Type:
Research Article

Nonnormal Frontal Dynamics

Yizhak Feliks Department of Mathematics, Israel Institute for Biological Research, Ness-Ziona, Israel

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Eli Tziperman Department of Earth and Planetary Sciences, and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts

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Brian Farrell Department of Earth and Planetary Sciences, and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts

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Print Publication:
01 Apr 2010
DOI:
https://doi.org/10.1175/2009JAS3214.1
Page(s):
1218–1231
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Abstract

The generalized stability of the secondary atmospheric circulation over strong SST fronts is studied using a hydrostatic, Boussinesq, two-dimensional f-plane model. It is shown that even in a parameter regime in which these circulations are stable to small perturbations, significant nonnormal growth of optimal initial perturbations occurs. The maximum growth factor in perturbation total energy is 250 and is dominated by the potential energy, which obtains a growth factor of 219 two to five hours after the beginning of the integration. This domination of potential energy growth is consistent with the observation that the available potential energy (APE) of the secondary circulation is larger by two orders of magnitude than the kinetic energy as well as with the transfer of kinetic to potential perturbation energy at the beginning of the growth of the perturbations.

The norm kernel is found to significantly influence the structure of the optimal initial perturbation as well as the energy obtained by the mature perturbations, but the physical mechanism of growth and the structure of the mature perturbations are robust.

Corresponding author address: Yizhak Feliks, Dept. of Mathematics, Israel Institute for Biological Research, P.O. Box 19, Ness-Ziona, 70450 Israel. Email: feliks@iibr.gov.il

Abstract

The generalized stability of the secondary atmospheric circulation over strong SST fronts is studied using a hydrostatic, Boussinesq, two-dimensional f-plane model. It is shown that even in a parameter regime in which these circulations are stable to small perturbations, significant nonnormal growth of optimal initial perturbations occurs. The maximum growth factor in perturbation total energy is 250 and is dominated by the potential energy, which obtains a growth factor of 219 two to five hours after the beginning of the integration. This domination of potential energy growth is consistent with the observation that the available potential energy (APE) of the secondary circulation is larger by two orders of magnitude than the kinetic energy as well as with the transfer of kinetic to potential perturbation energy at the beginning of the growth of the perturbations.

The norm kernel is found to significantly influence the structure of the optimal initial perturbation as well as the energy obtained by the mature perturbations, but the physical mechanism of growth and the structure of the mature perturbations are robust.

Corresponding author address: Yizhak Feliks, Dept. of Mathematics, Israel Institute for Biological Research, P.O. Box 19, Ness-Ziona, 70450 Israel. Email: feliks@iibr.gov.il

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