Imperial College London
Alternate

ProfessorPavelBerloff

Faculty of Natural Sciences, Department of Mathematics

Professor in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 9662p.berloff Website

 
 
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Location

 

745Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Davies:2024:10.1016/j.physd.2024.134068,
author = {Davies, J and Shevchenko, I and Berloff, P and Sutyrin, GG},
doi = {10.1016/j.physd.2024.134068},
journal = {Physica D: Nonlinear Phenomena},
title = {Linear instability and weakly nonlinear effects in eastward dipoles},
url = {http://dx.doi.org/10.1016/j.physd.2024.134068},
volume = {460},
year = {2024}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - The linear instability and weakly nonlinear dynamics of eastward-propagating, steady-state Larichev–Reznik vortex dipoles are explored in terms of two-dimensional normal-mode analysis. To extract the fastest growing normal modes, we apply both breeding methodology based on solving the initial-value problem, as well as a direct-solution approach through the full-spectrum eigenproblem involving large matrices. We find that the amplification rate of dipole instability decreases with respect to increase in dipole intensity. In our study, both approaches yield consistent results and are systematically compared to provide guidance for further studies of vortex structures. We consider nonlinear self-interaction of the fastest growing mode, along with the induced eddy fluxes, their divergence and mechanical energy balance. Through this analysis, we find that the unstable mode leads to weakening of the dipole by extracting its energy and exchanging potential vorticity content in the down-gradient sense, thus, providing a nonlinear physical mechanism for the dipole destruction. In particular, we highlight the fundamental importance of the west-east asymmetry of the normal mode for destruction to be realized. In summary, we consider this work to be a foundational demonstration of useful methodology for future studies of dynamics and stability of isolated vortices without simplifying spatial symmetries, such as ubiquitous vortices in geophysical fluids.
AU  - Davies,J
AU  - Shevchenko,I
AU  - Berloff,P
AU  - Sutyrin,GG
DO  - 10.1016/j.physd.2024.134068
PY  - 2024///
SN  - 0167-2789
TI  - Linear instability and weakly nonlinear effects in eastward dipoles
T2  - Physica D: Nonlinear Phenomena
UR  - http://dx.doi.org/10.1016/j.physd.2024.134068
VL  - 460
ER  -
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