Linear Instability and Weakly Nonlinear Effects in Eastward Dipoles

12 Pages Posted: 14 Nov 2023

See all articles by Jack Davies

Jack Davies

Imperial College London

Pavel Berloff

Imperial College London

Igor Shevchenko

Imperial College London

Georgi Sutyrin

University of Rhode Island

Abstract

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 realised. 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.

Keywords: Linear instability, Nonlinear dynamics, Numerical breeding, Energetics

Suggested Citation

Davies, Jack and Berloff, Pavel and Shevchenko, Igor and Sutyrin, Georgi, Linear Instability and Weakly Nonlinear Effects in Eastward Dipoles. Available at SSRN: https://ssrn.com/abstract=4633026 or http://dx.doi.org/10.2139/ssrn.4633026

Jack Davies (Contact Author)

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, SW7 2AZ
United Kingdom

Pavel Berloff

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, SW7 2AZ
United Kingdom

Igor Shevchenko

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, SW7 2AZ
United Kingdom

Georgi Sutyrin

University of Rhode Island ( email )

Quinn Hall
55 Lower College Rd.
Kingston, RI 02881
United States

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