Evaluation of the Temporal Dynamics of Oceanic Eddies with Initial Peripheral Rate Shift
We consider the problem of the development of two-dimensional vortex with initial vorticity in the peripheral ring area of the circularly rotating incompressible viscous fluid. As a mechanism for the generation of vortex motion, we propose the model of plain circular rotation of incompressible viscous fluid with initial perturbation localized at the peripheral ring zone with rate shift. Based on the analytical solution axisymmetric nonstationary equation of plain evolution of vortex in viscous fluid we obtained the resulting integral for the vorticity in the whole area of rotating fluid. This allowed us to study the dynamic characteristics of oceanic vortex formations and the time duration of the vortex motion conservation in a viscous liquid. The presented calculations given here show that the process of vorticity generation is characterized by the complex of interacting movements from the main vortex in the center of the rotating system and from the peripheral secondary perturbations. Vortex formation occurs in such direction that the central vorticity intensifies due to the secondary perturbations, as a result forming two areas – vortex and potential – of the rotating system. The obtained calculation results for the vorticity generation time in rings forming at the meanders of Gulf Stream jets, when compared to the observational data, show that lifespan of rings of different scales distributes rather variously according to their sizes and viscosity, the value of which correspond to turbulent regimes of jet streams. We discuss the prospect of its possible applications for predictive analysis of the development dynamics of large-scale ocean eddies.
KeywordsEddy growth Vortex line stretching Finite-time singularities
The work was supported by the Ministry of Education and Science of the Russian Federation (Agreement No. 14.616.21.0035, unique identifier of the project RFMEFI61615X0035).
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