Vortices and Factorization
Igor Loutsenko, Oksana Yermolayeva
TL;DR
This paper explores the use of factorization methods to find stationary vortex patterns in 2D fluids, introduces new pattern classes linked to Schrödinger operators, and shows soliton solutions of the KdV hierarchy provide complete solutions for certain vortex systems.
Contribution
It introduces novel vortex pattern classes related to periodic Schrödinger operators and demonstrates the completeness of soliton solutions for specific vortex configurations.
Findings
New vortex patterns related to bi-spectral Schrödinger operators
Complete solutions for certain vortex systems via KdV solitons
Application of factorization methods to fluid vortex problems
Abstract
We review applications of factorization methods to the problem of finding stationary point vortex patterns in two-dimensional fluid mechanics. Then we present a new class of patterns related to periodic analogs of Schrodinger operators from the ``even" bi-spectral family. We also show that patterns related to soliton solutions of the KdV hierarchy constitute complete solution of the problem for certain classes of vortex systems. Keywords: Point vortices in ideal fluid, Factorization of second- and third-order differential operators, KdV and Sawada-Kotera hierarchies, Bispectral problem, Locus configurations
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Taxonomy
TopicsOcean Waves and Remote Sensing · Nonlinear Dynamics and Pattern Formation · Oceanographic and Atmospheric Processes