The modified method of contour dynamics and modeling of vertical structures
V.Yu. Belashov a∗∗, O.A. Kharshiladze b∗∗
a Kazan Federal University, Kazan, 420008 Russia
b Ivane Javakhishvili Tbilisi State University, Tbilisi, 0179 Georgia
E-mail: ∗vybelashov@yahoo.com, ∗∗o.kharshiladze@mail.ru
Received August 28, 2018
DOI: 10.26907/2541-7746.2019.1.5-23
For citation: Belashov V.Yu., Kharshiladze O.A. The modified method of contour dynamics and modeling of vortical structures. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2019, vol. 161, no. 1, pp. 5–23. doi: 10.26907/2541-7746.2019.1.5-23. (In Russian)
Abstract
This paper considers one of the most effective methods for modeling vortical structures, which are described by the 2-dimensional equation of carry of a vortex and by the Poisson equation for a flow function, namely, the contour dynamics method based on representation of a vortical stream by finite-area vortical regions. A modification of the contour dynamics method minimizing the errors arising at its direct application to description of vortical structures has been elaborated. The examples of the results of numerical experiments on the study of the dynamics of interaction of vortical structures for various configurations of their relative positioning, signs of vorticity, and distances between borders of the finite-area vortical regions have been presented.
Keywords: vortices, finite-area vortical regions, modeling, hydrodynamics, modified contour dynamics method, regimes of interaction, quasi-recurrence phenomenon, phase intermixing
Acknowledgments. The work is performed according to the Russian Government Program of Competitive Growth of Kazan Federal University and supported by the Shota Rustaveli National Science Foundation of Georgia (SRNF) (project no. RF17_252).
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