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Filimonova A. М. Dynamics and advection in a vortex parquet. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2019, vol. 27, iss. 4, pp. 71-84. DOI: 10.18500/0869-6632-2019-27-4-71-84

# Dynamics and advection in a vortex parquet

Issue. The article is devoted to a numerical study of the dynamics and advection in a vortex parquet. A vortex structure, consisting of vortex patches on the entire plane, is considered. The mathematical model is formulated as a system of two partial diﬀerential equations in terms of vorticity and stream function. The dynamics of the vortex structures is considered in a rectangular area under the assumption that periodic boundary conditions are imposed on the stream function. Investigation methods. The non-stationary problem is solved by the meshless vortex-in-cell method, based on the vorticity ﬁeld approximation by its values in liquid particles and stream function expansion in the Fourier series cut. Results. Vortex structure consisting of four patches with diﬀerent directions is investigated. The results of a numerical study of the dynamics and interaction of the structure are presented. The inﬂuence of the patch radius and the relative position of positively and negatively directed patches on the processes of interaction and mixing is studied. The obtained results correspond to the following possible scenarios: the initial conﬁguration does not change over time; the initial conﬁguration forms a new structure, which is maintained for longer times; the initial conﬁguration returns to its initial state after a certain period of time. The processes of mass transfer of vorticity by liquid particles on a plane were calculated and analyzed. The results of a numerical analysis of the particles dynamics and trajectories on the entire plane and the ﬁeld of local Lyapunov exponents are presented.

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