Dynamics of a pair of point vortices and a foil with parametric excitation in an ideal fluid
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 4, pp. 618-627
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In this paper we obtain equations of motion for a vortex pair and a circular foil with parametric excitation due to the periodic motion of a material point. Undoubtedly, such problems are, on the one hand, model problems and cannot be used for an exact quantitative description of real trajectories of the system. On the other hand, in many cases such 2D models provide a sufficiently accurate qualitative picture of the dynamics and, due to their simplicity, an estimate of the influence of different parameters. We describe relative equilibria that generalize Föppl solutions and collinear configurations when the material point does not move. We show that a stochastic layer forms in the neighborhood of relative equilibria in the case of periodic motion of the foil's center of mass.
Keywords:
point vortices, ideal fluid, Poincaré map, foil in a fluid, 2D hydrodynamics.
@article{VUU_2020_30_4_a5,
author = {I. A. Bizyaev and I. S. Mamaev},
title = {Dynamics of a pair of point vortices and a foil with parametric excitation in an ideal fluid},
journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
pages = {618--627},
publisher = {mathdoc},
volume = {30},
number = {4},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VUU_2020_30_4_a5/}
}
TY - JOUR AU - I. A. Bizyaev AU - I. S. Mamaev TI - Dynamics of a pair of point vortices and a foil with parametric excitation in an ideal fluid JO - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki PY - 2020 SP - 618 EP - 627 VL - 30 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VUU_2020_30_4_a5/ LA - ru ID - VUU_2020_30_4_a5 ER -
%0 Journal Article %A I. A. Bizyaev %A I. S. Mamaev %T Dynamics of a pair of point vortices and a foil with parametric excitation in an ideal fluid %J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki %D 2020 %P 618-627 %V 30 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/VUU_2020_30_4_a5/ %G ru %F VUU_2020_30_4_a5
I. A. Bizyaev; I. S. Mamaev. Dynamics of a pair of point vortices and a foil with parametric excitation in an ideal fluid. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 4, pp. 618-627. http://geodesic.mathdoc.fr/item/VUU_2020_30_4_a5/