Geodesic
Mathematical model of cavitational braking of a torus in the liquid after impact
Matematičeskoe modelirovanie, Tome 30 (2018) no. 8, pp. 116-130

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The process of cavity formation under vertical impact and subsequent braking of a torus of an elliptical cross-section semisubmerged into a liquid is investigated. The solution of the problem is constructed by means of a direct asymptotic method, effective at small times. A special problem with unilateral constraints is formulated on the basis of which the initial zones of a separation and contact of liquid particles are determined, as well as perturbations of the internal and external free boundaries of the liquid at small times. Limit cases of a degenerate and a thin torus are considered. In the case of a thin torus, the flow pattern corresponds to the 2D problem of cavitation braking of an elliptical cylinder in a liquid after a continuous impact.
Keywords: ideal incompressible liquid, torus of elliptical section, hydrodynamic impact, cavitation braking, asymptotics, free border, cavity, small times, Froude's number. 
@article{MM_2018_30_8_a7,
     author = {M. V. Norkin},
     title = {Mathematical model of cavitational braking of a torus in the liquid after impact},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {116--130},
     publisher = {mathdoc},
     volume = {30},
     number = {8},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_8_a7/}
}
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M. V. Norkin. Mathematical model of cavitational braking of a torus in the liquid after impact. Matematičeskoe modelirovanie, Tome 30 (2018) no. 8, pp. 116-130. http://geodesic.mathdoc.fr/item/MM_2018_30_8_a7/