About existence of stationary points for the Arnold-Beltrami-Childress (ABC) flowстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 24 апреля 2018 г.
Аннотация:The existence of stationary points for the dynamical system of ABC-flow is
considered. The ABC-flow, a three-parameter velocity field that provides a
simple stationary solution of Euler's equations in three dimensions for
incompressible, inviscid fluid flows, is the prototype for the study of
turbulence (it provides a simple example of dynamical chaos). But,
nevertheless, between the chaotic trajectories of the appropriate solutions of
such a system we can reveal the stationary points, the deterministic basis
among the chaotic behaviour of ABC-flow dynamical system. It has been proved
the existence of 1 point for two partial cases of parameters {A, B, C}: 1) A =
B = 1; 2) C = 1 (A^2 + B^2 = 1). Moreover, dynamical system of ABC-flow allows
3 points of such a type, depending on the meanings of parameters {A, B, C}.