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CASCADE BEHAVIORS OF VORTICES INTERACTIONS

Aokui Xiong
Department of Machine Intelligence and System Engineering, Tohoku University Sendai. 980-8579, Japan

Seiichiro Izawa
Department of Machine Intelligence and System Engineering, Tohoku University Sendai. 980-8579, Japan

Yu Fukunishi
Department of Machine Intelligence and System Engineering, Tohoku University Sendai. 980-8579, Japan

Abstract

The dynamic behaviors of four vortex rings' interaction are analyzed from several new viewpoints. A correlation function of rotation with deformation of a fluid particle, a measure of the nonlinear interaction between rotation and deformation in average of physical space, and the Kolmogorov entropy in rotation-deformation space are introduced to describe the behaviors of complex flows. The first two undergo nearly opposite experience in the cascade process and have steady asymptotic states. The entropy increases within the cascade process, which is consistent with the disordered nature of turbulence. To reveal the characteristics of the vector, Wi = ωjSji, which appears in the vorticity transport equation and whose role is to stretch and distort vorticity, a two-dimensional phase space is proposed, in which the relative orientations of the vector against vorticity vector are focused. It is found that the distribution of the vector in the phase space is limited in a well-bounded domain. The events of vorticity stretching are shown more than those of compressing and this is attributed to the nonnegative source term in its governing equation. While for the concentrated vorticity, the alignment of the vorticity stretching and distorting vector W with vorticity vector is obvious, the statistic alignment between them does not observed.