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Free keywords:
flow simulation; Gaussian distribution; numerical analysis; probability; statistical analysis; turbulence; vortices
Abstract:
A statistical analysis of the two-point vorticity statistics in the inverse energy cascade
of two-dimensional turbulence is presented in terms of probability density functions (PDFs). Evolution equations for the PDFs are derived in the framework of the
Lundgren–Monin–Novikov hierarchy, and the unclosed terms are studied with the
help of direct numerical simulations (DNS). Furthermore, the unclosed terms are
evaluated in a Gaussian approximation and compared to the DNS results. It turns out
that the statistical equations can be interpreted in terms of the dynamics of screened
vortices. The two-point statistics is related to the dynamics of two point vortices with
screened velocity field, where an effective relative motion of the two point vortices
originating from the turbulent surroundings is identified to be a major characteristics of the dynamics underlying the inverse cascade.
