Systematic drift experienced by a point vortex in two-dimensional turbulence

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Abstract
Using a linear response theory, we show that a point vortex in two-dimensional turbulence experiences a systematic drift superposed to its mean-field velocity. Taking this result into account, we derive a Fokker-Planck equation for the evolution of its distribution function and make the link with a maximum entropy production principle [R. Robert and J. Sommeria, Phys. Rev. Lett. 69, 2776 (1992)]. We also discuss an analogy with stellar systems [P. H. Chavanis, J. Sommeria, and R. Robert, Astrophys. J. 471, 385 (1996)]; in particular, the systematic drift of the vortex is the counterpart of the dynamical friction experienced by a star due to close encounters [S. Chandrasekhar, Rev. Mod. Phys. 20 (3) (1949); H. E. Kandrup, Astrophys. Space Sci. 97, 435 (1983)].