Abstract
We demonstrate a family of two-dimensional steady viscous flows which have singular continuous (fractal) Fourier spectra. Such flows represent a novel intermediate stage between order and Lagrangian chaos: The motion of individual fluid particles in them is neither entirely correlated nor completely disordered. In the considered setup these flows are presented by the exact solutions of the Navier-Stokes equations and occupy a parameter subset of positive measure. Onset of this unusual state follows the formation of steady eddies and is caused by the development of singularities of return times along the particle paths near the stagnation points.
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