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The title of the paper coincides with the title of a paragraph in the famousbook by U. Frisch (1995)on classical turbulence. In this paragraph the authordiscussed the role of statistical dynamics of vortex filaments in the theory ofturbulence and put the above question. In other words, whether the mainproperties of turbulence (cascade, scaling laws) are the sequence of the vortexline dynamics or the latter have only marginal signature. Quantum fluids, wherethe vortex filaments are the real objects, give an excellent opportunity toexplore the role of discrete vortices in turbulent phenomena. The aim of thispaper is to discuss which elements of vortex dynamics would lead to the mainingredients of the theory of turbulence. We discuss how the nonlinear dynamicsof vortex filaments can result in an exchange of energy between differentscales, the formation of the Kolmogorov-type energy spectra and the decay ofturbulence.

Statistical signature of vortex filaments: dog or tail? Talk given at QFS 2016