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Helical Fluid and (Hall)-MHD Turbulence: a Brief Review

Helicity, a measure of the breakage of reflectional symmetry representing the topology of turbulent flows, contributes in a crucial way to their dynamics and to their fundamental statistical properties. We review several of their main features, both new and old, as the discovery of bi-directional cascades or the role of helical vortices in the enhancement of large-scale magnetic fields in the dynamo problem. The dynamical contribution in magnetohydrodynamic (MHD) of the cross-correlation between velocity and induction is discussed as well. We consider next how turbulent transport is affected by helical constraints, in particular in the context of magnetic reconnection and fusion plasmas {under one- and two-fluid approximations}. Central issues on how to construct turbulence models for non-reflectionally symmetric helical flows are reviewed, including in the presence of shear, and we finally briefly mention the possible role of helicity in the development of strongly localized quasi-singular structures {at small scale).