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

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

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