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A physical mechanism of large-scale structure generation in a helical turbulent medium is discussed. The mechanism is described in terms of mathematical model involving new hydrodinamic, helical-vortex, instability caused by a feedback between solenoidal components of the velocity field. The role of a small-scale helical turbulent convection as a possible source of energy for sustaining large-scale intensive vortices is analyzed in the context of the problem on hydrodynamic alpha-effect in a convective system. To gain a better understanding of this phenomenon the results of theoritical and numerical investigation and laboratory and field experiments as well as observation data obtained by several Russian research teams since the early 1980s are reviewed. Finally, recent results of numerical simulation of helical-vortex instability development in a nonuniformly heated medium are discussed. Numerical analysis has shown that even in the case of laminar convection, helical feedback can initiate some new effects. Vivid examples of these phenomena are the formation of helical flow structure with linkage of streamlines of horizontal and vertical circulation, small convective cell merging during formation of large-scale flow srtucture, and a sharp increase in the kinetic energy of formed large-scale vortex due to the action of helical feedback.