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In many dynamical systems in nature energy is transferred to small or to large length scales by a forward or inverse cascade, respectively. In three-dimensional hydrodynamic (HD) turbulence energy cascades forward from large to small scales while in two-dimensional HD turbulence energy cascades inversely from small scales to large scales. There are some examples, however, that have a mixed behavior such as fast rotating fluids, conducting fluids in the presence of strong magnetic fields, flows in constrained geometry, and others. In these examples the injected energy cascades both forward and inversely in fractions that depend on the value of a control parameter (rotation rate/magnetic field/aspect ratio ect). In the presented work we demonstrate using the 2D-MHD model that the transition from a forward to an inverse cascade can occur by a critical transition, . In the absence of any external magnetic forcing the system reduces to hydrodynamic fluid turbulence with an inverse energy cascade. In the presence of strong magnetic forcing the system behaves as 2D-MHD turbulence with forward energy cascade. As the amplitude of the magnetic forcing is varied a critical value is met for which the energy flux towards the large scales becomes zero. Close to this point the energy flux scales as a power law with the departure from the critical point and the normalized amplitude of the fluctuations diverges. The generality of this behavior to other systems with variable inverse cascades will be discussed.
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