The model of a large-scale injection into a turbulent flow of immiscible fluid is considered. The long-time, large-scale asymptotic behavior of the energy dissipation rate ε is analyzed in the framework of renormalization group approach. It is shown that if the ordinary Kolmogorov dissipation regime (ε = const, in the inertial range) becomes unstable, the alternative asymptotic behavior would come true. In contrast to the standard Navier-Stokes turbulence, the alternative dissipation spectrum ε(k) has a minimum, which means that an optimal eddy size l exists in the model. This phenomenon provokes the flow into turbulence damping (the "bending effect" in combustion) or stimulates the magnetohydrodynamic system to a generation of a large-scale mean magnetic field ("turbulent dynamo" effect).