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Two different types of transitions of the superfluid $^4$He to quantumturbulence regimes are studied for $1{\rm D}$ geometry in the case when theinfluence of the normal fluid on superfluid flow is suppressed. It is shownthat the roton mechanism of transition to quantum turbulence leads to acritical velocity satisfying the relation $v_c\propto d^{-1/4}$. In thesuper-flow mechanism, the transition to quantum turbulence arises when the"quantum Reynolds number" is about $10^3$ and the critical velocity depends onchannel size $d$ as $v_c\propto d^{-1}$ in agreement with the equations ofmotion for a superfluid component of the liquid $^4$He being disturbed by smallfluctuations of the normal fluid.

Critical Velocities for Roton and Super-Flow Quantum Turbulence in Liquid $^4$He