[en] Tunneling of the Hartree liquid through opaque potential barriers separated by a well is considered. It is always unstable and is related to three distinctly different time scales. The shortest one is the period of classical oscillations in the well. It determines the period of tunneling current oscillations. Instability and specifically quantum turbulence develop on the scale of the quantum dwell time in the well. Dissipation yields the largest time scale. Analytical and numerical solutions are presented, and possible experiments are discussed