  The coupled dynamics of quantum turbulence (QT) and normal-fluid turbulence
(NFT) have been a central challenge in quantum hydrodynamics, since it is
expected to cause the unsolved T2 state of QT. We numerically studied the
coupled dynamics of the two turbulences in thermal counterflow. NFT is driven
by external forces to control its turbulent intensity, and the fast multipole
method accelerates the calculation of QT. We show that NFT enhances QT via
mutual friction. The vortex line density $L$ of the QT satisfies the
statistical law $L^{1/2} \approx \gamma V_{ns}$ with the counterflow velocity
$V_{ns}$. The obtained $\gamma$ agrees with the experiment of T2 state,
validating the idea that the T2 state is caused by NFT. We propose a
theoretical insight into the relation between the two turbulences.
