  We consider superfluid turbulence near absolute zero of temperature generated
by classical means, e.g. towed grid or rotation but not by counterflow. We
argue that such turbulence consists of a {\em polarized} tangle of mutually
interacting vortex filaments with quantized vorticity. For this system we
predict and describe a bottleneck accumulation of the energy spectrum at the
classical-quantum crossover scale $\ell$. Demanding the same energy flux
through scales, the value of the energy at the crossover scale should exceed
the Kolmogorov-41 spectrum by a large factor $\ln^{10/3} (\ell/a_0)$ ($\ell$ is
the mean intervortex distance and $a_0$ is the vortex core radius) for the
classical and quantum spectra to be matched in value. One of the important
consequences of the bottleneck is that it causes the mean vortex line density
to be considerably higher that based on K41 alone, and this should be taken
into account in (re)interpretation of new (and old) experiments as well as in
further theoretical studies.
