Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2006-12-08
Physical Review B 76, 024520 (2007)
Nonlinear Sciences
Chaotic Dynamics
9 pages, 2 figure, 2 appendixes. Extended in accordance with referees comments and other scientific discussions. Moved from PR
Scientific paper
10.1103/PhysRevB.76.024520
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.
L'vov Victor S.
Nazarenko Sergei V.
Rudenko Oleksii
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