2009/12/31 by Hiroyuki Adachi, Shoji Fujiyama, Makoto Tsubota · 127 citations
Physics and Astronomy · #Anisotropy #Biot number #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Mechanics #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Quantum turbulence #Quantum, superfluid, helium dynamics #Turbulence #Vortex #cond-mat.other
paper · pdf · doi:10.1103/physrevb.81.104511
published in Physical Review B 81(10) (American Physical Society) · 8 pages, 11 figures
openalex publication_date 2010/03/12 · arxiv created 2010/04/07 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We perform a numerical simulation of quantum turbulence produced by thermal counterflow in superfluid 4He by using the vortex filament model with the full Biot-Savart law. The pioneering work of Schwarz has two shortcomings: it neglects the nonlocal terms of the Biot-Savart integral [known as the localized induction approximation (LIA)] and it employs an unphysical mixing procedure to sustain the statistically steady state of turbulence. We have succeeded in generating the statistically steady state under periodic boundary conditions without using the LIA or the mixing procedure. This state exhibits the characteristic relation L=\ensuremathγ2vns2 between the line-length density L and the counterflow relative velocity vns and there is quantitative agreement between the coefficient \ensuremathγ and some measured values. The parameter \ensuremathγ and some anisotropy parameters are calculated as functions of temperature and the counterflow relative velocity. The numerical results obtained using the full Biot-Savart law are compared with those obtained using the LIA. The LIA calculation constructs a layered structure of vortices and does not proceed to a turbulent state but rather to another anisotropic vortex state; thus, the LIA is not suitable for simulations of turbulence.