Steady-state counterflow quantum turbulence: Simulation of vortex filaments using the full Biot-Savart law
Steady-state counterflow quantum turbulence: Simulation of vortex filaments using the full Biot-Savart law
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DOI：
10.1103/physrevb.81.104511
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发表时间：
2010-03-01
影响因子：
3.7
通讯作者：
Tsubota, Makoto
中科院分区：
文献类型：
--
作者：
Adachi, Hiroyuki;Fujiyama, Shoji;Tsubota, Makoto
本文采用具有完全Biot-Savart定律的涡丝模型，对超流体(4)He中热逆流产生的量子湍流进行了数值模拟。Schwarz的开创性工作有两个缺点：它忽略了Biot-Savart积分的非局部项[称为局部感应近似（LIA）]，并且它采用非物理混合过程来维持湍流的统计稳定状态。我们成功地在周期边界条件下产生了统计稳态，而没有使用LIA或混合过程。该状态表现出线长密度L与逆流相对速度v（ns）之间的特征关系L=gamma(2)v(ns)(2)，且系数gamma与某些测量值之间存在定量的一致性。计算了参数γ和一些各向异性参数作为温度和逆流相对速度的函数。用全比奥-萨瓦定律得到的数值结果与用LIA得到的数值结果进行了比较。LIA计算构建了涡的分层结构，不进入湍流状态，而是进入另一种各向异性涡状态；因此，LIA不适合模拟湍流。
We perform a numerical simulation of quantum turbulence produced by thermal counterflow in superfluid (4)He 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=gamma(2)v(ns)(2) between the line-length density L and the counterflow relative velocity v(ns) and there is quantitative agreement between the coefficient gamma and some measured values. The parameter gamma 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.