Energy spectra of developed turbulence in helium superfluids
Energy spectra of developed turbulence in helium superfluids
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DOI：
10.1007/s10909-006-9230-8
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发表时间：
2006-11-01
影响因子：
2
通讯作者：
Skrbek, L.
中科院分区：
文献类型：
--
作者：
L'vov, V. S.;Nazarenko, S. V.;Skrbek, L.
基于超流体的双流体描述，我们提出了一个超流体三维湍流能谱的“最小模型”。我们从正常流体的Navier-Stokes方程和超流组分的粗粒度流体动力学方程出发（在涡线上求平均后，从欧拉方程获得超流速度），并引入互摩擦耦合项，与逆流速度、平均超流涡度和温度相关参数q = α/（1+ α '），其中α和α'表示表征量化的涡流和液体的法向分量之间的相互摩擦的无量纲参数。然后，我们推导出的能量平衡方程，考虑到交叉速度的相关性。我们得到了所有的渐近解正常和超流的能量谱的小/大正常超流密度比和耦合的极限情况下。我们讨论了我们的模型的适用性超流He II和He-3-B。
We suggest a "minimal model" for the 3D turbulent energy spectra in superfluids, based on their two-fluid description. We start from the Navier-Stokes equation for the normal fluid and from the coarse-grained hydrodynamic equation for the superfluid component (obtained from the Euler equation for the superfluid velocity after averaging over the vortex lines) and introduce a mutual friction coupling term, proportional to the counterflow velocity, the average superfluid vorticity and to the temperature dependent parameter q = alpha/(1+alpha'), where alpha and alpha' denote the dimensionless parameters characterizing the mutual friction between quantized vortices and the normal component of the liquid. We then derive the energy balance equations, taking into account the cross-velocity correlations. We obtain all asymptotical solutions for normal and superfluid energy spectra for limiting cases of small/big normal to superfluid density ratio and coupling. We discuss the applicability of our model to superfluid He II and to He-3-B.