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arXiv 0909.3799cond-mat.other
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超流$^4$ He中的涡旋运动:正常流体流动的影响

Vortex Motion in Superfluid $^4$He: Effects of Normal Fluid Flow

Bhimsen K. Shivamoggi

摘要:

利用Hall-Vinen-Bekarevich-Khalatnikov(HVBK)唯象模型研究了超流~ 4 He中涡丝的运动.首先在固有几何参数空间中解析地制定HVBK方程,以获得对与摩擦系数α和α ′(在Hall-Vinen符号中)相关联的摩擦项的物理含义以及与摩擦系数α ′相关联的摩擦项的先前忽略的洞察。包括了沿涡丝方向和横截涡丝方向的法向速度分量。这一分析性发展也有助于突出说明在这条道路上取得进一步进展所遇到的困难。在外部涡丝坐标空间的HVBK方程的重新制定,然后给出这是已知的(Shivamoggi),在这方面提供了一个有用的替代分析方法。在考虑广义正常流体流动的情况下,给出了超流体中非线性Kelvin波在涡丝上传播的非线性薛定谔方程。与α撇相关的摩擦项,即使在存在垂直于涡丝的正常流体速度分量的情况下,也只产生开尔文波的代数增长,因此为忽略该项提供了进一步的理由。另一方面,不稳定性所产生的摩擦项与α通过正常的流体速度分量沿涡丝显示,表现为一个参数放大考虑的问题,在超流体中的旋转平面涡丝。

英文摘要:

The motion of a vortex filament in superfluid 4He is considered by using the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) phenomenological model for the scattering process between the vortex and thermal excitations in liquid 4He. The HVBK equations are analytically formulated first in the intrinsic geometric parameter space to obtain insights into the physical implications of the friction terms, associated with the friction coefficients alpha and alpha^prime (in the Hall-Vinen notation) as well as the previous neglect of the friction term associated with the friction coefficient alpha^prime. The normal fluid velocity components both along and transverse to the vortex filament are included. This analytical development also serves to highlight the difficulties arising in making further progress on this route. A reformulation of the HVBK equation in the extrinsic vortex filament coordinate space is then given which is known (Shivamoggi) to provide a useful alternative analytical approach in this regard. A nonlinear Schrodinger equation for the propagation of nonlinear Kelvin waves on a vortex filament in a superfluid is given taking into account the generalized normal fluid flow. The friction term associated with alpha^prime, even in the presence of the normal fluid velocity components transverse to the vortex filament, is shown to produce merely an algebraic growth of the Kelvin waves hence providing further justification for the neglect of this term. On the other hand, the instability produced by the friction term associated with alpha via the normal fluid velocity component along the vortex filament is shown to manifest itself as a parametric amplification on considering the problem of a rotating planar vortex filament in a superfluid.

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