The fundamental difference between incompressible ideal magnetohydrodynamics and the dynamics of a non-conducting fluid is that magnetic fields exert a tension force that opposes their bending; magnetic fields behave like elastic strings threading the fluid. It is natural, therefore, to expect that a magnetic field tangled at small length scales should resist a large-scale shear in an elastic way, much as a ball of tangled elastic strings responds elastically to an impulse. Furthermore, a tangled field should support the propagation of ‘magnetoelastic waves’, the isotropic analogue of Alfvén waves on a straight magnetic field. Here, we study magnetoelasticity in the idealised context of an equilibrium tangled field configuration. In contrast to previous treatments, we explicitly account for intermittency of the Maxwell stress, and show that this intermittency necessarily decreases the frequency of magnetoelastic waves in a stable field configuration. We develop a mean-field formalism to describe magnetoelastic behaviour, retaining leading-order corrections due to the coupling of large- and small-scale motions, and solve the initial-value problem for viscous fluids subjected to a large-scale shear, showing that the development of small-scale motions results in anomalous viscous damping of large-scale waves. Finally, we test these analytic predictions using numerical simulations of standing waves on tangled, linear force-free magnetic-field equilibria.

中文翻译：

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纠缠磁场的弹性

不可压缩的理想磁流体动力学与非导电流体动力学之间的根本区别在于，磁场施加了与它们的弯曲相反的张力。磁场的行为就像穿过流体的弹性线。因此，很自然地，期望在小长度尺度上缠结的磁场应该以弹性方式抵抗大尺度的剪切，就像缠结的弹性弦球对脉冲做出弹性响应一样。此外，纠缠场应该支持“磁弹性波”的传播，这是阿尔文波在直磁场上的各向同性类似物。在这里，我们在平衡纠缠场配置的理想化背景下研究磁弹性。与以前的处理相比，我们明确考虑了麦克斯韦应力的间歇性，并表明这种间歇性必然会降低稳定场配置中磁弹性波的频率。我们开发了一种平均场形式来描述磁弹性行为，由于大尺度和小尺度运动的耦合而保留了前导校正，并解决了粘性流体受到大尺度剪切的初始值问题，表明小尺度运动的发展导致大尺度波的反常粘性阻尼。最后，我们使用对缠结的线性无力磁场平衡的驻波的数值模拟来测试这些分析预测。由于大尺度和小尺度运动的耦合，保留了先导修正，解决了粘性流体在大尺度剪切作用下的初值问题，表明小尺度运动的发展导致粘性阻尼异常的大规模波浪。最后，我们使用对缠结的线性无力磁场平衡的驻波的数值模拟来测试这些分析预测。由于大尺度和小尺度运动的耦合，保留了先导修正，解决了粘性流体在大尺度剪切作用下的初值问题，表明小尺度运动的发展导致粘性阻尼异常的大规模波浪。最后，我们使用对缠结的线性无力磁场平衡的驻波的数值模拟来测试这些分析预测。