欧拉势模拟中的磁场演化
Magnetic field evolution in simulations with Euler potentials
摘要：
使用二维和三维磁流体模拟的范围内的不同的流量，包括层流和湍流的，它表明，解决方案表示的领域在欧拉势（EP）一般是不正确的，如果EP演变与人工扩散项。在三维空间中，标准的方法使用的磁矢势被发现允许发电机行动时，EP给衰减的解决方案。在施加场的情况下，EP方法在小尺度下产生过多的功率。这种效应在动态情况下更加夸张，表明来自洛伦兹力的反馈不切实际地减少。EP方法同意标准方法，只有在早期的时候，磁扩散率没有时间采取行动。它表明，即使是一个小的人工磁扩散率EP的使用不收敛到一个适当的解决方案的磁流体湍流。这种不一致的根源与磁螺旋度或磁场的三维性无关，而仅仅是由于这样一个事实，即依赖于相同坐标的用EP表示的磁场的非线性表示与感应方程中的线性扩散算子不相容。
英文摘要：
Using two- and three-dimensional hydromagnetic simulations for a range of different flows, including laminar and turbulent ones, it is shown that solutions expressing the field in terms of Euler potentials (EP) are in general incorrect if the EP are evolved with an artificial diffusion term. In three dimensions, standard methods using the magnetic vector potential are found to permit dynamo action when the EP give decaying solutions. With an imposed field, the EP method yields excessive power at small scales. This effect is more exaggerated in the dynamic case, suggesting an unrealistically reduced feedback from the Lorentz force. The EP approach agrees with standard methods only at early times when magnetic diffusivity did not have time to act. It is demonstrated that the usage of EP with even a small artificial magnetic diffusivity does not converge to a proper solution of hydromagnetic turbulence. The source of this disagreement is not connected with magnetic helicity or the three-dimensionality of the magnetic field, but is simply due to the fact that the nonlinear representation of the magnetic field in terms of EP that depend on the same coordinates is incompatible with the linear diffusion operator in the induction equation.
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