Numerical studies on the regularity properties of the fluid dynamical equations

流体动力学方程正则性的数值研究

基本信息

批准号：
16540103
负责人：
OHKITANI Koji
金额：
$ 2.3万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2005
项目状态：
已结题

项目摘要

In order to clarify fast reconnection phenomena in magnetohydrodynamics, we performed numerical experiments on the basis of the Eulerian-Lagrangian formalism.In 2004, we extended the Eulerian-Lagrangian formalism for the Navier-Stokes equations to magnetohydrodynamical equations. There are two Weber transforms corresponding to conservation of two kinds of helicities. For the case of unit Prandtl number, we have shown that one connection tensor is sufficient to reformulate the magnetohydrodynamical system. By using it, direct numerical simulations of 2D Orszag-Tang were done and it was found that correspondence between diffusive labels A and spatial positions x becomes non-invertible (resetting phenomena). We showed that it is related with magnetic reconnection. Furthermore, numerical simulations were done with initial conditions of 3D generalized O-T vortices and orthogonally offset magnetic flux tubes. Resetting phenomena also take place for these cases.In 2005, more practical numerical simulations with twisted magnetic flux tubes were performed. Parallel/anti-parallel flux tubes and linked flux rings were used as initial conditions. It was confirmed that magnetic reconnections are associated with resetting phenomena. The time scales defined by the resetting intervals are smaller that those estimated by global characteristics and are closer to time-scales of fast reconnections. In this sense we showed that this method can quantify fast reconnections. We also found by visualizations that a spatial correspondence between reconnecting magnetic fields and the resetting phenomena.A regularity criterion for ideal magnetohydrodynamical equations is known to be given in terms of the vorticity and the current density fields A simple argument respecting helicity invariants shows that if the magnetic field is smooth, then so is the velocity field, thereby suggesting some room for improving the above criterion.

为了澄清磁流失动力学中的快速重新连接现象，我们根据欧拉 - 拉格朗日形式主义进行了数值实验。在2004年，我们扩展了eulerian-lagrangian形式主义的Navier-Stokes方程，以使磁性水平方程式。有两个韦伯变换，对应于两种螺旋性的保护。对于单位prandtl数字，我们表明一种连接张量足以重新重新制定磁流体动力学系统。通过使用它，进行了2D Orszag-Tang的直接数值模拟，发现扩散标签A与空间位置X之间的对应关系X变得不可固化（重置现象）。我们表明它与磁重新连接有关。此外，在3D通用O-T涡流的初始条件和正交偏移磁通管的初始条件下进行数值模拟。这些情况也发生了重置现象。在2005年，进行了更实用的数值模拟，并进行了扭曲的磁通管。并行/反行通量管和连锁的通量环用作初始条件。已确认磁重复与重置现象有关。由重置间隔定义的时间尺度较小的时间尺度较小，该时间尺度比全局特征估计的时间尺度更接近快速重新连接的时间尺度。从这个意义上讲，我们表明该方法可以量化快速重新连接。 We also found by visualizations that a spatial correspondence between reconnecting magnetic fields and the resetting phenomena.A regularity criterion for ideal magnetohydrodynamical equations is known to be given in terms of the vorticity and the current density fields A simple argument respecting helicity invariants shows that if the magnetic field is smooth, then so is the velocity field, thereby suggesting some room for improving the above criterion.