Boldyrev Stanislav, Cattaneo Fausto
Department of Astronomy and Astrophysics, University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637, USA.
Phys Rev Lett. 2004 Apr 9;92(14):144501. doi: 10.1103/PhysRevLett.92.144501. Epub 2004 Apr 8.
We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, v(l) approximately l(alpha), alpha<1. This regime is relevant to the problem of magnetic field generation in fluids with small magnetic Prandtl number, i.e., with Ohmic resistivity much larger than viscosity. We propose that the smaller the roughness exponent alpha, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamic turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.
我们分析了在具有粗糙速度场(v(l)\approx l^{\alpha})（(\alpha\lt1)）的各向同性均匀湍流导电流体中磁场演化的初始运动学阶段。这种情况与小磁普朗特数流体中的磁场产生问题相关，即欧姆电阻率远大于粘性的情况。我们提出，粗糙度指数(\alpha)越小，激发磁涨落所需的磁雷诺数就越大。这意味着对小普朗特数磁流体动力学湍流的数值或实验研究需要达到极高的分辨率，以便充分描述磁现象。
