On the decay of low-magnetic-Reynolds-number turbulence in an imposed magnetic field
On the decay of low-magnetic-Reynolds-number turbulence in an imposed magnetic field
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外加磁场中低磁雷诺数湍流的衰减
DOI：
10.1017/s0022112009994137
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发表时间：
2010
影响因子：
3.7
通讯作者：
P. Davidson and Y. Kaneda
中科院分区：
文献类型：
--
作者：
N. Okamoto;P. Davidson and Y. Kaneda
本文研究了低磁雷诺数条件下磁场B 0作用下自由衰减的均匀磁流体动力学（MHD）湍流的积分性质。我们确认，像传统的各向同性湍流一样，充分发展的状态具有Loitsyansky样的积分不变量，在这种情况下I// = − <$r <$2 < u <$·u′ <$> dr，其中<u（x）·u（x + rc）> =是通常的两点速度相关，下标<$表示垂直于施加场的分量。充分发展湍流的I//守恒对积分尺度的发展方式有一个基本的限制，即它意味着u 2 4//是常数，其中u，和//是积分尺度。这个约束可以用来估计u_n（t; B 0），u_n（t; B 0）和u_n//（t; B 0）的演化，这些理论衰减规律与数值模拟结果吻合得很好.
We examine the integral properties of freely decaying homogeneous magnetohydrodynamic (MHD) turbulence subject to an imposed magnetic field B0 at low-magnetic Reynolds number. We confirm that, like conventional isotropic turbulence, the fully developed state possesses a Loitsyansky-like integral invariant, in this case I// = − ∫ r⊥2 < u⊥·u′⊥> dr, where <u(x) ·u(x + rc)> = is the usual two-point velocity correlation and the subscript ⊥ indicates components perpendicular to the imposed field. The conservation of I// for fully developed turbulence places a fundamental restriction on the way in which the integral scales can develop, i.e. it implies u⊥2 ℓ⊥4 ℓ// ≈ constant where u⊥, ℓ⊥ and ℓ// are integral scales. This constraint can be used to estimate the evolution of u⊥(t; B0), ℓ⊥(t; B0) and ℓ//(t; B0), and these theoretical decay laws are shown to be in good agreement with numerical simulations.