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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Magnetohydrodynamic turbulence ： ウィキペディア英語版 Magnetohydrodynamic turbulence Magnetohydrodynamic turbulence concerns the chaotic regimes of magnetofluid flow at high Reynolds number. Magnetohydrodynamics (MHD) deals with what is a quasi-neutral fluid with very high conductivity. The fluid approximation implies that the focus is on macro length-and-time scales which are much larger than the collision length and collision time respectively. == Incompressible MHD equations == The incompressible MHD equations are :$$ \begin \frac + \mathbf \cdot \nabla \mathbf & = & -\nabla p + \mathbf \cdot \nabla \mathbf + \nu \nabla^2 \mathbf \\ \frac + \mathbf \cdot \nabla \mathbf & = & \mathbf \cdot \nabla \mathbf + \eta \nabla^2 \mathbf \\ \nabla \cdot \mathbf & = & 0 \\ \nabla \cdot \mathbf & = & 0. \end where u, B, ''p'' represent the velocity, magnetic, and total pressure (thermal+magnetic) fields, $\backslash nu$ and $\backslash eta$ represent kinematic viscosity and magnetic diffusivity. The third equation is the incompressibility condition. In the above equation, the magnetic field is in Alfvén units (same as velocity units). The total magnetic field can be split into two parts: $\backslash mathbf\; =\; \backslash mathbf\; +\; \backslash mathbf$ (mean + fluctuations). The above equations in terms of Elsässer variables ($\backslash mathbf^\; =\; \backslash mathbf\; \backslash pm\; \backslash mathbf$) are :$$ \frac}}\mp\left(\mathbf _0\cdot\right)}\cdot\right)p + \nu_+ \nabla^2 \mathbf^ + \nu_- \nabla^2 \mathbf^ where $\backslash nu\_\backslash pm\; =\; \backslash nu\; \backslash pm\; \backslash eta$. Nonlinear interactions occur between the Alfvénic fluctuations $$ z^ . The important nondimensional parameters for MHD are :$$ \begin \text Re & = & U L /\nu \\ \text Re_M & = & U L /\eta \\ \text P_M & = & \nu / \eta. \end The magnetic Prandtl number is an important property of the fluid. Liquid metals have small magnetic Prandtl numbers, for example, liquid sodium's $P\_M$ is around $10^$. But plasmas have large $P\_M$. The Reynolds number is the ratio of the nonlinear term $\backslash mathbf\; \backslash cdot\; \backslash nabla\; \backslash mathbf$ of the Navier-Stokes equation to the viscous term. While the magnetic Reynolds number is the ratio of the nonlinear term and the diffusive term of the induction equation. In many practical situations, the Reynolds number $Re$ of the flow is quite large. For such flows typically the velocity and the magnetic fields are random. Such flows are called to exhibit MHD turbulence. Note that $Re\_M$ need not be large for MHD turbulence. $Re\_M$ plays an important role in dynamo (magnetic field generation) problem. The mean magnetic field plays an important role in MHD turbulence, for example it can make the turbulence anisotropic; suppress the turbulence by decreasing energy cascade etc. The earlier MHD turbulence models assumed isotropy of turbulence, while the later models have studied anisotropic aspects. In the following discussions will summarize these models. More discussions on MHD turbulence can be found in Biskamp〔D. Biskamp (2003), Magnetohydrodynamical Turbulence, (Cambridge University Press, Cambridge.)〕 and Verma.〔M. K. Verma (2004), Statistical theory of magnetohydrodynamic turbulence, Phys. Rep., 401, 229.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Magnetohydrodynamic turbulence」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.