论文标题
层状和湍流中的线性和非线性水磁稳定性
Linear and nonlinear hydromagnetic stability in laminar and turbulent flows
论文作者
论文摘要
我们考虑了电动传导流体的规定纯流体动力流的任意大扰动的演变。我们研究流动扰动以及产生的磁场衰减还是随着时间的推移而生长并构成发电机过程。为此，我们得出了一个广义的雷诺克尔方程，以用于流体动力扰动和磁能的动能之和。流量限制在有限体积中，因此边界处的速度的正常成分为零。与以前的工作相比，切向组件是任意的。对于磁场，我们主要采用经典边界条件，该条件在整个空间中延伸。我们建立了流体动力和磁性雷诺数的临界值，在该数字下，该数字任意大型的水动力流衰变初始扰动。这涉及对椭圆操作员最小的特征值的雷利·弗伯·克拉恩不等式的概括。对于高雷诺数的湍流，我们提供了临界磁性雷诺数的估计值，该数字是磁场衰减的任意波动。
We consider the evolution of arbitrarily large perturbations of a prescribed pure hydrodynamical flow of an electrically conducting fluid. We study whether the flow perturbations as well as the generated magnetic fields decay or grow with time and constitute a dynamo process. For that purpose we derive a generalized Reynolds-Orr equation for the sum of the kinetic energy of the hydrodynamic perturbation and the magnetic energy. The flow is confined in a finite volume so the normal component of the velocity at the boundary is zero. The tangential component is left arbitrary in contrast with previous works. For the magnetic field we mostly employ the classical boundary conditions where the field extends in the whole space. We establish critical values of hydrodynamic and magnetic Reynolds numbers below which arbitrarily large initial perturbations of the hydrodynamic flow decay. This involves generalization of the Rayleigh-Faber-Krahn inequality for the smallest eigenvalue of an elliptic operator. For high Reynolds number turbulence we provide an estimate of critical magnetic Reynolds number below which arbitrarily large fluctuations of the magnetic field decay.
