湍流磁流体动力耗散率的无量纲测度
Dimensionless Measures of Turbulent Magnetohydrodynamic Dissipation Rates
摘要：
磁雷诺数R_M被定义为特征尺度和相关流速的乘积除以微物理磁扩散率。对于层流，R_M也近似于总磁能方程中对流项与耗散项的比值，但对于湍流，后者的比值取决于能谱，在稳态时接近1。为了推广到任意谱的流，我们定义了一个有效磁耗散数，R_{M,e}，作为总磁能方程中平流项与微物理耗散项的比值，将全谱尺度，任意磁普朗特数，以及磁谱和动力学谱的不同内外尺度对结合起来。如所预期的，对于大的参数范围R_{M,e} \sim {0}（1）<< R_M。我们还区分了R_{M,e}和{ \tilde R}_{M，e}，其中后者是当湍流扩散率被明确地施加为封闭时平均磁场方程的有效磁雷诺数。即使R_M>>1，R_{M,e}和{ \tilde R}_{M，e}也接近1，这突出表明，正如在流体动力学湍流中一样，湍流中大尺度结构通过叶栅的能量耗散可能比层流中大尺度结构的耗散快得多。这说明，能量耗散率的磁重联是快得多的湍流，和微物理重联率相比，层流。
英文摘要：
The magnetic Reynolds number R_M, is defined as the product of a characteristic scale and associated flow speed divided by the microphysical magnetic diffusivity. For laminar flows, R_M also approximates the ratio of advective to dissipative terms in the total magnetic energy equation, but for turbulent flows this latter ratio depends on the energy spectra and approaches unity in a steady state. To generalize for flows of arbitrary spectra we define an effective magnetic dissipation number, R_{M,e}, as the ratio of the advection to microphysical dissipation terms in the total magnetic energy equation, incorporating the full spectrum of scales, arbitrary magnetic Prandtl numbers, and distinct pairs of inner and outer scales for magnetic and kinetic spectra. As expected, for a substantial parameter range R_{M,e}\sim {O}(1) << R_M. We also distinguish R_{M,e} from {\tilde R}_{M,e} where the latter is an effective magnetic Reynolds number for the mean magnetic field equation when a turbulent diffusivity is explicitly imposed as a closure. That R_{M,e} and {\tilde R}_{M,e} approach unity even if R_M>>1 highlights that, just as in hydrodynamic turbulence,energy dissipation of large scale structures in turbulent flows via a cascade can be much faster than the dissipation of large scale structures in laminar flows. This illustrates that the rate of energy dissipation by magnetic reconnection is much faster in turbulent flows, and much less sensitive to microphysical reconnection rates compared to laminar flows.
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