Pietarila Graham Jonathan, Blackman Eric G, Mininni Pablo D, Pouquet Annick
Solid Mechanics and Fluid Dynamics (T-3) and Center for Nonlinear Studies, Los Alamos National Laboratory MS-B258, Los Alamos, New Mexico 87545, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066406. doi: 10.1103/PhysRevE.85.066406. Epub 2012 Jun 20.
Understanding the in situ amplification of large-scale magnetic fields in turbulent astrophysical rotators has been a core subject of dynamo theory. When turbulent velocities are helical, large-scale dynamos that substantially amplify fields on scales that exceed the turbulent forcing scale arise, but the minimum sufficient fractional kinetic helicity f(h,C) has not been previously well quantified. Using direct numerical simulations for a simple helical dynamo, we show that f(h,C) decreases as the ratio of forcing to large-scale wave numbers k(F)/k(min) increases. From the condition that a large-scale helical dynamo must overcome the back reaction from any nonhelical field on the large scales, we develop a theory that can explain the simulations. For k(F)/k(min)≥8 we find f(h,C)≲3%, implying that very small helicity fractions strongly influence magnetic spectra for even moderate-scale separation.
理解湍流天体物理旋转体中大规模磁场的原位放大一直是发电机理论的核心课题。当湍流速度呈螺旋状时，会出现能在超过湍流强迫尺度的尺度上大幅放大磁场的大规模发电机，但此前尚未很好地量化最小足够分数动螺旋度f(h,C)。通过对一个简单螺旋发电机进行直接数值模拟，我们表明f(h,C)随着强迫波数与大规模波数之比k(F)/k(min)的增加而减小。基于大规模螺旋发电机必须克服大尺度上任何非螺旋磁场的反作用这一条件，我们发展了一种能够解释模拟结果的理论。对于k(F)/k(min)≥8，我们发现f(h,C)≲3%，这意味着即使对于中等尺度分离，非常小的螺旋度分数也会对磁谱产生强烈影响。
