子过滤尺度物理对正则化模型的影响
The effect of subfilter-scale physics on regularization models
摘要：
研究正则化模型的子滤波器尺度（SFS）物理，以了解正则化作为SFS模型的性能。在拉格朗日平均的Navier-Stokes α模式（LANS α）中，对局部SFS相互作用和小尺度环流守恒的强烈抑制导致了刚体的形成.当SFS谱被分辨时，这些粒子会以接近k^1的尺度污染超滤波器尺度的能谱。Clark-alpha和Leray-alpha模型是LANS-alpha的截断，不保留小尺度循环，也不发展刚体。然而，LANS-α在不透明度性质上最接近于Navier-Stokes。所有这三个模型被发现是稳定的，在高雷诺数。阐明了L^2和H^1范数模型之间的区别。对于磁流体力学（MHD），洛伦兹力作为环流的源（或汇），以及作为光谱非定域的大小尺度相互作用和局域SFS相互作用的促进剂，阻止了拉格朗日平均MHD（LAMHD-alpha）中刚体的形成。我们发现LAMHD-α作为超滤器尺度能谱和高雷诺数下间歇性电流片的预测器表现良好。我们希望它可以被证明是一个普遍适用的MHD-LES。
英文摘要：
The subfilter-scale (SFS) physics of regularization models are investigated to understand the regularizations' performance as SFS models. The strong suppression of spectrally local SFS interactions and the conservation of small-scale circulation in the Lagrangian-averaged Navier-Stokes alpha-model (LANS-alpha) is found to lead to the formation of rigid bodies. These contaminate the superfilter-scale energy spectrum with a scaling that approaches k^1 as the SFS spectra is resolved. The Clark-alpha and Leray-alpha models, truncations of LANS-alpha, do not conserve small-scale circulation and do not develop rigid bodies. LANS-alpha, however, is closest to Navier-Stokes in intermittency properties. All three models are found to be stable at high Reynolds number. Differences between L^2 and H^1 norm models are clarified. For magnetohydrodynamics (MHD), the presence of the Lorentz force as a source (or sink) for circulation and as a facilitator of both spectrally nonlocal large to small scale interactions as well as local SFS interactions prevents the formation of rigid bodies in Lagrangian-averaged MHD (LAMHD-alpha). We find LAMHD-alpha performs well as a predictor of superfilter-scale energy spectra and of intermittent current sheets at high Reynolds numbers. We expect it may prove to be a generally applicable MHD-LES.
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