可压缩磁化湍流中的标量耗散临界性
Scalar Dissipation Criticality in Compressible Magnetized Turbulence
- ETH Zürich（苏黎世联邦理工学院）
- Flatiron Institute, Simons Foundation（西蒙斯基金会平顿研究所）
- School of Mathematics, IAS, Princeton（普林斯顿高等研究院数学学院）
- GSSI, L’Aquila, Italy（意大利拉奎拉全球南方科学研究所）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
该研究将标量湍流理论推广至可压缩磁化流动，证明在特定标度指数条件下反常耗散不可能发生，并给出Yaglom定律的可压缩类比，为等离子体输运提供诊断依据。
中文摘要 AI 辅助
我们将Obukhov-Corrsin标量湍流理论推广到具有空间变化、各向异性扩散率的可压缩流动。将密度和扩散率合并为一个正定矩阵场，即输运景观，可以实现精确的逐尺度平衡，其中滤波与扩散之间的符号不定交换子被消除而非估计。如果密度加权的三阶速度和标量增量分别按$\ell^\alpha$和$\ell^\beta$缩放，我们证明当$\alpha+2\beta>1$时，反常标量耗散不可能发生。值得注意的是，该阈值与扩散率的各向异性和空间正则性无关，只要其保持一致椭圆性。速度和标量中的余维一激波具有$\alpha=\beta=1/3$，因此恰好位于临界阈值处。对于统计平稳湍流，我们进一步获得了精确的密度加权常数通量关系，提供了Yaglom定律所依据关系的可压缩类比。这些结果直接适用于气体和磁化等离子体中的被动标量输运，并为可压缩磁流体动力学湍流的模拟提供了可测试的诊断方法。由于相同的算子控制各向异性热传导，这些结果适用于磁化等离子体的电子温度，并意味着此类流动中的梯度统计必须与输运景观而非密度进行缩并。
英文摘要
We extend the Obukhov-Corrsin theory of scalar turbulence to compressible flows with spatially variable, anisotropic diffusivity. Combining density and diffusivity into a single positive matrix field, a transport landscape, permits an exact scale-by-scale balance in which the sign-indefinite commutator between filtering and diffusion is eliminated rather than estimated. If the density-weighted third-order velocity and scalar increments scale as $\ell^α$ and $\ell^β$, respectively, we prove that anomalous scalar dissipation is impossible when $α+2β>1$. Remarkably, this threshold is independent of the anisotropy and spatial regularity of the diffusivity, provided it remains uniformly elliptic. Codimension-one shocks in both velocity and scalar have $α=β=1/3$ and therefore lie exactly at the critical threshold. For statistically stationary turbulence we further obtain an exact density-weighted constant-flux relation, providing a compressible analogue of the relation underlying Yaglom's law. The results apply directly to passive-scalar transport in both gases and magnetized plasmas and provide testable diagnostics for simulations of compressible magnetohydrodynamic turbulence. Because the same operator governs anisotropic heat conduction, the results carry over to the electron temperature of a magnetized plasma, and they imply that gradient statistics in such flows must be contracted with the transport landscape rather than with the density.
