径向电导率变化对Ponomarenko发电机的影响
Effects of radial conductivity variation on the Ponomarenko dynamo
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中文总结 AI 辅助
本研究探讨电导率径向变化对Ponomarenko发电机的影响，发现阈值和增长率强烈依赖速度不连续处的电导率局部梯度，并推导出大Rm下的修正表达式。
中文摘要 AI 辅助
我们研究了电导率变化对Ponomarenko发电机的影响。通过采用单调递增/递减以及正弦变化的径向剖面，我们研究了运动学发电机问题。发电机的阈值由临界磁雷诺数Rm$_c$给出，发现该阈值强烈依赖于速度场不连续处（剪切占主导地位）附近的电导率变化形式。对于急剧变化极限下的单调变化剖面，该阈值映射到具有电导率跳跃的发电机问题；而对于具有大变化量/波数的正弦剖面，由于电导率快速变化引起的有效扩散率，阈值增加。远离阈值时，发现增长率仅取决于不连续处附近的电导率局部梯度，剪切与电导率梯度的符号相反会导致更大的增长率，从而有助于发电机不稳定性从B$_r$再生B$_{\phi}$。我们计算了大Rm$(\gg 1)$极限下增长率的表达式，发现电导率变化导致与电导率局部梯度乘以Rm$^{-1/2}$成正比的修正。该修正被发现仅取决于不连续处电导率的局部梯度。对于现实的平滑速度剖面和不同的磁边界条件，也发现了类似的依赖性。
英文摘要
We study the effects of conductivity variation on the Ponomarenko dynamo. Taking monotonically increasing/decreasing and sinusoidally varying radial profiles, we study the kinematic dynamo problem. The threshold of the dynamo, given by the critical magnetic Reynolds number Rm$_c$, is found to strongly depend on the form of conductivity variation near the discontinuity of the velocity field where the shear is dominant. For monotonically varying profiles in the limit of sharp variation, this threshold maps to the problem of the dynamo with a jump in conductivity, while for the sinusoidal profile with large variations/wavenumbers, the threshold increases due to effective diffusivity arising from the rapid changes in conductivity. Far from the threshold, it is found that the growth rate depends only on the local gradient of the conductivity near the discontinuity, with the opposite sign of shear and conductivity gradient leading to a larger growth rate, thereby aiding the dynamo instability in regenerating B$_ϕ$ from B$_r$. We calculate the expression for the growth rate in the limit of large Rm$(\gg 1)$ and find that the conductivity variation leads to a modification proportional to the local gradient of conductivity times Rm$^{-1/2}$. This correction is found to depend only on the local gradient of the conductivity at the discontinuity. Similar dependencies are found for realistic, smooth velocity profiles and for different magnetic boundary conditions.
发表机构
- Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）
- Indian Institute of Technology Madras（印度理工学院马德拉斯分校）
机构由 AI 辅助整理，请以论文原文为准。
