线性化Navier-Stokes算子在局部Couette层流附近的特征值
Eigenvalues of the linearized Navier-Stokes operator near locally Couette laminar flows
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中文总结 AI 辅助
本文研究大雷诺数下无限二维通道中层流附近的线性化Navier-Stokes算子谱，证明对一类局部Couette流，存在与Wasow形式结果一致的特征值。
中文摘要 AI 辅助
我们考虑Orr-Sommerfeld算子的谱，该算子是在大雷诺数极限下，由无限二维通道中层流附近的线性化Navier-Stokes（LNS）算子得到的。对于一类相当一般的层流，其在边界附近局部表现为Couette流，并且被一个线性递增（递减）函数从下方（上方）界定，我们证明LNS算子存在一个特征值，其与Couette流附近LNS算子的特征值在前导阶上一致，该特征值由Wasow于1953年形式化获得。
英文摘要
We consider the spectrum of the Orr-Sommerfeld operator, which is obtained from the linearized Navier-Stokes (LNS) operator near a laminar flow in an infinite two-dimensional channel in the large Reynolds number limit. For a rather general class of laminar flows, which behave locally near the boundary like a Couette flow and are bounded from below (above) by a linear increasing (decreasing) function, we show that there exists an eigenvalue of the LNS operator which coincides, to leading order, with the eigenvalue of LNS near Couette flow, which was formally obtained by Wasow in 1953.
发表机构
- Braude College of Engineering（布劳德工程学院）
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