Resolvent Estimates for Plane Couette Flow
Resolvent Estimates for Plane Couette Flow
复制标题
平面 Couette 流的溶解估计
DOI：
10.1137/s0036139903426940
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
P. B. E. Silva
中科院分区：
文献类型：
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作者：
P. B. E. Silva
我们讨论了导出与平面库埃特流的三维扰动相关的线性算子的解的估计值的问题，并确定其对雷诺数 R 的依赖性。根据所涉及的参数值，我们通过分析导出估计值。对于参数的其余值，我们证明了求解方程的推导可以简化为估计具有非齐次边界条件的四阶线性齐次常微分方程的解。我们用数值方法研究这些边值问题。我们的结果表明解决方案的 L2 范数与 R2 成正比。
We discuss the problem of deriving estimates for the resolvent of the linear operator associated with three-dimensional perturbations of plane Couette flow and determining its dependence on the Reynolds number R.Depending on the values of the parameters involved, we derive estimates analytically. For the remaining values of the parameters, we prove that deriving estimates for the resolvent can be reduced to estimating the solutions of a 4th-order linear homogeneous ordinary differential equation with nonhomogeneous boundary conditions. We study these boundary value problems numerically. Our results indicate the L2 norm of the resolvent to be proportional to R2 .